Unconfined gravity current interactions with orthogonal topography: Implications for combined-flow processes and the depositional record

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Sedimentology (2025) 72, 67–99 doi: 10.1111/sed.13227

ED KEAVNEY* , JEFF PEAKALL* , RU WANG*, DAVID M. HODGSON* ,

IAN A. KANE† , GARETH M. KEEVIL*, HELENA C. BROWN*, MICHAEL A. CLARE‡ and MIA J. HUGHES*

*School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK (E-mail: d.hodgson@leeds. ac.uk)

†Department of Earth and Environmental Science, University of Manchester, Manchester M13 9PL, UK ‡Ocean BioGeoscience, National Oceanography Centre, Southampton SO14 3ZH, UK

Associate Editor – Kyle Straub ABSTRACT

Turbidity current behaviour is affected by interactions with seafloor topogra- phy. Changes in flow dynamics will depend on the orientation and gradient of the topography, and the magnitude and rheology of the incoming flow. A better understanding of how unconfined turbidity currents interact with topography will improve interpretations of the stratigraphic record, and is addressed herein using three-dimensional flume tank experiments with unconfined saline density currents that enter a horizontal basin before inter- acting with a ramp orientated perpendicular to flow direction. The incoming flow parameters remained constant, whilst the slope angle was indepen- dently varied. On a 20° slope, superelevation of the flow and flow stripping of the upper, dilute region of the flow occurred high on the slope surface. This resulted in a strongly divergent flow and the generation of complex multidirectional flows (i.e. combined flows). The superelevation and extent of flow stripping decreased as the slope angle increased. At 30° and 40°, flow reflection and deflection, respectively, are the dominant flow process at the base of slope, with the reflected or deflected flow interacting with the paren- tal flow, and generating combined flows. Thus, complicated patterns of flow direction and behaviour are documented even on encountering simple, pla- nar topographies orientated perpendicular to flow direction. Combined flows in deep-water settings have been linked to the interaction of turbidity cur- rents with topography and the formation of internal waves with a dominant oscillatory flow component. Here, combined flow occurs in the absence of an oscillatory component. A new process model for the formation and distri- bution of hummock-like bedforms in deep-marine systems is introduced. This bedform model is coupled to a new understanding of the mechanics of onlap styles (draping versus abrupt pinchout) to produce a spatial model of gravity-current interaction, and deposition, on slopes to support palaeogeo- graphical reconstructions.

Keywords Combined flows, flow confinement, flume experiments, hum- mocky bedforms, low-density turbidity currents, onlap styles, orthogonal topography.

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

68 E. Keavney et al. INTRODUCTION

Turbidity currents are the principal mechanism for sediment transfer from shallow-water to deep-water environments (Kuenen & Migliorini, 1950; Middleton & Hampton, 1973; Simp- son, 1997), resulting in the largest accumula- tions of sediment on Earth (Curray & Moore, 1971; Emmel & Curray, 1983). Seafloor topogra- phy, which acts as a first order control on tur- bidity current behaviour, may be generated by depositional relief associated with mass trans- port deposits (e.g. Armitage et al., 2009; Mart ́ı- nez-Don ̃ate et al., 2021; Allen et al., 2022), leve ́es and lobes (e.g. Groenenberg et al., 2010; Kane & Hodgson, 2011), folds and faults (e.g. Haughton, 2000; Hodgson & Haughton, 2004; Cullen et al., 2019), salt and mud diapirism (e.g. Kneller & McCaffrey, 1995; Toniolo et al., 2006; Cumberpatch et al., 2021; Howlett et al., 2021), seamounts (e.g. Seabrook et al., 2023) and abys- sal plain mountains (e.g. Harris et al., 2014).

Turbidity current behaviour is strongly influ- enced by the flow characteristics (i.e. velocity, thickness, concentration) and the nature of the seabed topography (i.e. gradient, form, substrate) (e.g. Kneller et al., 1991; Edwards et al., 1994; Patacci et al., 2015; Tinterri et al., 2016, 2022; Dorrell et al., 2018a; Soutter et al., 2021). Tur- bidity currents can be reflected, deflected and/or ponded, generating spatial variations in flow competence and capacity, and hence the loci of deposition and depositional character (Allen, 1991; Hiscott, 1994; Kneller & McCaffrey, 1995, 1999). Recent technological advances have enabled direct velocity measurements of natural turbidity currents, and estimations of their con- centration; however, these measurements have solely been acquired in submarine canyons or channels (e.g. Talling et al., 2023, and references therein). To date, no such measurements have been made where unconfined flows interact with seafloor topography, although palaeocurrent records from deposits show that complicated flow fields are established (e.g. Pickering & His- cott, 1985; Kneller et al., 1991; Hodgson & Haughton, 2004).

The superimposition of unidirectional, and multidirectional and/or oscillatory flow compo- nents (i.e. combined flows), produces distinctive bedforms with a high degree of spatial and mor- phological variability (Clifton, 1976). Such bed- forms include hummocky cross-stratification (HCS) (e.g. Arnott & Southard, 1990; Duke et al., 1991; Dumas & Arnott, 2006; Wu et al., 2024)

and sigmoidal cross-lamination in small-scale and large-scale ripples (e.g. Yokokawa, 1995; Dumas & Arnott, 2006; Tinterri, 2006, 2007). Hummock-like structures, large asymmetrical rip- ples, biconvex ripples and symmetrical megaripples have been documented in several deep-water systems (e.g. Privat et al., 2021, 2024; Tinterrietal.,2022;Mart ́ınez-Don ̃ateetal.,2023; Siwek et al., 2023; Taylor et al., 2024), and are typically postulated to have formed as a result of the generation of combined flows (cf. Mulder et al., 2009). However, the combined flow para- digm in deep-water systems is based upon two-dimensional experimental observations.

Observations from 2D experiments of turbidity currents rebounding against topographic slopes (e.g. Pantin & Leeder, 1987; Edwards et al., 1994; Kneller & McCaffrey, 1995; Kneller et al., 1997) have been used to support outcrop-based models for the formation of combined flows and the formation of hummock-like structures in deep-water systems (Fig. 1) (e.g. Tinterri, 2011; Tinterri et al., 2016, 2022; Privat et al., 2021, 2024; Mart ́ınez-Don ̃ate et al., 2023). Tin- terri (2011) suggests that flow transformations following the deceleration of flows upon inci- dence with slopes produce a hydraulic jump, akin to bores described semi-quantitatively with time-lapse photography and particle tracking by Edwards et al. (1994). It is hypothesized that the superimposition of the subcritical, unidirec- tional turbidity current, and an oscillatory flow component from the internal waves generated by supercritical upstream-migrating bores, pro- duces combined flow in density currents (Tin- terri, 2011; Tinterri et al., 2016). Whether the same mechanisms for combined flow generation are active following the interaction of 3D, unconfined density currents with planar con- taining topography has not been explored exper- imentally. Understanding the flow process interactions of unconfined low-density gravity currents with orthogonal containing slopes is therefore crucial for interpreting turbidity cur- rent evolution and onlap geometries, and bed- form and facies variability in 3D space on slopes.

Although previous physical experiments have varied flow parameters and topographic configu- ration to examine turbidity current flow dynam- ics and deposits (e.g. Kneller et al., 1991, 1997; Edwards et al., 1994; Amy et al., 2004; Brunt et al., 2004; Patacci et al., 2015; Howlett et al., 2019; Reece et al., 2024) only one has investi- gated the interaction of 3D, unconfined gravity

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Tinterri (2011); Tinterri et al. (2016) Internal waves

Sourced from flow reflections against topography and the generation of bores

Edwards et al. (1994)

Bores generated from reflections against topography

Bores (Frd > 1)

Flow processes in unconfined flows

currents with simple, planar topographic slopes (Soutter et al., 2021). Soutter et al. (2021) explored the depositional patterns around erod- ible basinal topography. With the basinal topo- graphy positioned orthogonal (90°) to the primary flow direction, and with sediment-laden gravity flows (17% by volume concentration), the denser material within the flow was observed to onlap the base of the containing slope, whereas the low density, finer grained material bypassed down-dip as it surmounted the topographic bar- rier (Soutter et al., 2021). Notably, the high con- centration sediment gravity flows and steep angle of the experimental platform (11°) pro- duced gravity currents on the slope and the proximal basin floor of the flume tank, upstream of the topographic barrier, with basal ‘slip- velocities’ (i.e. the streamwise velocity measured at the base of the flow is not zero). This suggests that the sediment gravity flows of Soutter et al. (2021) are more akin to grain-flows and debris-flows (sensu Me ́jean et al., 2022).

In contrast, the experiments herein, are low- density, fully-turbulent, gravity currents that were unable to surmount the containing topo- graphic slope. This experimental configuration permits observations of unconfined gravity cur- rent dynamics and evolution both at the base of, and on, the slope surface, which has not been previously explored. The influence of the topo- graphic containment on flow processes is expressed by the topographic containment factor (h0), where h0 = h/hmax, and h is flow height and hmax is the maximum run-up height. The con- tainment factor increases as the slope angle increases from 20° to 30° to 40°. Increasing the slope angle affects the degree of flow stripping, and the velocity structure and evolution on the slope surface and at the base of the slope.

The aim of the current study is to document the interaction between scaled, unconfined saline density currents and partially containing orthogonal topography using 3D flume tank experiments. The objectives are to: (i) assess

Ponded interface

Input flow

Internal interface

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Concentration and grain-size gradient

Patacci et al. (2015)

Internal waves

Sourced from the flow input and dissipate against the topography

Fig. 1. Schematic diagram of existing models proposed for the generation of internal waves in turbidity currents. The generation of internal waves in ponded turbidity currents in two-dimensional experimental conditions was demonstrated by Patacci et al. (2015). Tinterri (2011) and Tinterri et al. (2016) derived their model from outcrop following flow reflections against topography, based on observations by Edwards et al. (1994) on the generation of bores. The question mark indicates the existing uncertainty in unconfined (three-dimensional) flow process behav- iour. Frd, densiometric Froude number.

Complex flows above simple slopes 69

Input flow (Frd < 1) Reversing flow

70 E. Keavney et al.

how the angle of the containing frontal topogra- phy (independently varied at 20°, 30° and 40°) affects density current evolution and the genera- tion of combined flows; (ii) investigate how the mechanisms of flow reflection and deflection, and the novel observation of flow divergence, operate on the slope surface and influence inter- actions with the incoming flow at the base of the slope in unconfined settings; and (iii) dis- cuss the effect of combined flows on the deposit character and onlap geometry in deep-water settings.

METHODS Experimental set-up

Experiments were performed in the Sorby Envi- ronmental Fluid Dynamics Laboratory, Univer- sity of Leeds, UK, using a 10 m long, 2.5 m wide and 1m deep flume tank (Fig. 2A and B). A 1400 l saline solution (2.5% excess density) was prepared in a 2000l mixing tank. The saline solution was pumped (using an inverter con- trolled centrifugal pump) into the main tank through an inlet pipe centred on the experimen- tal platform and into a straight-sided 0.62m long, 0.26m wide channel, before the flow debouched into the main tank. The main tank and inlet channel were both set on a horizontal basin floor (i.e. 0° slope angle). The main tank was filled with tap water to a depth of 0.6m. The pump speed was manually adjusted when the flow rate deviated from the reference value of 3.6 l s1. The flow rate variability was accu- rate to 0.05 l s1 of the reference value through- out the duration of the experiment (<2% error) (Table 1).

Unconfined flow properties

Three initial experiments were performed with- out any containing topography. Firstly, the unconfined flow was visualized for the full duration of the experiment through the free-water surface, using an overhead camera above the flume tank (Video 1). Fluorescent tracer dye was used to aid visualization of the flow. Measurements of the flow were recorded along the tank axis, at 3m downstream of the channel mouth, to provide a base case for com- parison with the flows interacting with the con- taining topography (Fig. 3A and B; Table 2). An Ultrasonic velocimeter Doppler profiler (UVP)

(Met-Flow, UVP DUO, 4 MHz, Met-Flow SA, Lausanne, Switzerland) was used to record the instantaneous downstream flow velocity (Fig. 4A and B). The UVP recorded the multi- plexed velocity output from a vertically stacked array of 10 transducers from the entire flow height (see Table 2 for details of UVP parame- ters). Positive values of streamwise velocity are measured as the flow travels into the basin (Fig. 3A). A Nortek Vectrino Acoustic Doppler velocity profiler (ADV) (Nortek Group, Rud, Nor- way) was used to record the instantaneous flow velocities of the unconfined flow at 3m down- stream of the channel mouth, before the flow interacted with the slope. Where the ADV was used, positive streamwise velocities are measured as the flow travels towards the slope, whereas negative values record flow reversal. Addition- ally, for the ADV data (Fig. 3B), positive and neg- ative values of cross-stream velocity data correspond to left-lateral and right-lateral move- ment of the flow, respectively, while positive and negative values of vertical velocity data corre- spond to the up – and down – movement of the flow, respectively. Such cross-stream and vertical data are not available from the UVP, which mea- sures streamwise velocity only. Flow density was also measured (Fig. 4G and H), using an array of 12 syphons, and also for two additional experi- ments performed with frontally containing topog- raphy (Fig. 4I). Syphon sampling was initiated 5 s after the head passed, and lasted for 30 s. Twelve stacked syphons with 5 mm diameter tub- ing were deployed over a 0.095m height, with the lowermost syphon 0.005 m above the base of the tank floor (Fig. 4G). The syphon array was connected to a peristaltic pump set to a constant withdrawal rate. The fluid was collected in sam- ple pots and the density was measured using an Anton Paar DMA 35 portable densitometer (Anton Paar GmbH, Graz, Austria), with a resolu- tion of 0.1 kg m3. The density was measured at a background temperature of 12°C, where the ambi- ent density of water is 999.58 kg m3.

Froude scaling

Calculations of the Reynolds number (Re) and densiometric Froude number (Frd), permit the Froude scaling of experimental saline density currents with natural turbidity currents (Yalin, 1971) (see Table S1). Here, the measured parameters of the unconfined flow 3m down- stream of the channel mouth were used. The measurements were initiated 5s after the head

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Fig. 2. (A) Flume tank and mixing tank configuration. (B) Plan view of flume tank and slope position. Right-side and left-side is with respect to the primary flow direction. (C) to (E) Configurations of the 20°, 30° and 40° topographic slopes.

left-side

10 0

passed, and lasted for 30 s. Froude scale model- ling considers the Reynolds number (Re) relaxed compared to natural systems, but still within the fully turbulent regime, whereas the densiometric Froude number (Frd) is held as similar (e.g. Graf, 1971; Peakall et al., 1996). In this study, the Reynolds number is taken to be:

where ps is the depth-averaged density of the gravity flow measured using the density syphon array, U is mean depth-averaged velocity, μ is dynamic viscosity, and h is the height at which

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mixer

1400 L 2.5% salinity

pump flow meter

0 1 2

channel mouth 3

straight-sided inlet channel

water table

primary flow direction

20° slope 0

distance from channel mouth: 3m

30° slope 0 distance from channel mouth: 3m

4 5 6 7 8 9

upstream

topographic slope

downstream

tank axis

-1.25

0 width (m)

1.25

right-side

40° slope distance from channel mouth: 3m

Re= psUh (1) μ

control valve

inlet pipe

water table

to the drain

Complex flows above simple slopes 71

2.5 m

10 m

length (m)

Height (m) Height (m) Height (m)

0.6 m

72 E. Keavney et al.

Table1. Experimental configuration and data instrumentation [Ultrasonic Doppler velocity profiler (UVP), Acoustic Doppler velocity profiler (ADV) and density syphon] positions for all experiments. The instrumentation was placed along the tank axis. Unconfined-b and Unconfined-c: each instrument was positioned 3 m downstream of the channel mouth. For the experiments with the topographic slope, the slope was positioned 3 m downstream of the channel mouth and perpendicular to the primary flow direction. The reference values for mean flow rate (l s1) and the excess density of the input current (%) were 3.6 l s1 and 2.5%, respectively.

Run Slope angle (°)

Unconfined-a –
Unconfined-b –
Unconfined-c –

FC-20a 20
FC-20b 20
FC-20c 20
FC-20d 20
FC-20e 20
FC-20f 20

FC-30a 30
FC-30b 30
FC-30c 30
FC-30d 30

FC-40a 40
FC-40b 40
FC-40c 40
FC-40d 40

Instrumentation [height upslope (m)]

Mean flow rate (l s1) 3.61

3.60 3.60 3.61 3.60 3.61 3.60 3.60 3.60 3.59 3.60 3.59 3.59 3.59 3.59 3.60 3.58

Input current density (%)

2.50 2.50 2.50 2.50 2.49 2.50 2.51 2.50 2.50 2.49 2.50 2.49 2.49 2.49 2.50 2.49 2.50

the streamwise velocity recorded by the UVP reaches zero at the top of the flow. The depth-averaged density and velocity values are calculated by taking measurements at regularly-spaced intervals (0.05 m) from the pro- files in Fig. 3A, for the velocity over the full depth of the flow recorded by the UVP, and for the density over the available depth profile and extrapolated points at the base and top of the flow (Fig. 3A). The flow height was 0.11 m.

The Reynolds number is used as an indicator of turbulence, where Re > 2000 represents a fully-turbulent flow (Simpson, 1997). Based on the unconfined reference experiments, the mod- elled flow had a Reynolds number of 3203 (Re = 3203), 3 m downstream of the channel mouth (i.e. a fully turbulent flow).

The Froude number (Fr) describes the ratio of inertial to gravitational forces for stratified flows. To indicate which of these forces is dominant, flows of Fr > 1 are termed supercritical, while flows of Fr < 1 are termed subcritical (Ellison & Turner, 1959). Hydraulic jumps occur when flows transition from supercritical to subcritical, here the critical Froude number (Frc), is denoted by Frc = 1, although this can vary in strongly strati- fied density currents (e.g. Sumner et al., 2013; Car- tigny et al., 2014). For turbidity currents, the densiometric Froude number (Frd) is used to account for the reduced gravity (g0) derived from the density difference between the flow and the ambient fluid (Kneller & Buckee, 2000):

pffiffiffiffiffiffiffi

Frd =U= g0h (2)

Visualization UVP

Density syphon ADV (0)

ADV (0.10)

ADV (0.15) Visualization

Density syphon (0) Density syphon (0.10) ADV (base)

ADV (0.10) ADV (0.20) Visualization ADV (0) ADV (0.08) ADV (0.14) Visualization

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Video 1: Time-lapse video of the evolution of the unconfined density current throughout the experimental run (3× playback speed). The field of view is the full width of the tank (2.5 m). To aid flow visualization, the input flow is dyed with fluorescent, purple tracer dye. The flow is observed to exit from the channel at the channel mouth and begins to radially expand into the basin. At 3 m from the channel mouth, the incoming head of the flow is unconfined. For the subsequent experiments with the orthogonal slope, the leading edge of the base of slope was positioned at 3 m from the channel mouth.

g =g pspa =pa (3)

where g is acceleration due to gravity, and pa is the density of the ambient fluid, measured at 12°C. [Correction added on 15 November, after first online publication: rho subscript ‘s’ at the end of Equation 3 has been corrected to rho subscript ‘a’.]

Based on the unconfined reference experi- ments, the modelled flow had a densiometric Froude number of 0.50 (Frd = 0.50) (i.e. a sub- critical flow). This value, and the visually- observed hydraulic jump following debouching of the flow at the channel mouth, may be con- sidered analogous to basin floor flows that have passed through the channel-lobe transition zone, experiencing a loss in flow confinement (e.g. Komar, 1971; Hodgson et al., 2022).

Containing topography

The topography was created using a linear, non-erodible slope. The 1.5 m wide planar slope, not spanning the full width of the 2.5 m wide flume tank, was positioned orthogonal (90°) to the pri- mary flow direction and across the tank axis, 3 m downstream of the channel mouth (Fig. 2B). The angle was independently varied at 20°, 30° and 40° (Fig. 2C to E). The slope had a bevelled leading

edge, thus minimizing the step at the base of slope. For the 20°, 30° and 40° slope configurations the maximum height of the slope was 0.410, 0.585 and 0.760 m, respectively. The containment factor (h0 ) value for all three slope configurations describes a flow unable to surmount the containing topo- graphic slope (Fig. 5). Due to the width of the slope (1.5 m) compared to the width of the tank (2.5 m), the flow is partially-contained.

The use of 20°, 30° and 40° slope angles herein is motivated by outcrop examples of onlap angles, previous experimental models and the water depth of the experimental basin. The modelled flows herein are more dilute than in previous experiments on topographic interaction of density currents (e.g. Pantin & Leeder, 1987; Kneller et al., 1991; Edwards et al., 1994; Knel- ler, 1995; Patacci et al., 2015), making them more mobile upslope. This, coupled with the maximum water depth of the flume tank (0.6 m), meant that slope angles less than 20° were diffi- cult to achieve without the flow surmounting the topographic slope or the flow travelling upslope and interacting with the free-water sur- face. Examples of similar slope angles used in previous experimental studies, include: 20° (Kneller et al., 1991), 25° 5° (Soutter et al., 2021), 28° (Muck and Underwood, 1990) and 30° (Kneller, 1995). In Annot, France, the basin

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Complex flows above simple slopes 73

74 E. Keavney et al.

margin slope angle is between 10° and 30° (Sin- clair, 1994; Hilton and Pickering, 1995; Joseph et al., 2000; Puigdefa`bregas et al., 2004; Smith and Joseph, 2004; Tomasso and Sinclair, 2004; Soutter et al., 2019). Locally steep topography is common in deep-water settings, for example, related to fault scarps (e.g. Haughton, 1994; Hodgson & Haughton, 2004; Bakke et al., 2013) and mass-transport deposits (e.g. Mart ́ınez-Do- n ̃ate et al., 2021; Allen et al., 2022). That being said, slope angles less than 10° are common in many basins (e.g. Bakke et al., 2013; Spychala et al., 2017), and the implications of this work for lower angle slopes are discussed later.

An initial experiment was performed using a series of GoPro Hero 10 Black cameras (GoPro, Inc., San Mateo, CA, USA) to visualize the flow at each topographic configuration. Fluorescent tracer dye was injected through a series of tubes (5 mm in diameter) onto the slope surface to aid visualization (Videos 2–4). The dye injection tubes were inserted into an array of evenly-spaced drilled holes and were flush with the slope surface, thus minimizing any surface irregularities. The rate of dye injection was con- trolled using a peristaltic pump, set to a con- stant discharge rate for all experimental runs. The net input of fluid into the tank will lead to

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Fig. 3. Comparative velocity profiles measured along the tank axis, 3 m downstream of the channel mouth. (A) Time-averaged streamwise velocity [using the Ultrasonic Doppler velocity profiler (UVP)] and density profiles of the unconfined flow. Both measurements were initiated 5 s after the head passed, and lasted for 30s. Umax, U and h denote the maximum streamwise velocity, depth-averaged streamwise velocity and flow height, respectively. For the density profile, ps is the depth-averaged density. The dashed line indicates the measured density data, and the dotted line is density data extrapolated below 0.05 m flow depth and above 0.09 m flow depth. The den- sity of the ambient water (pa) as measured at a background temperature of 12°C, where the ambient density of water is 999.6 kg m3. (B) 5 s time-averaged velocity profiles [using the Acoustic Doppler velocity profiler (ADV)] measured from the first 5 s from the head of the flow at the 3 m position (base of slope), prior to the collapse of the flow downslope. The three components of measured velocity, i.e. streamwise (X), cross-stream (Y) and vertical (Z) are indicated.

Table2. Parameters for the Ultrasonic Doppler velocity profiler (UVP) and Acoustic Doppler velocity profiler (ADV) used in the current study. UVP is used to quantify instantaneous flow velocities of the unconfined flow, measured 3 m downstream of the channel mouth and along the tank axis. ADV is used to measure the instanta- neous flow velocities 3 m downstream of the channel mouth along the tank axis, at the base of each slope configu- ration and two positions on each slope surface.

UVP parameters

Instrument name

Sampling frequency

Probe height above tank floor

Velocity of ultrasound in water Number of bins

Number of profiles per transducer Sampling period

Velocity range

Minimum velocity

Maximum velocity

Minimum measurement distance Maximum measurement distance

Met-flow UVP monitor 4

4Hz

1,2,3,4,5,6,7,9, 11, 13 cm

1480 m s1

128

1000

11 ms

256 mm s1 128 mm s1 128 mm s1 4.99 mm 99.71 mm

ADV parameters

Instrument name

Sampling frequency Speed of sound in water

Number of transducers Number of cells

Cell start below head of probe Cell end below head of probe Cell size

Velocity range (streamwise) Horizontal velocity range Vertical velocity range Instrument run time

Vectrino doppler velocimeter

100 Hz 1465 m s1

40 mm

70 mm 1mm

500 mm s1 497 mm s1 130 mm s1 240 s

a diffuse compensatory return flow in the upper part of the water column, however this could not be visually observed, and the orthogonal ori- entation of the slope stops any return flow from directly affecting the experiments. For each slope configuration, three subsequent runs with an ADV were performed to quantify the instanta- neous three-dimensional flow velocities, at a fre- quency of 100 Hz (see Table 2 for details of ADV parameters). The ADV can measure 30 measure- ment points with three component velocities (downstream and cross-stream components, X and Y, respectively, and two measurements of the vertical component, Z1 and Z2, associated with the X and Y receivers of the ADV probe, respectively) over a depth range of 0.03 m. The measurement zone starts 0.04 m below the probe head, and with the basal measurement recorded at the interface of the tank floor and the slope (Fig. 4C to F). The five lowermost ADV measure- ment points were clipped from all experimental runs due to excessive data noise resulting from signal interferences with the floor/slope. The ADV was positioned along the tank axis, at

the base of each slope configuration to quantify the instantaneous velocities of the flow interact- ing with the topographic slope. The position of the ADV on the slope surface was dependent on the slope angle and determined with the aid of the flow visualization videos (see Table 1 for ADV positions). For the experiments performed with the UVP and ADV, the saline density cur- rents were seeded with neutrally-buoyant, hol- low glass microspheres (Sphericel 110-P8) (Potters Industries, Malvern, PA, USA) to pro- vide an acoustic contrast to the flow, which produces the white colour to the flows observed in Videos 2–4. The lowermost ADV was located at the approximate height upslope at which a stable flow front developed. The uppermost position was located where the flow height was approximately 0.07 m thick; at flow thicknesses below 0.07m, the precision of the ADV data measurement window is not considered accurate enough. All instantaneous velocity data recorded by the UVP and ADV were post-processed to remove any data spikes more than two standard deviations away from the mean and replaced with

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Complex flows above simple slopes 75

E. Keavney et al.

A 0.13 m 0.11 m

probe array

probe Z

X tank surface

0.09 m

0.07 m 0.06 m 0.05 m 0.04 m 0.03 m 0.02 m 0.01 m

unconfined distance from channel mouth: 3 m

0.04 m 30° slope 0 distance from channel mouth: 3 m

F 1 X base

Fig.4. (A)Schematicdiagramof the Ultrasonic Doppler velocity profiler (UVP), with the probe heights annotated. (B) Configuration of the UVP used to quantify the velocity of the unconfined density current. (C) Schematic diagram of the Acoustic Doppler velocity profiler (ADV). The basal 0.03 m is the data acquisition window of the ADV instrument. (D), (E) and (F) Configuration for the 20°, 30° and 40° slopes, respectively, with the three ADV positions annotated. For (A) and (C), X, Y and Z are with respect to the velocity components. (G) Schematic diagram of the density syphon array. The syphon array was connected to a peristaltic pump set to a constant withdrawal rate to measure the density of the flow for the duration of the experiment. (H) and (I) Configuration of the syphon array used to quantify the density of the unconfined flow and for the 20° slope.

tank/slope surface

0.03 m

erroneous data 0.08 m

primary flow direction tank/slope surface

base

5 mm diameter 0.10 m

bins removed

connection to peristaltic pump

tubing mount

0.14 m

distance from channel mouth: 3 m

tubing

20° slope distance from channel mouth: 3 m

primary flow direction

base 0.10 m 0.15 m

20° slope 0 distance from channel mouth: 3 m

base 0.10 m 0.20 m

unconfined

distance from channel mouth: 3

water table

40° slope

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0.095 m

density siphon array

density

siphon

ADV

ADVs

UVP

height (m) height (m) height (m) height (m) height (m) height (m)

UVP

Containment factor (h0) for each slope configuration (h0 = h/ hmax), where h = flow height

(0.11 m) and hmax = maximum run- up height. The observed hmax for the 20°, 30° and 40° slopes is

0.30 m, 0.24 m and 0.23 m, respectively. For all experimental configurations, the incoming flow was unable to surmount the containing topographic slope.

40°

30°

0.8 0.7 0.6 0.5

20° 0.4 0.3 0.2 0.1

Fig. 5.

primary flow direction flow height (h)

distance from channel mouth: 3 m

Video 2: Annotated real-time video illustrating the temporal evolution of the flow with a 20° slope. Fluorescent dye injected at a series of lateral points onto the slope surface was used to visualize the interaction of the density current and the containing topography. Gridded white lines were marked on the slope surface to aid the identification of the height at which the stable flow front developed and the maximum run-up height (hmax).

an 11-point moving average (see Buckee et al., 2001; Keevil et al., 2006).

RESULTS Unconfined flow

Velocity and density structure

The flow measured at 3m downstream of the channel mouth is quasi-steady, with a radially spreading front (Video 1). Both the UVP velocity and density measurements of the unconfined flow were initiated 5s after the head passed, and lasted for 30 s (Fig. 3A). The time-averaged streamwise velocity recorded by the UVP

(Fig. 3A) gives a maximum streamwise velocity (Umax) of 0.059 m s1, at a height of 0.02 m (Fig. 3A). The flow height is 0.11m, and the mean depth-averaged streamwise flow velocity is 0.029 m s1 (Fig. 3A). Prior to the interaction of the unconfined flow with the slope, the ADV measured the three components of velocity for the incoming front of the head of the current, over a 5 s period. The Umax of the incoming flow is 0.065 0.005 m s1 (Fig. 3B); albeit the height over which the ADV measures may not quite capture the Umax position in the 40° case (see unbroken yellow velocity profile in Fig. 3B), and thus may be an underestimate. Over the 5 s win- dow in which it was recording the unconfined flow velocity, the ADV measured the cross-

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Complex flows above simple slopes 77

maximum run-up height (hmax)

Height (m)

h’: 0.47

h’: 0.45

h’: 0.36

78 E. Keavney et al.

stream velocity component as 9 to 12% of the maximum streamwise velocity, and the vertical velocity component ranges as 9 to 2% of the maximum streamwise velocity (Fig. 3B). The flow is well-stratified at a distance of 3 m down- stream of the channel mouth (Fig. 6B). The dense, basal region of the flow (0.03 m thick) is separated from the dilute, upper region of the flow (0.06m thick) by a distinct density inter- face (Figs 3A and 6B). The density of the flow decreases upward from 1009 kg m3 (0.9% excess density) in the basal region of the flow to 1000 kg m3 at 0.09 m flow height (Fig. 3A).

Flow interactions with containing topography

The distance downstream from the channel mouth to the containing topography (3m) and input flow parameters were uniform for all experimental runs. The slope was positioned orthogonal to the primary flow direction, with the slope angle independently varied at 20°, 30° and 40°. Comparing how changes in slope angle affect the flow velocity and density structure, and evolution, provides a better understanding of processes active at the base of, and on, the slope surface. The flow visualization (Videos 2– 4; Figs 7 and 11) permits qualitative observa- tions of the flow processes across the width of the slope surface and at the base of slope, while, at a quantitative level, the ADV (Figs 8, 9, 10, 12 and 13) and density (Fig. 6B to D) measurements provide data on the central axis of the flow.

Lateral flow spreading on the slope surface

Upon incidence with the containing topography, the flow visualization videos show that the superelevation of the flows, and the nature of the radially spreading front, differ as a function of slope angle (Videos 2–4; Fig. 7). At 20°, the flow continues to spread radially on the slope surface, diverging away from its central stream- line, with a high degree of spreading towards the lateral edges of the slope (Video 2). At 20°, hmax occurs along the flow axis, approximately 0.30m upslope, 2.73 times the flow height (Video 2; Fig. 7A). The initial degree of lateral flow spreading on the 30° slope is like that observed at 20° (Video 3). However, because of the increased containment at 30°, the compo- nent of flow reflection on the slope surface is enhanced, resulting in less lateral flow spread- ing (Video 3). At 30°, hmax occurs along the flow axis, approximately 0.24 m upslope, 2.19 times the flow height (Video 3; Fig. 7B). At 40°, the

radially spreading head decelerates rapidly at the base of slope and is deflected along the basal edge of the slope (Video 4). The enhanced topo- graphic steering generated at 40° decreases the flow’s upslope momentum compared with the 20° and 30° slopes, and hence decreases the degree of lateral flow spreading on the slope. At 40°, hmax occurs towards the lateral edges of the slope, approximately 0.23 m upslope, 2.10 times the flow height (Video 4; Fig. 7C).

Degree of flow thinning and stripping

The flow visualization from each slope configura- tion, shows that the flow thins as it decelerates upslope (Videos 2–4). Density measurements 3 m downstream show a well-stratified flow with a distinct interface between the dense, basal region and the dilute, upper region of the flow (Fig. 6B). The density measurements recorded at 0.1 m upslope of the 20° slope show that the dilute region of the flow decouples from the dense region of the incoming flow (Fig. 6D) and con- tinues to thin upslope before reaching hmax (Video 2). The thinning and density decoupling of the flow is akin to the process of flow strip- ping (Piper & Normark, 1983). The zone of flow stripping that develops at each slope configura- tion is defined qualitatively (Fig. 6A), using the flow visualization (Videos 2–4), and supported quantitatively for the 20° slope using density measurements of the flow (Fig. 6C and D). The lower limit of the zone of flow stripping is demarcated by the height upslope at which the basal region of the flow reverses downslope (Videos 2–4), hence marking the onset of flow thinning upslope (termed ‘height of initial flow reversal’) (Fig. 6A). The upper limit of the zone of flow stripping is defined by hmax (Fig. 6A). Upon incidence with the 20° slope, the height of initial flow reversal occurs approximately 0.09 m upslope (Video 2). The dense region of the decel- erating flow reverses downslope, causing the flow to thicken and mix as it interacts with the incom- ing flow at the base of slope, generating a non- stratified flow (Fig. 6C). The degree of flow thin- ning and zone of flow stripping generated on the 20° slope is enhanced compared to the 30° slope (Fig. 6A). At 30°, the initial flow reversal occurs approximately 0.13 m upslope (Video 3) and the zone of flow stripping extends to 0.24 m upslope (Fig. 6A). At 40° slope, the flow decelerates strongly at the base of slope and there is little decoupling observed between the dense region of the flow and the more dilute region of the flow on the slope surface (Video 4). The height of the

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Complex flows above simple slopes 79

Fig. 6. (A) The extent of the zone of flow stripping that is generated on the slope surface for each topographic configuration. The lower limit of the zone of flow stripping is demarcated by the height of initial flow reversal. The upper limit is defined by the maximum run-up height (hmax) of the flow. The extent of the zone of flow stripping decreases with an increasing containment factor (B), (C) and (D). Density time series of (B) the unconfined flow recorded at the same position as the base of slope in the topographic slope experiments, (C) at the base of the 20° slope (FC-20e) and (D) 0.1 m upslope (FC-20f) along the tank axis.

0.085 0.070 0.055 0.038 0.020 0.005

0.091 0.076 0.061 0.042 0.026 0.011

10 20 30 40 50 60 70 80 Time (s)

primary flow direction

distance from channel mouth: 3 m

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

999.6

10 20 30 40 50 60 70 80 90 Time (s)

density (kg m-3)

Density (g/cm3)

0.9996

1.0125

slope angle 20° 30° 40°

hmax

flow front development

initial flow reversal

1012.5

ambient water

dilute, upper region

density interface

dense, lower region

Unconfined-d

ambient water

flow mixing and thickening

FC-20e

ambient water

dilute region stripped from dense region

FC-20f

Flow height (m) Flow height (m) Flow height (m)

Height (m)

80 E. Keavney et al.

initial flow reversal in this 40° case is approxi- mately 0.18m, slightly higher than that on the 20° and 30° slopes. Despite this, the smaller hmax value of approximately 0.23m upslope led to a smaller zone of flow stripping (Fig. 6A). The degree of flow stripping and thinning strongly influences the character of the reversed flow at the base of slope.

Primary and secondary flow reversals

The first recorded negative streamwise velocity signal corresponds to the primary flow reversal (Figs 8, 9 and 10). The subsequent repeated fluc- tuations correspond to the secondary flow

reversals (Figs 8, 9 and 10). The flow visualiza- tion (Videos 2–4) and depth-constrained ADV velocity time-series data (Figs 8, 9 and 10) dem- onstrate how the magnitude of the primary flow reversal and the fluctuations of the secondary flow reversals are a function of slope angle. The magnitude of the primary flow reversal is char- acterized by the arrival time of the primary reversal at the base of the slope, the periodicity of the reversal, and its velocity signal.

On a slope of 20°, before the primary flow reversal is recorded at the base of slope, the parental flow decelerates due to the interaction with the weakly reversing flow as it travels downslope. The primary flow reversal occurs approximately 12s after the parental flow ini- tially arrived (Video 2), with a recorded stream- wise velocity of approximately 0.03 m s1 (Fig. 8C). The arrival of the primary flow reversal at the base of slope marks the onset of enhanced cross-stream velocity fluctuations as the two flow components interact (Fig. 8D). The primary flow reversal is recorded at the base of slope over a 9 s window (Fig. 8C). Before the parental flow re- establishes at the base of slope, a 4s period of stasis, where the streamwise velocity is negligible (Fig. 8C), marks the period of the greatest cross- stream velocity variability (Fig. 8D). At 30°, there is limited deceleration of the parental flow at the base of slope before the primary flow reversal is recorded (Fig. 9C). The arrival of the primary flow reversal is recorded 6s after the parental flow initially arrived at the base of slope (Fig. 9B), with a streamwise velocity of approxi- mately 0.04 m s1 (Fig. 9C). The interaction between the primary flow and the reversal gener- ates an increased cross-stream velocity compo- nent at the base of slope (Fig. 9D). The primary flow reversal is maintained for approximately 10 s before the parental flow re-establishes (Video 3). At 30°, following the interaction of the primary flow reversal with the parental flow, the body of the density current appears to inflate, thickening for approximately 30 s, becoming flat- topped and subsequently propagating upstream of the topographic slope (Video 3). The highest degree of flow thickening is observed at the 30° slope (Video 3). At 20° and 40°, the inflated, flat-topped cloud generated at the base of slope is maintained for approximately 10 s and 20 s, respectively, before then propagating upstream of the topographic slope and dissipating throughout the experimental basin (Videos 2 and 4). Despite the propagation of the thickened cloud upstream, no soliton wave trains or bores were observed, as

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Fig.7. Photographs captured using underwater cam- eras, with the maximum run-up height (hmax) and degree of lateral flow spreading annotated. (A) 20° slope. (B) 30° slope. (C) 40° slope. Fluorescent dye is injected at a series of lateral points onto the slope sur- face using a peristaltic pump set at a constant flow rate, to aid in the visualization of the incoming flow interacting with the slope. The hmax and degree of lat- eral flow spreading decreases as the angle of the slope, and hence the topographic containment factor, increases.

has been observed in more confined, 2D experi- ments (e.g. Pantin & Leeder, 1987; Edwards et al., 1994; Kneller et al., 1997). At 40°, the pri- mary flow reversal arrives at the base of slope, approximately 12s after the parental flow first arrived with a decreased streamwise velocity of approximately 0.02 m s1 (Fig. 10C). The paren- tal flow at the base of slope re-establishes approx- imately 7s after the primary flow reversal was first recorded (Fig. 10C). There is negligible streamwise velocity variability in the basal 0.005 to 0.01m of the flow during the primary flow reversal (from 12 to 17 s of Fig. 10C), whereas the cross-stream velocity component during the pri- mary flow reversal operates over the full height of the data acquisition window, at approximately 0.03 m s1 (Fig. 10D).

A quasi-stable flow front develops on the slope surface following the primary flow reversal (Videos 2–4). The flow front is maintained for the remainder of the experiment following

repeated episodes of secondary flow reversal on the slope surface and the re-establishment of the parental flow (Videos 2–4). The height upslope at which the flow front develops, the velocity structure, and the frequency of secondary flow reversals recorded on the slope surface and at the base of slope, is a function of slope angle.

At 20°, a flow front with a linear trace, forms at an average height of 0.11m upslope, one times the flow height, across the width of the slope (Video 2; Fig. 11A). However, the height of the flow front fluctuates between 0.10 and 0.14m upslope as the flow repeatedly reverses downslope before the flow re-establishes (Video 2). The streamwise velocity fluctuates between 0.02 and 0.02 m s1, and the cross- stream velocity between 0.01 and 0.01 m s1 (Fig. 8A and B). At 30°, the flow front develops approximately 0.10 m upslope, 0.91 times the flow height, with a weakly sinusoidal trace (Video 3; Fig. 11B). At 30°, the streamwise

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Complex flows above simple slopes 81

0.03 0.025 0.02 0.015 0.01 0.005

7 20 40 60 80 100

0 20 40 60 80 100 0 20 40 60 80 100

Time since arrival of the density current (s)

0 0.15 CroCsrso-sstr-esatrmeavmelvoecliotyci(tmy /(sm) s-1)

-0.15 0 0.15 StSretraemawmiwseisveevloecloitcyit(ym(/ms)s-1)

-0.15

Fig. 8. Acoustic Doppler velocity profiler (ADV) velocity time series of saline density currents interacting with the 20° slope. (A) and (B) Streamwise and cross-stream velocity time series respectively (z = 0.10 m upslope). (C) and (D) Streamwise and cross-stream velocity time series respectively (z = 0 m, base of slope). The clipped data from the first 7 s in (A) and (B) represents the time taken for the flow to travel from the base of slope to 0.1 m upslope.

Flow height (m)

Flow height (m) z = 0 m

Flow height (m)

Flow height (m) z = 0.10 m

82 E. Keavney et al.

velocity of the flow front fluctuates between 0.01 and 0.01 m s1 (Fig. 9A), and the episodes of secondary flow reversal and re-establishment are less defined compared to the 20° slope (Fig. 8A). At 40°, the initial development of the flow front coincides with greatest cross-stream velocity fluctuations (approximately 0.05 m s1) of any slope configuration (Fig. 10B). For approximately 40 s following the establishment of the flow front, the cross-stream velocity signal is maintained at approximately 0.05 m s1, whereas the streamwise velocity signal is negli- gible (Fig. 10A and B). As the positive stream- wise velocity at the flow front re-establishes after approximately 50s (Fig. 10A), the cross- stream velocity becomes negative (approximately

fluctuations (cf. Dorrell et al., 2018b), at the low- ermost ADV measurement point (0.005 m above the base of the tank/slope), was used to assess the frequency of secondary flow reversals (Fig. 12). The lowermost ADV measurement point was used for these analyses as this is clos- est to the floor, and thus most representative of the conditions affecting sediment transport and deposition. Following the development of the flow front on the slope surface at the 20° and 40° slope (>40 s into flow), low frequency oscil- lations in the range of approximately 100 to 101 Hz are observed at the middle ADV posi- tion (Fig. 12D and P, respectively). The increased power of the oscillations compared to the 30° slope (Fig. 12J) is due to the greater observed fluctuations in the streamwise velocity component (Figs 8A, 9A and 10A). At 20° and 40° the power spectra decrease with height upslope (Fig. 12B, H and N) and dissipate at the base of slope (Fig. 12F, L and R); whereas, at

0.02 m s1) (Fig. 10B). At 40°, the flow develops approximately 0.13 m upslope, times the flow height (Video 4; Fig. 11C).

front 1.19

Single-sided amplitude spectral analysis using a Fast Fourier Transform of the velocity

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0.03 0.025 0.02 0.015 0.01 0.005

-0.15 0 0.15 -0.15 0 0.15 StrSetarmeawmisweisvelvoecliotyci(tmy(/sm)s-1) CroCsrso-sst-rsetaremamvelvoecliotyci(tym(/ms)s-1)

Fig. 9. Acoustic Doppler velocity profiler (ADV) velocity time series of saline density currents interacting with the 30° slope. (A) and (B) Streamwise and cross-stream velocity time series respectively (z = 0.10 m upslope). (C) and (D) Streamwise and cross-stream velocity time series respectively (z = 0 m, base of slope). The clipped data from the first 4 s in (A) and (B) represents the time taken for the flow to travel from the base of slope to 0.1 m upslope.

4 20 40 60 80 100

0 20 40 60 80 100 0 20 40 60 80 100 Time since arrival of the density current (s) Time since arrival of the density current (s)

Flow height (m)

Flow height (m) z = 0 m

Flow height (m)

Flow height (m) z = 0.10 m

30°, the power spectra increase between the middle ADV position (Fig. 12J) and the base of slope (Fig. 12L).

Temporal velocity variability

Flow visualization shows the development of complex, multidirectional flows qualitatively, on the slope surface and at the base of slope (Videos 2–4). To better understand the generation of complex, multidirectional flows (i.e. combined flows), the nature of temporal streamwise and cross-stream velocity variations with position (height) on the slope are considered. Here, analy- sis focusses on the lowermost ADV measurement point (0.005 m above the base of the tank/slope), as measured on the axis of the flow. The incoming flow recorded at the base of each slope (<15 s into flow) has a similar streamwise and cross-stream velocity signal (Fig. 13G to I). The streamwise and cross-stream velocity magnitude and variability decrease through time and with height upslope, in

all cases (Fig. 13). The interaction between the pri- mary flow and the parental flow marks the onset of increased cross-stream velocity variations at the base of the 20° and 30° slopes (Fig. 13G and H). At the base of the 40° slope (Fig. 13I), the streamwise velocity of the primary flow reversal and the cross- stream velocity variability before the establish- ment of the flow front (<40s into flow) is decreased compared to the lower slope angle con- figurations. Whereas, on the slope surface, the ADV data from the 40° slope (Fig. 13F) demon- strate increased streamwise and cross-stream velocity variability compared with the lower slope angle configurations (Fig. 13D and E).

Summary of flow processes

On the slope surface

The increasing slope angle affects the velocity evo- lution of the density currents (Figs 8, 9 and 10) and the dominant flow processes that operate on the

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Complex flows above simple slopes 83

0.03 0.025 0.02 0.015 0.01 0.005

2 20 40 60 80 100

0 20 40 60 80 100 0 20 40 60 80 100

Time since arrival of the density current (s)

-0.15 0 0.15 CrCosros-sst-rsetaremamvevloecloitycit(ym(/ms) s-1)

-0.15 0 0.15 StSretraemamwiwseisevevleolcoitcyity(m(m/s)s-1)

Fig. 10. Acoustic Doppler velocity profiler (ADV) velocity time series of saline density currents interacting with the 40° slope. (A) and (B) Streamwise and cross-stream velocity time series respectively (z = 0.08 m upslope). (C) and (D) Streamwise and cross-stream velocity time series respectively (z = 0 m, base of slope). The clipped data from the first 2 s in (A) and (B) represents the time taken for the flow to travel from the base of slope to 0.08 m upslope.

Flow height (m) Flow height (m) z = 0 m

Flow height (m) Flow height (m) z = 0.08 m

84 E. Keavney et al.

Video 3: Annotated real-time video illustrating the temporal evolution of the flow with a 30° slope. Fluorescent dye injected at a series of lateral points onto the slope surface was used to visualize the interaction of the density current and the containing topography. Gridded white lines were marked on the slope surface to aid the identification of the height at which the stable flow front developed and the maximum run-up height (hmax).

Video 4: Annotated real-time video illustrating the temporal evolution of the flow with a 40° slope. Fluorescent dye injected at a series of lateral points onto the slope surface was used to visualize the interaction of the density current and the containing topography. Gridded white lines were marked on the slope surface to aid the identification of the height at which the stable flow front developed and the maximum run-up height (hmax).

slope surface (Fig. 14). At 20°, the parental flow is observed to decelerate upslope, with the denser, basal region of the flow becoming weakly reflective as it reverses downslope (Video 2). The upper, dilute region of the flow decouples (or is ‘stripped’) at the density interface and continues upslope whilst rapidly thinning (Fig. 6C and D), with a high degree of lateral flow spreading before reaching hmax (Video 2; Fig. 7A). In the zone of flow strip- ping on the slope surface, the thin, dilute flow

(Fig. 6D) is observed to diverge away from its axial streamline (Video 2), generating a complex, multi- directional flow (Fig. 13D). The diverging flow reverses downslope, and interacts with the paren- tal flow to generate combined flows high on the slope surface (Video 2; Figs 13D and 14A). At 30°, a change in the dominant flow process compared to the 20° slope (Video 2; Fig. 8C) is supported by: (i) the decreased rate of lateral flow spreading and flow thinning observed on the slope surface

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(Video 3); and (ii) the increased magnitude of the primary flow reversal recorded by the earlier arrival time and increased negative streamwise velocity of the primary flow reversal at the base of slope (Fig. 9C). The increased degree of contain- ment acts to enhance the rate of deceleration at the base of slope (Fig. 9C) and limit the upslope- momentum of the incoming flow (Video 3). As a result, the flow becomes strongly reflective (Fig. 14B). At 40°, the observed decrease in hmax and the degree of flow thinning on the slope sur- face (Video 4) indicate that the increased topo- graphic containment dramatically decreases the upslope-momentum of the incoming flow. Follow- ing the arrival of the flow at the base of slope, part

of the flow is observed to flow approximately nor- mal to the orientation of the slope (Video 4; Fig. 10C). The limited upslope-momentum and flow deflection at the base of slope has the effect of reducing the magnitude of the primary flow rever- sal at the base of slope (Fig. 10C) compared with the 20° and 30° slopes (Figs 8C and 9C, respec- tively), and increasing the cross-stream velocity of the flow both on the slope surface and at the base of slope (Fig. 14C, F and I). The superimposition of the strongly deflective flow with the parental flow generates highly multidirectional flows (i.e. com- bined flows) both at the base of, and low down on, the slope surface (Fig. 13I and F).

At the base of slope

In all topographic configurations, highly multi- directional flows are generated at the base of each flow, both at the base of, and on, the slope (Fig. 13D to I), and flow inflation occurs at the base of slope (Videos 2–4). These changes in flow behaviour result from the interaction of the primary flow reversal with the parental flow (Videos 2–4). The decreased magnitude of the primary flow reversal and degree of flow infla- tion recorded at the base of the 20° and 40° topographic configurations is attributed to the high-degree of lateral flow spreading at 20° (Fig. 8C), and the reduced upslope-momentum of the flow at 40° (Fig. 10C). Flow divergence and flow deflection are the primary flow process at 20° and 40°, respectively (Fig. 14A and C). At 30°, the magnitude of the first flow reversal recorded at the base of slope is greater than the other slope configurations (Fig. 9C), which is attributed to flow reflection being the dominant flow process (Fig. 14B) and an enhanced interac- tion between the reflected flow and the parental flow at the base of slope (Video 3). The observed episodes of secondary flow reversal and flow stasis (Figs 8C, 9C and 10C) indicate the quasi- steady state of the density current as it inflates at the base of slope, before subsequently dissi- pating farther into the experimental basin, upstream of the topographic slope (Videos 2–4).

DISCUSSION

Effect of topographic containment on flow processes

On the slope surface

Here, the incidence of unconfined, 3D density currents upon planar frontal topographic slopes

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Complex flows above simple slopes 85

Fig.11. Photographs captured using an underwater camera, with the height (annotated) at which a quasi- stable flow front develops. (A) 20° slope. (B) 30° slope. (C) 40° slope. At each topographic configura- tion, a quasi-stable flow front develops on the slope surface following the primary flow reversal of the flow downslope and the subsequent re-establishment of the parental flow.

86 E. Keavney et al.

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Fig.12. Acoustic Doppler velocity profiler (ADV) streamwise velocity time series and associated single-sided amplitude spectrum of the streamwise velocity fluctuations from each slope configuration and ADV position. The lowermost ADV data point was used (0.005 m above the base of the tank/slope surface), as this is the most repre- sentative of the conditions affecting sediment transport and deposition. (A), (C) and (E) 20° slope, (H), (J) and (L) 30° slope, and (N), (P) and (R) 40° slope, streamwise velocity time series. z = height of the ADV upslope. The inset boxes display the region used in calculating the single sided amplitude spectrum of the streamwise velocity fluc- tuations, (B), (D) and, (F) 20° slope, (I), (K) and (M) 30° slope, and (O), (Q) and (S) 40° slope.

is shown to result in differences in the superele- vation, the degree of flow thinning, and the velocity structure of the flow between the three slope angle configurations. In previous 2D experi- mental studies (e.g. Pantin & Leeder, 1987; Knel- ler et al., 1991, 1997; Edwards et al., 1994; Patacci et al., 2015) where flows were strongly confined by the experimental basin, flow reflec- tion has been documented as the dominant flow process with both orthogonal (e.g. Pantin & Lee- der, 1987; Edwards et al., 1994; Kneller et al., 1997; Patacci et al., 2015) and oblique (e.g. Kneller et al., 1991) slopes. The inability of the density currents to radially-expand in 2D experi- ments poorly models the behaviour of natural turbidity currents in unconfined and weakly con- fined settings. Where unconfined gravity currents have been documented to interact with orthogo- nal counter-slopes, both in physical (e.g. Soutter et al., 2021) and numerical (e.g. Howlett et al., 2019) models, the decreased containment factor compared to the current study permits the flows to surmount the topography and bypass down-dip. The model presented here shows how the flow process regime changes from divergence-dominated, through reflection- dominated, to deflection-dominated as the slope angle increases from 20° to 30° to 40°, respec- tively. The new model has implications for the generation of combined flows and potentially for facies and bedforms on topographic slopes.

At the base of slope

The experiments show how a sustained flow input in an unconfined experimental setting results in the inflated density current dissipating throughout the basin, upstream of the topo- graphic slope and/or being diverted around the basal edges of the slope, and the absence of flow ponding. By contrast, in experimental mini- basin settings, sustained flow input results in the progressive infilling of sediment in the first basin (up-dip of the topographic sill), until com- plete flow ponding results in overspill into the second basin (Brunt et al., 2004). The conditions

for flow ponding, and the development of a marked density boundary in the suspension, are further promoted in 2D flume tank experiments due to the high degree of flow confinement and topographic containment (e.g. Lamb et al., 2004; Patacci et al., 2015). Internal waves have been described as forming at a prominent density boundary in ponded suspensions (Patacci et al., 2015).

Absence of internal waves in unconfined density currents

The lack of distinct peaks in the frequency spec- tra generated at the mid-slope and base of slope positions (Fig. 12), and the observed absence of well-defined internal wave-like structures (Videos 2–4), suggests that features including solitons and bores are not present in these unconfined density current experiments. Instead, these experiments demonstrate the gen- eration of combined flows both on the slope sur- face and at the base of slope. Combined flows are generated due to the interaction of uncon- fined density currents with topographic slopes, and the superimposition of multidirectional flow components (Fig. 13), following flow thinning, deceleration and reversal on the slope surface (Videos 2–4). Solitons and internal bores recog- nized in 2D experiments have been linked to the generation of an oscillatory flow component and the inception of combined flow (e.g. Pantin & Leeder, 1987; Edwards et al., 1994; Kneller et al., 1997). These observations have been invoked to explain the presence of combined flow bedforms, such as hummock-like structures and symmetrical megaripples above topographic slopes in deep-water settings following flow interactions with seafloor topography (e.g. Privat etal.,2021,2024;Tinterrietal.,2022;Mart ́ınez- Don ̃ate et al., 2023; Siwek et al., 2023). A new model for the generation of combined flow in unconfined density currents has implications for interpreting the degree of flow confinement and topographic containment in deep-water systems.

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Complex flows above simple slopes 87

88 E. Keavney et al.

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Fig. 13. Streamwise and cross-stream velocity vector variability for the duration of the experimental runs. (A), (B) and (C) at the uppermost ADV position on the slope surface, (20°, 30° and 40° respectively), (D), (E) and (F) at the middle ADV position (20°, 30° and 40° respectively), (G), (H) and (I) at the base of each slope configuration (20°, 30° and 40° respectively). z = height of the ADV upslope. For each experimental run, the 100 Hz ADV data were decimated to 10 Hz, and the lowermost ADV data point was used (0.005 m above the base of the tank/slope sur- face), as this is most representative of the conditions affecting sediment transport and deposition. The colour gra- dient represents time (s) in the experiments.

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Complex flows above simple slopes 89

Fig.14. Schematicthree- dimensional summary of the primary flow processes active upon the incidence of the unconfined density current, as a function of the three slope configurations. (A) 20° slope – flow divergence is active in the enhanced zone of flow stripping that forms on the slope surface. (B) 30° slope – flow reflection is the dominant process and produces a flow reversal with an increased magnitude and enhanced flow thickening at the base of slope. (C) 40° slope – flow deflection at the base of slope limits run-up potential and generates a weakly collapsing flow.

40°

quasi-steady, radially expanding unconfined flow

highly multidirectional flows high on the slope surface

flow divergence

20°

thin, dilute flow high on the slope surface

weak reflection at base of slope

decreased superelevation and flow stripping

flow thickening at base of slope

enhanced reflection at base of slope

limited up-slope momentum of the incoming flow

flow deflection at base of slope

Flow outline in cross-section

Flow outline in plan view

Flow vectors measured along flow axis Flow direction observed visually

30°

90 E. Keavney et al.

A new model for combined flow generation

Here, the generation of combined flows from physical 3D experiments of density currents is explored. At 20°, compared to the 30° and 40° slope configurations, the increased degree of flow stripping, lateral flow spreading and hmax (Video 2), is observed to generate thin, dilute cur- rents high on the slope surface (Fig. 6D). In this position, the diminished gravitational forces that would otherwise act to ‘pull’ the flow back down the slope allows for the dilute flow to spread lat- erally and strongly diverge away from the axial centreline (Video 2). The superimposition of the multi-directional, diverging flow as it begins to reverse downslope with the unidirectional, yet radially-expanding, parental flow, produces velocity signals with a high-degree of spatio- temporal, streamwise and cross-stream velocity variability on the slope surface (Fig. 13D) and at the base of slope (Fig. 13G). At 30°, the genera- tion of complex, multi-directional flows is focussed towards the base of slope (Fig. 13H). The increased topographic containment leads to flow reflection and the enhanced interaction between the primary flow reversal and the paren- tal flow (Video 3). At 40°, the enhanced flow deflection at the base of slope, due to the increased degree of containment, produces com- plex, multidirectional flows with a strong cross- stream component, both at the base of slope (Fig. 13I) and low on the slope surface (Fig. 13F). Critically, the results herein document how flow reflection is not the dominant flow process in 3D, unconfined experiments on low angle slopes, unlike in previous 2D experiments (e.g. Pantin & Leeder, 1987; Edwards et al., 1994; Kneller et al., 1997). This highlights that the superelevation of gravity currents, flow divergence and the genera- tion of highly multidirectional flows (i.e. com- bined flows) is likely to be further enhanced on lower angle slopes, less than 20°, with implica- tions for bedform distribution and onlap styles discussed herein. For each topographic configura- tion, there is an absence of internal waves (Videos 2–4; Fig. 12). This variability in velocity and direction suggests that the generation of com- bined flows at different positions at the base of, and on, the slope is a function of the degree of topographic containment.

In deep-marine settings, one mechanism invoked for the generation of combined flows is the superimposition of high-frequency flow oscillations over periods of hours and/or days, against a unidirectional turbidity current (e.g.

Tinterri, 2011). These oscillations are postulated to be generated by the interaction of turbidity currents with seafloor topography, leading to the formation of internal waves. Previous field-based outcrop models (e.g. Tinterri et al., 2016, 2022; Privat et al., 2021, 2024; Mart ́ınez-Don ̃ate et al., 2023) have invoked this model to interpret sedi- mentary structures. However, the model is based largely on semi-quantitative (Edwards et al., 1994) and quantitative (Kneller et al., 1997) observations from 2D, non-ponded flume tank experiments.

A second mechanistic model for combined flow generation exists for ponded turbidity currents, whereby the formation of internal waves is inde- pendent of flow interactions with a containing slope (e.g. Patacci et al., 2015). The intensity of the internal waves was attenuated with depth (Patacci et al., 2015), seemingly exerting no direct influence on the bedload. The observations from the Patacci et al. (2015) model suggest that inter- nal wave generation is: (i) promoted in 2D, ponded experimental settings, due to the strong stratification focussed at the internal velocity, and concentration and grain-size interface; (ii) depen- dent on the flow magnitude in 2D experimental settings; and (iii) not applicable to combined flow generation in 3D density current experiments. Internal wave formation in ponded suspensions is hypothesized to exploit the contrast between the velocity, and the concentration and grain-size layers (e.g. Patacci et al., 2015). From experimen- tal modelling of 2D gravity currents, internal wave formation has also been observed to occur at a crit- ical layer within the body of gravity currents, at the height of the maximum internal velocity, thus suggesting that the ‘steady’ body of gravity cur- rents has inherent instabilities in the form of inter- nal waves, and may not be as steady as first assumed (e.g. Marshall et al., 2021, 2023). Internal wave generation has been documented to enhance flow stratification, by maintaining the momentum in the lower-part of the flow and limiting the entrainment of ambient water in the upper-part (Dorrell et al., 2019). The experiments herein model low-density gravity currents with the absence of a strong density stratification. It is hypothesized that gravity currents with a stronger density stratification may have a propensity to develop internal waves and reflected bores, as has been observed in the previous 2D experiments with increased flow densities compared to the cur- rent study (e.g. Kneller et al., 1991; Edwards et al., 1994; Kneller, 1995; Patacci et al., 2015). The effects of flow stratification regarding the

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implications for the formation of sedimentary structures and different onlap styles is considered in the Effects of flow stratification Discussion section. Whether the same mechanisms for inter- nal wave generation are applicable in 3D, uncon- fined settings with low-density gravity currents is yet to be explored.

Based on the observations from these experi- ments, a new model is proposed for the genera- tion of combined flows at the base of density currents that interact with simple containing topographies. Combined flows are established following flow deceleration, thinning and spread- ing on the slope surface, and the superimposition of the reversing flow with the parental flow at the base of slope. Hence, combined flows in uncon- fined flows are generated in the absence of inter- nal waves. The temporal nature of the complex, multidirectional flows (i.e. combined flows) var- ies markedly in 3D space depending on the slope angle. Furthermore, the interaction of flows with non-planar seafloor relief, rugose flow fronts and unsteady flows, likely further enhance the gener- ation of combined flows above slopes.

Implications for facies variations

A new model for the formation of hummocks in the deep sea

Hummock-like structures have been documented in a range of deep-marine settings, including basin-plain lobes (e.g. Mulder et al., 2009; Bell et al., 2018), channel-lobe transition zones (e.g. Hofstra et al., 2018) and intraslope lobes (e.g. Privat et al., 2021, 2024; Mart ́ınez-Don ̃ate et al., 2023). They are dominantly aggradational and differ in their internal architecture compared to both true HCS, and to supercritical bedforms such as antidunes (see reviews in Tinterri, 2011, and Hofstra et al., 2018); thus they are considered to be the product of subcritical flows. Prave & Duke (1990) and Mulder et al. (2009) invoke standing to weakly migrating waves formed by Kelvin–Helmholtz instabilities at the upper flow interface to explain the development of HCS-like bedforms. However, the primary model ascribed to their genesis is based on observations of bores in 2D reflected density current experiments (e.g. Edwards et al., 1994) and applied to outcrop models in confined/contained-reflected basins (e.g. Tinterri, 2011; Tinterri et al., 2016).

The documentation of combined flow in unconfined, subcritical, density currents that interact with planar topography, which form in the absence of oscillatory flow from internal and

surface waves, allows a new mechanistic model for the deposition of hummock-like structures to be proposed. Hummock-like bedforms in these settings are proposed to form via rapid sediment fallout as flows decelerate on the slope, under combined flows that show marked temporal vari- ations in flow directions (Fig. 13). High-up on low angle slopes where the range of flow direc- tions is diverse, and the primary current velocity is low, the hummock-like structures will be com- posed of convex or concave draping laminae that may largely lack cross-cutting relationships (Figs 15A and 16C), as observed in examples in outcrop and core (Privat et al., 2021, 2024; Taylor et al., 2024). In part, these are analogous to iso- tropic hummocky cross-stratification, although the absence of cross-cutting relationships is in marked contrast to true HCS (Harms, 1969). Fur- ther down the slope where the primary flow is greater and reversals more important, cross- cutting relationships are likely to be more fre- quent (e.g. Hofstra et al., 2018), producing bed- forms in part analogous to anisotropic HCS (Figs 15C and 16C). In all cases, however, higher frequency wave oscillations are not a factor in the generation of the hummocks.

Spatial distribution of bedforms on the slope

As particulate currents decelerate upon inci- dence with seafloor topography, suspended sedi- ment fallout rates increase, the unidirectional component of the flow decreases, and the flows become strongly multi-directional high up on the slope surface (Fig. 16A and B). More isotro- pic hummock-like structures are predicted to form under such combined flows high up on low angle slopes (Figs 15A, 16B and 16C), including slopes lower than 20°, where enhanced superelevation and flow divergence are hypothesized to occur. In contrast, the superimposition of the primary flow reversal with the unidirectional flow at the base of each slope configuration is predicted to lead to the deposition of 2D, anisotropic hummock-like structures perpendicular to the slope (Fig. 15C). At 40°, the flow lines of the depletive density currents are observed to converge at the base of slope (accumulative flow), before running paral- lel to the slope surface (uniform flow) (see Knel- ler & McCaffrey, 1999) (Video 4), resulting in a quasi-uniform flow component being generated at the base of the simple orthogonal, steep slope. Towards the base of slope, the superimposition of the uniform flow component running parallel to the slope surface and the depletive, parental

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Complex flows above simple slopes 91

92 E. Keavney et al.

flow would support the generation of combined flow bedforms with multidirectional palaeoflow directions (Fig. 16B). Where subcritical density currents decelerate, often towards the base of

impinging slopes or basin margins, outcrop (e.g. Tinterri & Muzzi Magalhaes, 2011; Bell et al., 2018; Tinterri et al., 2022) and experimen- tal (e.g. Allen, 1971, 1973, 1975; McGowan et al., 2024) observations of erosional features (for example, flutes and tool marks) can act to record the regional palaeoflow direction of tur- bidity currents and/or more mud-rich flows (Peakall et al., 2020). As such, the 2D, hummock-like structures are hypothesized to overprint the regional palaeoflow direction at the base of slope. The new model for the genera- tion of combined flows, and the presence of combined flow bedforms in 3D space on seafloor topography, can be used to reconstruct the form and angle of the topography (Fig. 16B and C).

Development of thick massive sands at the base of slope

Compared to lower angle slope configurations (Videos 2 and 3), the observed rapid flow deceler- ation at the base of the 40° slope, coupled with the limited upslope momentum (Video 4), is hypothesized to result in high rates of suspended sediment fallout and the formation of thick mas- sive sandstone beds (Fig. 15B), which terminate abruptly at the base of slope (e.g. Schofield & Serbeck, 2000; McCaffrey & Kneller, 2001; Lee et al., 2004) (Fig. 16B and C). The presence of thick massive sandstone beds at the base of slope could therefore provide evidence of flow inter- actions with seafloor topography. The proposed mechanism for massive sand formation at the base of slope can be considered alongside other mecha- nisms for the deposition of deep-water massive sands (e.g. Kneller & Branney, 1995; Cantero et al., 2012; Hernandez-Moreira et al., 2020).

Draping onlap of low angle slopes

The increased run-up potential of the dilute flow on the 20° slope that decouples from the co- genetic dense lower region (Fig. 6D; Video 2), demonstrates how lower-concentration flows and the more dilute regions of co-genetic flows are able to drape low-angle onlap surfaces (e.g. Bakke et al., 2013) (Fig. 16). Where the slope angle is below 20°, the superelevation of the dilute part of the flow is hypothesized to increase, further draping the onlap surface with fine-grained mate- rial high on the slope surface. As the dilute, upper region of the flow thins and decelerates upslope, the denser region has limited upslope momentum, and rapidly decelerates at the base of slope (Video 3). The modelled behaviour of the denser region of the flow would result in the

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Fig. 15. Facies photographs of turbidites deposited following the interaction with containing topography. (A) Isotropic hummock-like structures displayed in bed-tops (Neuque ́n Basin, Argentina). (B) Thick, mas- sive sandstone bed (Canyon San Fernando, Baja Cali- fornia, Mexico). (C) Fine sandstone bed displaying ripples with opposing palaeoflow directions, overlain by anisotropic hummock-like structures (Canyon San Fernando, Baja California, Mexico).

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Complex flows above simple slopes 93

Fig. 16. Summary schematic diagram showing: (A) the dominant flow processes observed from these experiments as a result of low-density gravity currents interacting with topographic slopes of varying angles; (B) the hypotheti- cal deposit geometry for each topographic configuration, and the key facies and palaeo-current dispersal trends; and (C) the onlap styles for each slope configuration and the differences between two-dimensional anisotropic and three-dimensional isotropic hummock-like bedforms (part C modified from Tinterri, 2011).

94 E. Keavney et al.

deposition of the coarser-grained sediment frac- tion and the abrupt termination lower on the slope, as observed in previous experimental stud- ies (see fig. 13A and B in Soutter et al., 2021). However, the behaviour of the more dilute (i.e. finer-grained) part of the flow on the slope sur- face was not explored in the previous experimen- tal studies due to the configuration of the topographic slope (e.g. Soutter et al., 2021). Sout- ter et al. (2019) observed in the Annot Basin, France, the abrupt pinch-out of high-density tur- bidites and the draping onlap of low-density tur- bidites onto the same onlap surface. The observations from the experiments herein show that, higher on the slope surface, the thin and decelerated flow would generate combined flows and lead to the deposition of the finer-grained sediment fraction (for example, silt – fine sand) and the development of isotropic hummock-like bedforms (Fig. 16B and C). Coupled with the new model for the generation of combined flow, the onlap style of the resulting deposits can sup- port reconstructions of the orientation and gradi- ent of seafloor topography in deep-water settings.

The effects of flow stratification

The present experiments utilized saline flows; however, stratification is a key aspect of sediment gravity flows, particularly those with a sand-grade component, and is more pronounced than in saline flows (Menard & Ludwick, 1951; Gladstone et al., 2004; Amy et al., 2005; Dorrell et al., 2014). The effects of flow stratification will influence the nature of processes as flows interact with topogra- phy, albeit that the full influence is difficult to assess a priori. Furthermore, density profiles are absent in the few documented unconfined natural sediment gravity flows (e.g. Lintern et al., 2016; Hill & Lintern, 2022). There are three main aspects of the current study to be considered when asses- sing how flow stratification may affect flow pro- cesses. Firstly, it is hypothesized that the effects of density decoupling and increased superelevation of the upper, dilute region of density currents is enhanced when a strongly stratified flow deceler- ates upon interacting with topography. Thus, increasing stratification is expected to result in dilute flows with a strong multidirectional flow component higher on the slope surface. Second, it is hypothesized that flows with a pronounced stratification have a propensity for internal wave formation and may produce distinctive bedforms up-dip of topography as internal waves propagate upstream. Finally, it is difficult to predict the

patterns of sedimentation and bedform develop- ment linked to the interaction between a well- stratified flow at the base of slope with a dilute, and better mixed, less-stratified flow collapsing downslope. These factors suggest the need for future physical experiments and numerical simu- lations to explore the effects of more strongly strat- ified flows as they encounter topography, and more direct monitoring efforts in unconfined settings.

CONCLUSIONS

Froude-scaled physical models of three- dimensional, unconfined density currents inter- acting with a planar orthogonal slope are used to develop a new mechanistic model for the for- mation of combined flows in turbidity currents. Flow visualization and high-resolution 3D Acoustic Doppler velocity profiler (ADV) data demonstrate how flow divergence, reflection and deflection are observed to be the dominant flow processes active above 20°, 30° and 40° slopes, respectively. The increased ‘superelevation’ and flow stripping active on the 20° slope promotes flow divergence and generates complex, multi- directional flows high on the slope surface. At 30°, the extent of flow stripping and lateral flow spreading on the slope surface decreases, and flow reflection becomes the dominant flow pro- cess, producing an enhanced flow reversal. This generates increased streamwise and cross-stream velocity variations at the base of slope. At 40°, the increased degree of topographic containment limits the upslope momentum of the flow, and instead deflects the flow at the base of slope.

The generation of complex, multidirectional flows (i.e. combined flows) in the experiments herein are formed due to the superimposition of diverging, reflecting and deflecting flow compo- nents with the parental flow at the base of, and on, the slope surface. A new model is developed for the generation of combined flow in uncon- fined flows, which highlights the 3D nature of the flow and the behaviour of the thin, dilute flow on the slope surfaces. This contrasts with previous 2D experimental studies where combined flows are invoked from the interaction of the unidirec- tional input flow with an oscillatory flow compo- nent generated by internal waves following the interaction of turbidity currents with topographic counter-slopes. Observations from previous 2D experimental studies have provided the basis for the existing outcrop models that document

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combined flow bedforms in a host of deep-water settings. The new model for combined flow gener- ation from these 3D experiments provides a novel mechanism for the formation and distribution of combined flow bedforms in turbidites, such as isotropic and anisotropic hummock-like bed- forms, and the mechanics of draping onlaps ver- sus abrupt pinch-outs. The onlap style of the resulting deposits when coupled with the new model for the generation of combined flow, can support enhanced palaeogeographical reconstruc- tions and assessments of the degree of flow con- tainment within deep-water systems.

ACKNOWLEDGEMENTS

This work has been conducted by EK as part of his PhD project. We thank Chris Stevenson, an anonymous reviewer, and associate editor Kyle Straub for their perceptive comments that helped to improve the manuscript.

CONFLICT OF INTEREST STATEMENT

The authors have no conflict of interest to declare.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

NOMENCLATURE

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densiometric Froude number acceleration due to gravity (m s2) reduced gravity

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Manuscript received 31 January 2024; revision accepted 16 July 2024

Supporting Information

Additional information may be found in the online version of this article:

Table S1. Reynolds Number (Re) and Densiometric Froude Number (Frd) calculations. The Ultrasonic velocimeter Doppler profiler (UVP) measurements were recorded 3 m downstream of the channel mouth, along the flow’s axis, and were initiated 5 s after the head of the unconfined passed, and lasted 30 s.

Ó 2024 The Author(s). Sedimentology published by John Wiley & Sons Ltd on behalf of International Association of Sedimentologists, Sedimentology, 72, 67–99

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