Download the full PDF ➡
Read the full paper ⬇
International Journal of Multiphase Flow 136 (2021) 103540
Contents lists available at ScienceDirect
International Journal of Multiphase Flow
journal homepage: www.elsevier.com/locate/ijmulflow
 |
Measurement of the inner structure of turbidity currents by ultrasound velocity profiling
1 Laboratory for Flow Control, Hokkaido University, Kita 13 Nishi 8, Kita-ku Sapporo 060-0808, Japan
2 Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 3173-25 Showa-machi, Yokohama 2360001, Japan
3 Plateforme de Constructions Hydrauliques, EPFL, Station 18, CH-1015, Lausanne, Switzerland
4 Laboratory for Food Research Engineering, ETH Zurich, Rämistrasse 101, Zurich CH-8092, Switzerland
a r t i c l e i n f o a b s t r a c t
Article history:
Received 3 March 2020
Revised 11 November 2020
Accepted 7 December 2020
Available online 13 December 2020
Keywords:
Turbidity current Velocity field Two-fluid model
Ultrasound Doppler velocity profiling, Flume experiment
The inner velocity structure and particle concentration profile of opaque turbidity currents were mea- sured simultaneously by ultrasound velocity profilers. Currents consisting of a quartz particle suspension were generated by using the lock-exchange method in a flume to experimentally reproduce the quasi- steady state of a turbidity current. A pair of ultrasound transducers captured the horizontal and vertical velocities from Doppler frequencies, and the particle concentration profile was extracted from the echo amplitude. The data obtained were analyzed in terms of momentum conservation according to the two- fluid model. We found that: i) the viscous and Reynolds shear stresses balance in the top half of the current; and ii) the lower border of the stress balancing appears around the depth of the maximum ver- tical density gradient. These findings indicate that the reduction of flow resistance inside the body region of the turbidity current is maintained downstream, which enables the current to transport particles over a long distance.
© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Introduction
Turbidity currents, driven by the density difference between a heavy particle-laden fluid and an ambient fluid, have been a great research subject for a long time, because these currents con- vey large amounts of sediment to downstream areas and form large-scale submarine structures as a result of sediment accu- mulation (Simpson, 1997; Mulder and Alexander, 2001). Studies of these currents are also critical to civil and marine engineer- ing for the estimation of potential risks and management of en- vironmental hazards (e.g. Piper et al., 1999, Peakall et al., 2000; De Cesare et al., 2001; McCaffrey et al., 2003; Talling et al., 2007, 2012; Dorrell et al., 2014; Kneller et al., 2016; and references therein). Chamoun et al. (2016) and Schleiss et al. (2016) pointed out the potential reservoir sedimentation problems and Oehy and∗ Corresponding author: Shun Nomura, Dr. Eng. Research Institute for Value- Added-Information Generation, Japan Agency for Marine-Earth Science and Tech- nology (JAMSTEC), 3173-25 Showa-machi, Yokohama, 236-0001, Japan. Phone: +81- 45-778-5784E-mail address: nomura.shun@jamstec.go.jp (S. Nomura).Schleiss (2007) and Oehy et al. (2010) evaluated the positive effects of artificial solid obstacles and inclined jet screens on unavoidable reservoir sedimentation. In nature, turbidity cur- rents propagate several hundred or thousand kilometers along the sea floor, as has been known from marine geological stud- ies since the 1960s (Kneller and Buckee, 2000, Meiburg and Kneller, 2010). Previous reports have investigated long-range sed- iment transport (e.g. Dorrell et al., 2014; Kneller et al., 2016; Luchi et al., 2018; Dorrell et al., 2019 and references therein). Re- cently, Azpiroz-Zabala et al. (2017) reported field measurements obtained by an acoustic Doppler current profiler in the Congo Canyon; currents with a maximum height of 45–80 m were generated six times in seven months and continued for 5 to10 days. Simmons et al. (2020) noted that the retarding fric- tion force of the flow was surprisingly low, meaning that previ- ous models were likely to have underestimated the flow veloc- ity and traveling distance. Xu et al. (2010, 2014), Xu (2010), and Symons et al. (2017) reported seasonally repeated events in Mon- terey Bay (California) and discussed their effects on the underwa- ter terrain. To represent the flow systems observed in the field, Parker et al. (1986) theoretically explained the physical descriptionhttps://doi.org/10.1016/j.ijmultiphaseflow.2020.1035400301-9322/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)of turbidity currents: sediments entrained from the seabed con- tinuously supply potential energy to the current, enabling the cur- rent to persist over a long distance. Many other numerical studies have assessed the long-range sediment transport system of turbid- ity currents (Meiburg and Kneller, 2010 and references therein).In parallel with field observations and numerical simulations, a number of laboratory studies have examined the inner structures of turbidity currents to understand long-range sediment trans- port systems (e.g. Sequeiros et al., 2010, 2018; de Leeuw et al., 2018; Eggenhuisen et al., 2019 and references therein). In the early stage, many lock-gate type experiments were conducted because of the ease of the experimental setup and the high consistency with numerical analysis (e.g. Kneller et al., 1999; Samothrakis and Cotel, 2006; Cenedese and Adduce, 2008). Several studies using lock-gate flumes have confirmed the crucial role of the initial and boundary conditions in generating effective buoyancy of an initially organized multi-layer density stratification (Gladstone et al., 2004; Amy et al., 2005). The aim of the majority of these laboratory ex- periments was to visualize the outline of the current; i.e. the bor- der between the sediment-laden layer and the ambient fluid as a function of time and space. Several trials have been conducted to observe the inner flow structure of a density or particle-laden flow by laser Doppler velocimetry (Kneller et al., 1999) or by particle tracking velocimetry (Thomas et al., 2003). However, it is difficult to observe the inner parts of a particle-laden turbidity current be- cause of its opacity; thus, insights into the inner flow dynamics are limited.In contrast, acoustic measurement methods are applicable toopaque fluids, non-invasive, and measure a wide range of veloci- ties. Thus, an ultrasound velocity profiler (UVP; e.g., Takeda, 1995) is an effective tool for turbidity currents, because it can mea- sure the spatio-temporal velocity distribution along the ultra- sonic beam. Several previous studies described the use of UVP for measuring the velocity profiles of turbidity currents in laboratory flumes (Baas et al., 2005; McCaffrey et al., 2003; Choux et al., 2005; Gray et al., 2006). Those studies arranged and traversed ultrasound transducers to detect the inflection points of the local velocity profile as well as the turbulence intensity. For example, to measure profiles along ultrasonic beams with high resolution, Oehy and Schleiss (2007), Oehy et al. (2010), Sequeiros et al. (2018), and Nomura et al. (2020) installed UVP transducers at specific angles to the flume bottom. Particle concen- trations in those experiments were measured by local sampling ofexplain the experimental facility used to produce the turbidity cur- rents, the particle properties, and the details of the measurement method utilizing UVP. In the second half, we report the visualized flow characteristics and quantify the flow structure inside the main body of a turbidity current. Data analysis, coupled with basic equa- tions of turbulent dispersed two-phase flow, provides the turbulent shear stress profile in the main body of the current, which is a key factor for understanding long-range current migration in natu- ral systems.Experimental Method
- Experimental Facility and ConditionsA schematic diagram of the experimental facility is shown in Fig. 1. The test section is an inclined (1.38°) rectangle flume 4548 mm long, 210 mm high, and 143 mm wide. The side and bottom walls are made of smooth acrylic material, and the top boundary is a free surface. The front wall is transparent, whereas the back wall is coated with a non-reflective black film to produce a dark uni- form background for the visual assessments. The region enclosed by a dotted line in Fig. 1 indicates the visualization area for captur- ing the interface between the turbidity current and ambient water. A lock gate made of a plastic plate is placed approximately halfway along the flume. As an initial condition, the left (higher) side of the flume is occupied by a particle-laden heavier fluid with bulk den- sity ρH, while the right (lower) side is filled with tap water with density ρW as an ambient fluid. The temperature and density of tap water are almost constant, 8.0°C and 999.9 kg/m3, respectively; thus, the viscosity of water μW is 1.385 mPa•s. After gate opening, the heavier fluid intrudes under the ambient fluid with front ve- locity Uf because of the density difference between the two fluids. The horizontal rightward displacement of the current is defined as the x axis and the height from the bed is the y axis.Quartz particles mainly composed of SiO2 (Carlo Bernasconi S.A., Switzerland) were used as suspended particles in the left side of the flume. The particle-size distribution measured with a Mas-tersizer 3.0 (Malvern S.A., United Kingdom.) is shown in Fig. 2. The mean diameter of the particles is d50 = 12.2 μm. The specific grav- ity of the particles is 2.65, and the weighted settling velocity vs in water can be estimated by Stokes’ law as follows (Altinakar et al., 1996):= Σvpd2 (ρp − ρW )gsediment fluids. Felix et al. (2005) carried out combined measure- ments of the velocity and concentration of turbidity currents bypiWs 18μ i i(1)applying UVP and an ultrasonic high concentration meter to mea- sure the velocity and concentration profile simultaneously.Since 2005, the capability of UVP has been extended to enable measurement of dispersions and interfaces involved in multiphase flows (Murakawa et al., 2008; Murai et al., 2010; Hitomi et al., 2017; Park et al., 2019). For a flow with a high sediment concentra- tion, the degree of attenuation of the ultrasound beam can be used to estimate the spatial distribution of the flow. For bubbles and oil droplets in water, reflection and attenuation theory can be used in combination to reconstruct the dispersion distribution, as exam- ined by Murai et al. (2009), Dong et al. (2015), Su et al. (2017), and Shi et al. (2019). For solid particles much smaller than the ul- trasound wavelength in water, the echo intensity and its attenua- tion has been recently discussed while also considering the acous- tic impedance of the particles (Rice et al., 2014, 2015; Bux et al., 2017), thereby highlighting the potential for further innovative in- vestigations using UVP.In this study, we present an interpretation of the flow mech- anism by making use of the precise measurements facilitated by the extended utility of the UVP and the framework of momentum conservation in multiphase flow. In the first half of this paper, wewhere dpi , ρp, and g (= 9.8 m/s2) are the particle size, particle density, and gravitational acceleration, respectively. The value of vs from Eq. (1) is 0.38 mm/s, which is too small for significant depo- sition to occur during the experiment; thus, sedimentation effects are negligible in this research. The volume fraction of quartz parti- cles fs in heavier fluid is 0.5%, resulting in the mixture density ρH being 1008 kg/m3.Although we conducted a series of flume experiments with dif- ferent types of particles, particle size distributions, and concentra- tions (i.e. 0.25%–2.00%), here we focus on quartz particles for the above-mentioned conditions because this setup well represents the quasi-steady structure inside the turbidity current within the lim- ited downstream length of the flume.
- Velocity Profile MeasurementAs shown in Fig. 3, a single turbidity current can be roughly classified into two parts: the head region, which is in an unsteady state and generates particle uplift, and the body region, which exhibits quasi-stationary stratified layers following the head re- gion. To measure the velocities in both regions, a pair of 4-MHz
Fig. 1. Experimental apparatus used to generate and observe a turbidity current by the lock-exchange technique.
Table 1
Parameters applied in the UVP measurement.Basic frequency
4 MHz
Speed of sound in water
1480 m/s
Maximum velocity range
179.1 mm/s
Velocity resolution along the beam
1.399 mm/s
Maximum measurement length
358.2 mm
Number of channels
285
Number of profiles
4096
Sampling period for each profile
50 ms (20 Hz)
Window start
8.88 mm
Window end
219.04 mm
Wavelength (i.e. Channel distance)
0.74 mm
Special resolution
0.74 mm
Number of cycles
4
Repetition
32
Fig. 2. Particle-size distribution of the quartz particles used in the flume experi- ments.
The horizontal and vertical velocity components (uI and vI) at the intersection are derived from the velocities along two measure- ment lines u1 and u2 as follows (Lhermitte and Lemmin, 1994):
u (y , t) = u1(yI, t) − u2(yI, t) , (2)I I 2 sin θv (y , t) = − u1(yI, t) + u2(yI, t) . (3)I I 2 cos θFig. 3. Schematic diagram of the arrangement of ultrasound transducers, where umTo obtain the horizontal and vertical velocity profiles of (u, v) along the y axis at x = xI, we proposed a time correction method of velocity distributions using a front velocity Uf Nomura et al., 2018, 2019). This interpolation is applicable in the case that the turbulence statistics are conserved in the measurement region. The details of Uf are described in section 3.1. The turbidity current pro- gresses with almost constant Uf in the case of high-volume release (the initial volume of the heavier fluids is relatively similar to that of the ambient fluid). On the basis of this concept, Eqs. (2) and ((3) are modified as follows:u1(y, t − ∆t) − u2(y, t + ∆t)denotes the maximum streamwise velocity, y = hm is the corresponding height, andy = ht is the zero-crossing point.u(y, t) =(4)2 sin θUVP transducers is used, which has the advantage of measuring velocity profiles without mechanically traversing the transducers (Finelli et al., 1999; Dombroski and Crimaldi, 2007). The selectionv(y, t) u1(y, t − ∆t) + u2(y, t + ∆t)= −2 cos θwhere(y − yI ) tan θ(5)of instruments depends on the data to be extracted. In our ap- proach, we employ UVP to resolve the vertical distributions of flow∆t =. (6)Ufvelocity and particle concentration, which is difficult to achieve us- ing ADV (Acoustic Doppler velocimetry) (Cossu and Wells, 2012).The transducers are installed at inclinations of θ = 25° to they axis and individually connected to two UVP Duo devices (Met- Flow S.A., Switzerland). In contrast to a multiplex system, this setup enables us to obtain two measurements simultaneously with no switching time. Two measurement lines along the transduc- ers cross at (xI, yI) = (1005 mm, 15 mm). Here the intersectional height yI is selected to be almost the height of the maximum ob- served velocity obtained from preliminary tests. The starting time of the two-UVP measurement is synchronized with the gate open- ing.Here, the interpolation quantity is varied due to y. The UVP mea- surement parameters (Takeda 2012) are presented in Table 1. From the UVP parameters applied in this experiment, the resolution in the vertical direction and the temporal resolution are 0.67 mm and 50 ms, respectively. As the velocity resolution of UVP was1.399 mm/s and the UVP inclination was 25°, the vertical and hor- izontal velocity resolutions were 1.399/(sin 25) = 3.31 mm/s and 1.399/(cos 25) = 1.54 mm/s, respectively. There is inevitably some inaccuracy in resolving the turbulence, due to the non-uniformity of turbulence structures during the time between crossing the two separate beams (Eq. (6)), which was estimated to be negligibly small in this experimental setup.Since d50 (12.2 μm) is less than one-tenth of the wavelength of the ultrasound echo of 4 MHz frequency in water (0.74 mm; Table 1), Rayleigh scattering, which is almost isotropic scatter- ing, is generated. In ordinary UVP measurements, the adequate diameter of the tracer particles acting as reflectors of the ultra- sound wave is appropriately quarter to half of the wavelength. Hitomi et al. (2018) evaluated whether velocity measurement can be performed correctly using the same particles as in this study and a 4-MHz transducer. They confirmed that the equipment can capture the correct velocity profile for volume fractions of 0.01%– 5.00% by comparison with measurements obtained using tracer particles of adequate size.
- Particle Concentration ProfileUltrasound echo amplitude distributions scattered by sus- pended particles provide useful information on the parti-
Table 2
Gain factors to amplify UVP echo signals (courtesy of Met Flow Corp.).Gain factor Gs / Ge Basic frequency of ultrasound transducer 4.0 [MHz]3 0.914 1.765 3.416 6.677 15.008 25.009 60.00dηBecause of non-linearity in the original form of Eq. (7), the solu- tion for M must be acquired by iterative analysis, whereas Lee and Hanes (1995) proposed an explicit form by introducing the con- centration at an initial point MI by differentiating the logarithm of Eq. (7) with respect to η as follows:cle concentration (e.g. Lee and Hanes, 1995; Thorne anddM(η)⎛ η d√(V 2 ⟩ + ,(V 2⟩ ⎞Hanes, 2002; Hurther et al., 2011; Pedocchi and García, 2012). Simmons et al. (2020) applied the technique to observe turbid- ity currents in a natural environment. Under Rayleigh scattering conditions, Thorne and Hanes (2002) suggested the relationshipdη − ⎝2η,(V 2⟩+ 4αW⎠M(η)2= 4ξ M(η)(12)between the mean-square amplitude of the echo signal <V2> re- ceived by ultrasound transducers and the mass concentration M in kg/m3 at η, the distance from the transducer, to be:where ψ (η) in Eq. (7) is assumed to be a constant for the case of measurements in the far field of an ultrasound wave (Downing et al., 1995), and disappears by the differentiationM(η) = V 2®µψηKsKt¶ e4αη = V 2®µψηKsKt20¶e4(αWη+. r ξ M(η)dη) (7)in Eq. (12), as do Ks and Kt. According to the general solu- tion of Bernoulli differential equations, the analytical solution of Eq. (12) can be presented as.(V 2⟩η2e4αW ηdη (13)2where ψ is the spreading effect of acoustic waves in the near fieldof a transducer and αW is the attenuation constant in clear waterpresented as a function of the temperature, as follows (Fisher andMV 2®η2e4αWη¡ ¢Simmons, 1977):αW = 10−15 55.9 − 2.37T + 4.477 × 10−2T 2 − 3.48 × 10−4T 3 F 2(8)where T is temperature (°C) and F is the acoustic frequency (Hz). The sediment attenuation constant ξ can then be written aswhere, C denotes the integral constant.(η) = C − 4ξA boundary condition is required to determine C in Eq. (13). Here we assume that the heavier fluid intruding into the am- bient fluid as a turbidity current maintains its initial concentra- tion close to the bed. This condition is reasonably applicable, ac- cording to previous reports by Felix et al. (2005) and Theiler and Franca (2016). The boundary condition, MB = 1008 kg/m3 at the=ξ 34asρPχ (9)bottom and η = ηB, is thus provided, and C is derived as follows:= +where as is the acoustic attenuation constant. χ is the normal-ized total scattering cross-section (Thorne and Hanes, 2002), rep-C B B 4ξMBr2V 2® e4αWrB∫ rB ®rIresented asApplying Eq. (14) to Eq. (13), we have:r2 V 2 e4αW rdr (14)1.1 · 4 · 0.18(kas)4 ®31 r2(V 2⟩ e4αW rB + 4ξB r2(V 2⟩e4αW rdrwhere k is the wave number of the acoustic wave in water, Ks isχ 3= 1 + 1.3(kas)2 + 4 · 0.18(kas)4(10)M(r) =MBBr2 V 2 e4αWr. rBr(15)e4αW ri−1a function of the scattering properties of the suspended sediment, and Kt is a constant for the ultrasound system. Pedocchi and Gar- cía (2012) applied this theory to the echo distributions obtainedBy discretizing Eq. (15), we finally obtainn ( ⟩nr 2 V 2 e4αWrn+4∆rξNr2(V 2⟩ e4αW ri + r2(V 2⟩Mn = · 1 r2(V 2⟩ e4αWrB¸ (16)by UVP, where the echo signal is the result of the acoustic Dopplerconversion for velocity profiling. In the UVP Duo, the echo signalsΣ ¡ MB B B ¢i=n+1iii−1i−1are represented as voltage variations with 14 bits within the range±2.5 V (8191 = 2.5 V; −8191 = −2.5 V). The device adopts time- variable gain values to amplify the echo signal by linear absolute gain with start Gs and end Ge. According to the technical manual for the device, the actual echo intensity V recorded as an electric voltage is derived asV=ampGsseηe −ηs(11)V ³ G ´ η−ηsGwhere n represents the order of measurement (i.e. i -th) pointsfrom the transducer.
Results
- Front Advection VelocityImages extracted every 1.5 s from 16.5 s after opening of thegate are shown in Fig. 4. The movie was taken with a digital cam-where Vamp is the amplified echo signal, and ηs and ηe are theminimum and maximum measurable distance from the transducer, respectively. The detailed characteristics of amplification by UVP Duo are summarized in Table 2.era (Nikon D5500) from the side window of the flume at 20 frames per second. The shooting area is around xI in Fig. 1. The frame rate was purposely set to be the same as the profile sampling rate of the UVP (temporal resolution 50 ms).
Fig. 4. (a) Snapshots of the experimental turbidity current from t = 16.0 to 23.5 s and (b) the template image that was used for correlation with other images to measure the front velocity.
tal run were determined from the slope angle using least squares (Table 3). The obtained values of Uf are similar; the average value is 50.6 mm/s with small fluctuations of 0.41 mm/s. As turbidity currents are regarded as a type of gravity current, the densiomet- ric Froude number Fr’ of the flow and the Reynolds number Re (following Simpson and Britter, 1979; Kneller et al., 1999) can be calculated as follows:,gr HF rr = Uf ρHUf H(17)Re = μ (18)Fig. 5. Temporal evolution of the location of the front of the turbidity current. The abscissa and ordinate indicate the elapsed time ∆t from t = 16 s and the displace- ment of the detected head position from the initial position, respectively.In the images obtained, unsteady interfaces were observed from the front edge to the upper boundary with the ambient water. This finding is in agreement with the observations of Simpson and Brit- ter (1979). To measure the front velocity Uf, pattern matching was applied to the sequential images. A template image with 451 × 451 pixels was prepared from the image at t = 16 s (Fig. 4(b)), and the corresponding head position of the turbidity current was deter- mined every 250 ms by computing the image correlation between the template and the visualized images. To confirm reproducibil- ity, the experiments were repeated six times using the same initial and boundary conditions. The head positions with time are shown in Fig. 5. In all cases, similar migration of the head position was observed with small deviation, proving experimental reproducibil- ity of the current.In Fig. 5, the slope gradient remains constant with time. This result implies a steady state of the current between the gravity- driven hydrostatic force and the flow resistance caused by the counterflow that balances the buoyancy force along the upper boundary of the current. The front velocities Uf of each experimen-where H is the height of the heavy fluid and g´ is the reduced gravitational acceleration. In the produced currents, the height H converged to a stable value in the downstream region. At the mea- surement window x = xI, the current height was H = 79 mm, giv- ing Fr’ = 0.63 and Re = 4.0E3 in this experiment. These values of the non-dimensional numbers indicate that the flow was fully tur- bulent and subcritical (e.g. Kneller et al., 1999).
- Visualization of the Inner Flow
- Velocity profileThe spatio-temporal distributions of horizontal and vertical velocities (u and v) of a typical run are shown in Fig. 6. This illustration was produced based on the theory described in Section 2.2 and transformation of the time series into a represen- tation of the 2D flow structure. As shown by the image of the ve- locity magnitude, u is dominant in the bottom half of the flume; i.e., y ≈ 0–70 mm. Due to intrusion of the flow, positive v (i.e. up- ward flow) is observed at t = 20–25 s, representing lifting up of the ambient water. As the lock-exchange flume is a closed system, a counter flow of ambient fluid is generated and a negative hori- zontal velocity is observed at y ≈ 50–70 mm. As the lower mea- surement limitation in this system is a particle concentration of 0.01% (Hitomi et al., 2018), the velocity values above that height are fluctuating and unreliable. The distribution of u describes a
Table 3
Summary of front velocity values computed by pattern matching.Exp. Number 1 2 3 4 5 6 Ave. Std. Dev.Uf [mm/s] 50.0 50.0 50.9 50.6 51.0 50.9 50.6 0.41
Fig. 6. Spatio-temporal distribution of the horizontal (upper illustration) and ver- tical (lower illustration) velocity components. y = height above the bed. Measure- ment data above y = 70 mm are unreliable due to the lack of particles.
Fig. 7. Spatio-temporal distribution of the backscatter echo intensity (upper illus- tration) and bulk density of the particle-suspended fluid computed from echo in- tensity (lower illustration). Measurement data above y = 70 mm are unreliable due to the lack of particles.quasi-periodic fluctuation in the main body of the current with time. This fluctuation can be attributed to the vortex structures emerging near the upper boundary of the current, which are also observed in the vertical velocity v.
- Concentration profileThe concentration profile of quartz particles was obtained from the spatio-temporal echo distribution measured by UVP by means of the algorithm explained in Section 2.3. To reduce the influence of measurement noise on the echo, the mean-square amplitude of the echo signal <V2> was calculated from 5 × 5 measurement points, yielding an equivalent resolution of 3.4 mm × 0.25 s in the space–time domain as follows:
Fig. 8. Time-averaged distribution of the horizontal velocity component (u˜) in the body region for 35 < t < 70 s. The hatched area indicates the region for which the data are unreliable due to the lack of particles for UVP measurement. The heights ht and hm are defined as the positions at zero-cross velocity and maximum velocity, respectively. The error bars indicate 95% confidence interval of the sample mean for the horizontal velocity in the sampled period, which becomes large at y>70 mm due to lack of particles necessary for UVP measurement.ier fluid, consistent with the findings of Felix et al. (2005). This result supports the hypothesis that the turbidity current lifts up particles in the front part of the current to raise its own poten- tial energy. In addition, particles are fed to the front bottom part from the lower high-density layer that slides from upstream; this process is visible as vertical stepwise stratification in Fig. 7. The combination of these structures in a turbidity current is consis- tent with previous reports (e.g. Pantin, 1979; Parker et al., 1986; McCaffrey et al., 2003; Pantin and Franklin, 2011); i.e., uplifting of heavier fluid at the front and re-supply of the density differ- ence between the main body of the current and the ambient fluid (Nomura et al., 2019).
- Velocity profileThe spatio-temporal distributions of horizontal and vertical velocities (u and v) of a typical run are shown in Fig. 6. This illustration was produced based on the theory described in Section 2.2 and transformation of the time series into a represen- tation of the 2D flow structure. As shown by the image of the ve- locity magnitude, u is dominant in the bottom half of the flume; i.e., y ≈ 0–70 mm. Due to intrusion of the flow, positive v (i.e. up- ward flow) is observed at t = 20–25 s, representing lifting up of the ambient water. As the lock-exchange flume is a closed system, a counter flow of ambient fluid is generated and a negative hori- zontal velocity is observed at y ≈ 50–70 mm. As the lower mea- surement limitation in this system is a particle concentration of 0.01% (Hitomi et al., 2018), the velocity values above that height are fluctuating and unreliable. The distribution of u describes a
- Data Analysis and Discussion
- Velocity and Concentration Profiles of the Body RegionThis section focuses on the body region, which is recognized as a local quasi-steady flow behind the head (Kneller and Buc- kee, 2000 and references therein). Previous studies provide no clear criteria to distinguish the head and body regions, because they observed mainly the outline of the sediment layer. We fo- cused on the distribution of v to define the beginning of the body region and concluded that this region arrives by t = 35 s, because the influence of the uplifted flow of the head region disappears ®V 2i, j 1 2Σ= 5 × 5Σ £V 2(i + ∆i, j + ∆j)¤ (19)after t ≈ 35 s in Fig. 6. Fig. 8 shows the profile of the mean hori-zontal velocity (u˜) in the body averaged for 35 s after t = 35 s. The profile shows the zero-crossing point on the y axis at y = ht = 502∆i=−2 ∆j=−2where i and j represent discrete coordinates in time and space, re- spectively.The spatio-temporal density distribution of the quartz suspen- sion calculated using Eq. (1 and the measured values are depicted in Fig. 7. The head region of the current has a high density of al- most 1008 kg/m3, corresponding to the initial density of the heav-mm, which corresponds to the thickness of the current defined by velocity. The maximum velocity um = 80 mm/s is observed at y = hm = 14 mm, which is located in the lower half of the current (i.e. hm < ht/2). This velocity is 1.6 times as high as the front ve- locity Uf; this difference results in recirculation of the flow within the body region. Outside the current at y > ht, a layer of reverse flow takes place as a counter flow.
Table 4
Summary of computed values of the friction velocity and the zero-velocity roughness height.Exp. Number
1
2
3
4
5
6
Ave.
Std. Dev.
u∗ [mm/s]
9.2
11.8
12.8
12.3
11.1
10.8
11.3
1.2
y0 [mm]
0.404
0.925
0.948
0.825
0.725
1.110
0.820
0.220
Fig. 9. Fitting result with log-law profile (Eq. (20)) for the averaged horizontal ve- locity profile (u˜) in the lower shear layer of the body region for 35 < t < 70 s. The error bars indicate the confidence interval the same as in Fig. 8.Altinakar et al. (1996) reported that the profile of u˜ is similar in shape to that of a jet flow parallel to a wall consisting of two vertical regions: a wall region (y < hm) and a free jet region (hm < y < ht). They suggested a model fitting for the wall region with a logarithmic profile of turbulent boundary layers:
Fig. 10. Time-averaged profiles of particle concentration (C¯) in the body region for 35 < t < 70 s, relative to the time-averaged velocity profile. The error bar for par- ticle concentration is estimated from the r.ms. of temporal fluctuations in echo in- tensity, V’rms, reflecting to variation of C in Eq. (14).u˜(y) = u∗ ln y
(20)κ y0where u∗ and y0 denote the friction velocity and the zero-velocity roughness height, respectively. Assuming a smooth bed condition (e.g. Zordan et al., 2018), substitution of the von Karman constant κ = 0.41 in Eq. (20) yields the values presented in Table 4 for six runs of the same current. The average values are u∗ = 11.3 mm/s and y0 = 0.82 mm. The value y0 is larger than the expected value for the smooth floor of the flume, implying a rough wall effect re- sulting from particle deposition on the floor. The logarithmic veloc- ity profile with these constants is indicated by the broken line in Fig. 8 on a normal scale and Fig. 9 on a semi-logarithmic scale; the fitting curve seems to represent the experimental data reasonably for y < hm.The time-averaged distribution of the normalized particle con-centration C¯ [%] = (ρf − ρL)/(ρH − ρL) × 100 from M for 35 s af- ter t = 35 s is shown in Fig. 10. The value decreases monotonically with respect to y from the maximum concentration at the bottom, and approaches zero at y = ht. The solid curve in Fig. 10 shows u˜, which is also illustrated in Fig. 8. These vertical gradients (Fig. 11) reveal a more precise structure, which appears to exhibit multiple steps in the concentration profile. The profile of C has three major inflection points that divide the whole structure into four layers: the wall shear layer at 0 < y < hm; the second layer at hm < y < hs = 25 mm; the third layer at hs < y < ht; and the outer region at y > ht. As is visible in the profile of u˜, the second and third layers exhibit a negative velocity gradient (du˜/dy < 0). This result implies that particle diffusion takes place non-analogously due to momen- tum diffusion inside these layers. The details of the mechanism are discussed in Section 4.2.
Fig. 11. Time-averaged vertical gradients in particle concentration and horizontal
flow velocity in the body region for 35 < t < 70 s. The velocity gradient is com- putable only at h < ht.
- Velocity and Concentration Profiles of the Body RegionThis section focuses on the body region, which is recognized as a local quasi-steady flow behind the head (Kneller and Buc- kee, 2000 and references therein). Previous studies provide no clear criteria to distinguish the head and body regions, because they observed mainly the outline of the sediment layer. We fo- cused on the distribution of v to define the beginning of the body region and concluded that this region arrives by t = 35 s, because the influence of the uplifted flow of the head region disappears ®V 2i, j 1 2Σ= 5 × 5Σ £V 2(i + ∆i, j + ∆j)¤ (19)after t ≈ 35 s in Fig. 6. Fig. 8 shows the profile of the mean hori-zontal velocity (u˜) in the body averaged for 35 s after t = 35 s. The profile shows the zero-crossing point on the y axis at y = ht = 502∆i=−2 ∆j=−2where i and j represent discrete coordinates in time and space, re- spectively.The spatio-temporal density distribution of the quartz suspen- sion calculated using Eq. (1 and the measured values are depicted in Fig. 7. The head region of the current has a high density of al- most 1008 kg/m3, corresponding to the initial density of the heav-mm, which corresponds to the thickness of the current defined by velocity. The maximum velocity um = 80 mm/s is observed at y = hm = 14 mm, which is located in the lower half of the current (i.e. hm < ht/2). This velocity is 1.6 times as high as the front ve- locity Uf; this difference results in recirculation of the flow within the body region. Outside the current at y > ht, a layer of reverse flow takes place as a counter flow.
- Momentum Conservation Law for the Body RegionTo discuss the shear stress profile in the body region, we incor- porate two-fluid model equations that are local volume-averaged descriptions of the momentum conservation equation for two phases:∂ fLρLuL∂t + ∇ · fLρLuLuL = − fL∇ p + MLL + MSL (21)∂ fSρSuS∂t + ∇ · fSρSuSuS = − fS∇ p + MSS + MLS (22)where the subscripts L and S denote liquid and solid phases, re- spectively. The primitive variables f, u, and p are the volume frac-Finally, the horizontal component of Eq. (32), which dominates the turbidity current in the body region, is described as follows:tion, velocity vector, and pressure, respectively, as local volume- averaged quantities. The terms MLL and MSS represent the inner phase momentum transport (e.g. Murai and Matsumoto, 2000),which is modeled in the case of particle-laden flow as follows:∂ρHu∂t +∂ρHuu∂x +∂ p∂ρHuv∂y +µ ∂ 2μHu∂ρHuw∂z∂ 2μHu∂ 2μHu ¶© }MLL + MSS= − ∂x +∂x2 +∂y2 +∂z2+ Fg (33)3= ∇ · μL ∇uL + (∇uL )T − 2 (∇ · uL ) + fLρLgS S S 3 S S S+∇ · μ n∇u + (∇u )T − 2 (∇ · u )} + f ρ g (23)where μ and g are the viscosity and the acceleration due to grav- ity, respectively. The slip velocity between uL and uS can be esti- mated by the following equation for the Stokes number:ρpd2U0where w is the spanwise velocity. Fg denotes the external force due to gravity.
- Shear Stress ComponentsWe separate the primitive variables into time-average and fluc- tuation components (analogous to Reynolds decomposition for two-phase flow; e.g., Murai et al., 2006) in the following manner:=St p 18μWL0(24)ρH =ρH +ρHr (34)where U0 and L0 are the characteristic velocity and length, repre- sented by the time-averaged values of the layer-averaged velocity u˜ and the thickness of the current ht. This equation yields St val- ues on the order of 10−5 << 1, which proves that the phases have a common fluid velocity field uL = uS = u. Hence, Eq. (16) can be rewritten asu = u + urv = v + vrw = w + wr
M + M = ∇ · μ n∇u + (∇u)T − 2 (∇ · u)} + f ρ g + f ρ g
LL SS H3 L LS S(25)μH = μH + μrHSubstituting these values into Eq. (33), an equation describingwhere μH is the effective viscosity of a particle-suspended fluid,which was empirically modeled by Davidson et al. (1977) as fol-lows:the shear stress balance is obtained:∂xH +H + H + H + ∂ ¡ρHuv + ρHur vr + ρr vr u + ρr ur v + ρr ur vr¢∂ρHuw + ρHur wr + ρr wr u + ρr ur w + ρr ur wr(35)∂ ¡ρ uu ρ ur ur 2ρr ur u ρr ur ur¢HWSμ = μ (1 − 1.35 f )−2.5 (26)∂y ¡ H H H ¢+∂zHHHHHHMSL and MLS in Eqs. (21) and (22) represent mutual phase mo-∂ 2³μH u+μr ur´∂ 2³μH u+μr ur´∂ 2³μH u+μr ur´∂pmentum transfers and satisfy the following relation due to New- =∂x2 +∂y2 +∂z2 − ∂x + Fg.ton’s third law (regarding action and reaction):In the body region, there is no mean current other than theMSL+ MLS= 0. (27)horizontal current to apply v = w = 0 in Eq. (35) and the gradient of the momentum in the streamwise and spanwise directions isρ ur vr + ρr vr u + ρr ur vr=∂ p+ + F .HHTaking the sum of Eqs. (21) and (22), the total momentum con-negligible; consequently, we have∂servation equation in terms of total mass can be described as∂( fL ρL + fS ρS )u + ∇ · ( fLρL + fSρS )uu = −( fL + fS )∇ p∂y¡H¢ ∂ 2¡μ u + μr ur¢g
HH+∇ · μH∇u + (∇u)— 3 (∇ · u)+ ( fLρL + fSρS )g∂t ©T 2 }(28)∂y2∂x(36)For mass conservation, the following relations apply to the present incompressible particle-laden flow:Eq. (36) is rewritten to explicitly show the terms balancing with the streamwise pressure gradient:fL + fS = 1 (29) ∂ Ã ∂μHu∂μ’ u’ ∂ p ∂xfLρL + fSρS = ρH (30)∂y ∂yH∂y H H H g!=+— ρ u’ v’ − ρ’ v’ u − ρ’ u’ v’+ F . (37)Rewriting Eq. (28) to incorporate Eqs. (29) and (30), we obtainConsequently, we extract five components that comprise the shear stress profile inside the turbidity current as follows:∂ρHun T 2 }∂μHuτ = (viscous shear stress), (38)∂t + ∇ · ρHuu = −∇ p + ∇ · μH∇u+ (∇u)— 3 (∇ · u)+ρHg.(31)1τ2 =∂y∂μrH ur, (39)For an incompressible divergence-free fluid velocity vector field, Eq. (31) can be further simplified as∂ρ u∂yτ3 = −ρHur vr (Reynolds shear stress), (40)H 2∂t + ∇ · ρHuu = −∇ p + ∇ (μHu) + ρHg. (32)τ4 = −ρHr vr u, (41)
Fig. 12. Shear stress distributions computed from UVP measurements, dominated by the viscous shear stress τ 1 and Reynolds shear stress τ 3. The symbols for τ 2, τ 4, and τ 5 overlap; the values of these parameters are less than 1% of the wall shear stress. Error bars are estimated from the spatial resolution of UVP. Error bars indicate the 95% confidence interval of the sample mean for measured local stress.τ5 = —ρHr ur vr . (42)Note that the term Fg in Eq. (37) is negligible, because the current is driven by a horizontal pressure gradient caused by differences in hydrostatic pressure between the far upstream and far downstream parts of the body region.
- Shear Stress CharacteristicsThe computed results of the five components of shear stress are shown in Fig. 12. The ordinate denotes the height from the bed normalized by ht and the abscissa plots the shear stress normal- ized by the wall shear stress τ W. The wall shear stress is computed from the formula for friction velocity u∗:2τW = ρHu∗ . (43)The estimated wall shear stress τ W is 0.086 Pa. The broken line in Fig. 12 indicates the position of hm/ht = 0.28, which sep- arates the lower and upper shear layers of the turbidity current. The results demonstrate that the viscous shear stress τ 1 and the Reynolds shear stress τ 3 govern the whole structure. Furthermore, these two parameters take opposite values above hm, implying balancing of the shear stress in the upper shear layer. In thelower layer, only the viscous shear stress τ 1 dominates, exceptnear the flume bottom. This indicates significant suppression ofFig. 13. Distribution of the sum of five shear stress components, showing signifi- cant shear stress relaxation in the upper layer at y > hm . Error bars indicate the 95% confidence interval the same as in Fig. 12.The total shear stress profile calculated by taking the sum of the five stress values is depicted in Fig. 13. Due to the mutual bal- ancing of τ 1 and τ 3, the shear stress disappears in the range 0.3< y/ht < 0.8. The friction characteristics are mostly determined by the lowest layer of the current at y/ht < 0.2, which balances the streamwise pressure gradient.A small negative total stress may be present close to the bor- der of the current at y/ht > 0.8, where we observed slow density propagation against the main stream due to a counter flow. This negative total stress is derived from an effect of the counter flow induced in the finite flume used in our experiments, and is not discussed further in this paper.A key finding from the present study is the fact that the layer at0.3 < y / ht < 0.8 induces a positive Reynolds shear stress against the negative mean velocity gradient. This result is consistent with the observations of Kneller et al. (1999). This effect means that negative momentum transfer can occur in a density-stratified medium; i.e. density increases with depth in the fluid with shear (Kneller et al., 2016; Sequeiros et al., 2010). In thermal stratifica- tion of single-phase flow, Komori et al. (1983), Piccirillo and van Atta (1997), and Nagata and Komori (2001) found similar nega- tive momentum transfer. According to Komori et al. (1983), such an inverse-gradient diffusion can be explained by a density wave overshadowing shear-induced waves at a frequency lower thanWfr =·H —ht' 1.25Hz. (44), g ρ ρ ρWthe Reynolds shear stress τ 3, which is attributed to relaminariza-tion caused by a high density of particles smaller than one-tenth of the estimated integral scale of turbulence (Gore and Crowe, 1989; Crowe et al., 1996). Cossu and Wells (2012) also found relaxation of Reynolds shear stress in the lower layer as a result of parti- cles. Their particles were 30 μm in mean diameter, whereas ours are 10 μm diameter. This size difference reduced the particle set- tling velocity in our experiments to (10/30)2 = 1/9 times thatHere, fr = 1.25 Hz is the estimated frequency under the present conditions. As most of the turbulence scales in our case satisfy fr< 1.25 Hz (see v-component in Fig. 6), analogy to the turbulence in thermal stratification is inferred. In shear flows, the following Richardson number describes the stability of the density stratifica- tion:Ri = g ∂ρ/∂y ' ∆ρ g(ht — hm ) = 0.008 9.8 · 0.035of Cossu and Wells (2012), resulting in further effective relami-narization in our experiments. In contrast, the rest of the stressρW (∂u/∂y)2 ρWum 20.082terms, τ2, τ4, and τ5, are almost zero, meaning that the turbidity= 0.6 ~ O(1) (45)current is less affected by coupling of velocity fluctuation with lo- cal fluid properties; i.e., density and effective viscosity fluctuations (μrH and ρrH ).In the present experiment, Ri takes O(1) in the upper shear layer, meaning that Richardson waves interact with tur- bulent shear. A similar conclusion was obtained by Stacey and
Fig. 14. Schematic diagram of the flow structure inferred from the present experimental results.
Bowen (1988), Kneller et al. (1997), and Sequeiros et al. (2010) for density destratification caused by shear. Dorrell et al. (2019) found the emergence of an anti-frictional layer that sharpened a gravity current. In their explanation based on a real long-distance current measured on the sea floor, the density gradient enhanced nega- tive turbulent momentum transfer to form a jet-like stream as the flow moved downstream. Our flume experiment yielded analogous results to that study at a point in a slowly developing turbidity current.A summary of the present findings for the body region is il- lustrated in Fig. 14. According to the simultaneous measurement of flow velocity and particle concentration profiles, the body re- gion consists of four layers: the near-bed layer, the lower shear layer, the upper shear layer, and the outer region. In the near- bed layer, there is a high particle concentration with spatial fluc- tuations, which acts as a rough wall. This roughness induces lo- cal Reynolds shear stress to have a turbulent frictional stress on the wall. The lower layer, which is between the near-bed layer and the maximum flow velocity height, maintains a laminar-like quasi- steady state with relatively minor turbulence. This behavior is at- tributed to relaminarization of turbulence caused by the particles being much smaller than the integral scale of turbulence. In the upper shear layer, Reynolds shear stress takes the opposite sign to the viscous shear stress, canceling out the total shear stress. This result could be explained by the excitation of a Richardson wave in the vertical density gradient field with shear because the ellip- tic fluid motion of the wave enhances backward momentum trans- fer from lower- to higher-velocity regions (counter-clockwise rota- tion in Fig. 14). Dorrell et al. (2019) suggested an analogous mecha- nism for a turbidity current in nature, and this proposal is verified by the shear stress profiles obtained from the present laboratory flume experiments.
- Front Advection VelocityImages extracted every 1.5 s from 16.5 s after opening of thegate are shown in Fig. 4. The movie was taken with a digital cam-where Vamp is the amplified echo signal, and ηs and ηe are theminimum and maximum measurable distance from the transducer, respectively. The detailed characteristics of amplification by UVP Duo are summarized in Table 2.era (Nikon D5500) from the side window of the flume at 20 frames per second. The shooting area is around xI in Fig. 1. The frame rate was purposely set to be the same as the profile sampling rate of the UVP (temporal resolution 50 ms).
Conclusions
Turbidity currents reproduced in a laboratory flume were visu- alized by means of UVP that was extended to capture 2D velocity and particle concentration profiles. Subsequently, we focused on the inner flow structures of the body of the current, in which the mechanism of reduced flow resistance was revealed. On the basis of the results, we obtained the following conclusions.
- We successfully explored the internal two-phase flow struc- ture of the optically inaccessible turbidity current by means of UVP. The use of two measurement lines for ultrasound Doppler signals enabled simultaneous measurement of both horizontal and vertical velocity components. Ultrasound echo amplitude was used to detect the particle concentration as a function of time together with velocity measurement. The combined infor- mation for all three components was used to reconstruct thetwo-phase flow field of the current. In the head region, we ob- served a rapid ascending flow that lifted up the particle-laden suspension supplied from the bottom layer. In the main body region, the current could be divided into layers on the basis of the measured velocity and concentration distribution. The par- ticle concentration exhibited steep stratification in the bottom layer, stepwise stratification in the upper shear layer, and con- vergence to zero in the outer layer.
- From two-fluid model equations for particulate two-phase flows, five kinds of two-phase turbulent shear stress were ex- tracted. Substituting the data obtained by UVP, the internal flow resistance inside the body region was quantitatively assessed. We detected two features of the current from the analysis. One feature is negative momentum transfer against the mean shear that is induced in the upper shear layer and associated with a Richardson wave; i.e., the shear rate and the density wave inter- act to enhance the sharpening of the flow velocity profile. This result supports the mechanism observed in nature reported by Dorrell et al. (2019). The other feature is suppression of turbu- lence in the lower shear layer, where only viscous stress dom- inates the flow resistance except in the near-bed layer that is influenced by particle deposition. Both features explain the re- duction of flow resistance within the body region of the turbid- ity current that is maintained downstream.
Author statement
Jumpei Hitomi: Conceptualization, Methodology, Investigation, Writing- Original draft preparation
Shun Nomura: Conceptualization, Methodology, Investigation, Data curation, Writing- Original draft preparation, Writing- Reviewing and Editing
Yuichi Murai: Visualization, Investigation, Writing- Original draft preparation, Writing- Reviewing and Editing
Giovanni De Cesare: Conceptualization, Methodology, English proofreading, Supervision
Yuji Tasaka: Data analysis, Visualization, Writing- Original draft preparation, Writing- Reviewing and Editing.
Yasushi Takeda: Conceptualization, Supervision
Hyun Jin Park: Data analysis, Visualization, Writing- Original draft preparation, Writing- Reviewing and Editing.
Hide Sakaguchi: Conceptualization, Supervision
Declaration of Competing Interest
The authors whose name are listed immediately below certify that they have NO affiliations with or involvement in any organiza- tion or entity with any financial interest (such as honoraria; educa- tional grants; participation in speakers’ bureaus; membership, em- ployment, consultancies, stock ownership, or other equity interest;
and expert testimony or patent-licensing arrangements), or non- financial interest (such as personal or professional relationships, af- filiations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.
Acknowledgments
The authors thank Dr. S. Chamoun for her support and helpful comments. This work was supported by the JAMSTEC Researcher Overseas Dispatch Budget and a Grant-in-Aid for Young Scientists [grant number 15K18115] from the Japan Society for the Promotion of Science.
References
Altinakar, M.S., Graf, W.H., Hopfinger, E.J., 1996. Flow structure in turbidity currents.
J. Hydrau Res. 34 (5), 713–718. doi:10.1080/00221689609498467.
Amy, L.A., Peakall, J., Talling, P.J., 2005. Density- and viscosity-stratified gravity cur- rents: Insight from laboratory experiments and implications for submarine flow deposits. Sediment Geol 179, 5–29. doi:10.1016/j.sedgeo.2005.04.009.
Azpiroz-Zabala, M., Cartigny, M.J., Talling, P.J., Parsons, D.R., Sumner, E.J., Clare, M.A., Simmons, S.N, Cooper, C., Pope, E.L., 2017. Newly recognized turbidity current structure can explain prolonged flushing of submarine canyons. Science ad- vances 3 (10), e1700200. doi:10.1126/sciadv.1700200.
Baas, J.H., McCaffrey, W.D., Haughton, P.D.W., Choux, C., 2005. Coupling between suspended sediment distribution and turbulence structure in a laboratory tur- bidity current. J. Geophys Res. 110, C11015. doi:10.1029/2004JC002668.
Bux, j., Paul, N., Hunter, T.N., Peakall, J., Dodds, J.M., Biggs, S., 2017. In situ character- ization of mixing and sedimentation dynamics in an impinging jet ballast tank via acoustic backscatter. AlChE J 63, 2618–2629. doi:10.1002/aic.15683.
Chamoun, S., De Cesare, G., Schleiss, A.J., 2016. Managing reservoir sedimentation by venting turbidity currents: A review. Int. J. Sediment Res. 31 (3), 195–204. doi:10.1016/j.ijsrc.2016.06.001.
Choux, C., Baas, J.H., McCaffrey, W.D., Haughton, P.D.W., 2005. Comparison of spatio– temporal evolution of experimental particulate gravity flows at two different initial concentrations, based on velocity, grain size and density data. Sediment Geol 179, 49–69. doi:10.1016/j.sedgeo.2005.04.010.
De Cesare, G., Schleiss, A.J., Hermann, F., 2001. Impact of turbidity currents on reservoir sedimentation. J. Hydrol. Eng. 127 (1), 6–16. doi:10.1061/(ASCE) 0733-9429(2001)127:1(6).
Dong, X., Tan, C., Yuan, Y., Dong, F., 2015. Oil–water two-phase flow velocity mea- surement with continuous wave ultrasound Doppler. Chem. Eng. Sci. 135, 155–
165. doi:10.1016/j.ces.2015.05.011.
Dorrell, R.M., Darby, S.E., Peakall, J., Sumner, E.J., Parsons, D.R., Wynn, R.B., 2014. The critical role of stratification in submarine channels: Implications for chan- nelization and long runout of flows. J. Geophys Res–Oceans. 119, 2620–2641. doi:10.1002/2014JC009807.
Dombroski, DE, Crimaldi, J.P., 2007. The accuracy of acoustic Doppler velocimetry measurements in turbulent boundary layer flows over a smooth bed. Methods 23–33. doi:10.4319/lom.2007.5.23.
Downing, A., Thorne, P.D., Vincent, C.E., 1995. Backscattering from a suspension in the near field of a piston transducer. J. Acous. Soc. Am. 97 (3), 1614–1620. doi:10.1121/1.412100.
Eggenhuisen, J.T., Tilston, M.C., Leeuw, J., Pohl, F., Cartigny, M.J.B., 2019. Turbulent diffusion modelling of sediment in turbidity currents: An experimental valida- tion of the Rouse approach. The Deposit Record 1–14. doi:10.1002/dep2.86.
Felix, M., Sturton, S., Peakall, J., 2005. Combined measurements of velocity and con- centration in experimental turbidity currents. Sedimentary Geology 179 (1–2), 31–47. doi:10.1016/j.sedgeo.2005.04.008.
Finelli, F., Hart, D.D., Fonseca, D.M., 1999. Evaluating the spatial resolution of an acoustic Doppler velocimeter and the consequences for measuring near-bed flows. Limnol. Oceanogr. Note 44 (7), 1793–1801. doi:10.4319/lo.1999.44.7.1793.
Fisher, F.H., Simmons, V.P., 1977. Sound absorption in sea water. J. Acous. Soc. Am.
62 (3), 558–564. doi:10.1121/1.381574.
Gladstone, C., Ritchie, L.J., Sparks, R.S.J., Woods, A.W., 2004. An experimental in- vestigation of density-stratified inertial gravity currents. Sedimentology 51 (4), 767–789. doi:10.1111/j.1365-3091.2004.00650.x.
Hitomi, J., Murai, Y., Park, H.J., Tasaka, Y., 2017. Ultrasound flow-monitoring and flow-metering of air-oil-water three-layer pipe flows. IEEE Access 5 (1), 15021–
15029. doi:10.1109/ACCESS.2017.2724300.
Hurther, D., Thorne, P.D., Bricault, M., Lemmin, U., Barnoud, J., 2011. A multi- frequency Acoustic Concentration and Velocity Profiler (ACVP) for boundary layer measurements of fine-scale flow and sediment transport processes. Coast Eng 58 (7), 594–605. doi:10.1016/j.coastaleng.2011.01.006.
Kneller, B.C., Bennett, S.J., McCaffrey, W.D., 1999. Velocity structure, turbulence and fluid stresses in experimental gravity currents. J. Geophys. Res-Oceans 104 (C3), 5381–5391. doi:10.1029/1998JC900077.
Kneller, B., Buckee, C., 2000. The structure and fluid mechanics of turbidity currents: a review of some recent studies and their geological implications. Sedimentol- ogy 47, 62–94. doi:10.1046/j.1365-3091.2000.047s1062.x.
Kneller, B., Nasr-Azadani, M.M., Radhakrishnan, S., Meiburg, E., 2016. Long-range sediment transport in the world’s oceans by stably stratified turbidity currents.
J. Geophys. Res. 121, 8608–8620. doi:10.1002/2016JC011978.
Lhermitte, R., Lemmin, U., 1994. Open-Channel Flow and Turbulence Measurement by High-Resolution Doppler Sonar. J. Atmos. Oceanic Technol. 11, 1295–1308. doi:10.1175/1520-0426(1994)0111295:OCFATM2.0.CO;2.
Luchi, R., Balachandar, S., Seminara, G., Parker, G., 2018. Turbidity currents with equilibrium basal driving layers: a mechanism for long runout. Geophys. Res. Lett. 45, 1518–1526. doi:10.1002/2017GL075608.
Meiburg, E., Kneller, B., 2010. Turbidity Currents and Their Deposits. Ann. Rev. Fluid Mech. 42, 135–156. doi:10.1146/annurev- fluid- 121108-145618.
Murai, Y., Matsumoto, Y., 2000. Numerical study of the three-dimensional structure of a bubble plume. J. Fluid. Eng. 122 (4), 754–760. doi:10.1115/1.1313245.
Murai, Y., Oishi, Y., Takeda, Y., Yamamoto, F., 2006. Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry. Exp. Fluids 41 (2), 343. doi:10.1007/s00348-006-0142-9.
Murai, Y., Tasaka, Y., Nambu, Y., Takeda, Y., 2010. Ultrasonic detection of moving interfaces in gas–liquid two-phase flow. Flow Meas. Instrum. 21 (3), 356–366. doi:10.1016/j.flowmeasinst.2010.03.007.
Murakawa, H., Kikura, H., Aritomi, M., 2008. Application of ultrasonic multi-wave method for two-phase bubbly and slug flows. Flow Meas. Instrum. 19 (3-4), 205–213. doi:10.1016/j.flowmeasinst.2007.06.010.
Nagata, K, Komori, S., 2001. The difference in turbulent diffusion between active and passive scalars in stable thermal stratification, J. Fluid Mech 430, 361–380. doi:10.1017/S0022112000003037.
Oehy, C.D., De Cesare, G., Schleiss, A.J., 2010. Effect of inclined jet screen on turbidity current. J. Hydraul. Res. 48 (1), 81–90. doi:10.1080/00221680903566042.
Oehy, C.D., Schleiss, A.J., 2007. Control of turbidity currents in reservoirs by solid and permeable obstacles. J. Hydraul.Eng. 133 (6), 637–648. doi:10.1061/(ASCE) 0733-9429(2007)133:6(637).
Pantin, H.M., 1979. Interaction between velocity and effective density in turbidity flow: phase-plane analysis, with criteria for autosuspension. Marine Geology 31 (1-2), 59–99. doi:10.1016/0025-3227(79)90057-4.
Pantin, H.M., Franklin, M.C., 2011. Improved experimental evidence for autosuspen- sion. Sedimentary Geology 237, 46–54. doi:10.1016/j.sedgeo.2011.02.002.
Parker, G., Fukushima, Y., Pantin, H.M., 1986. Self-accelerating turbidity currents. J. Fluid Mech 171, 145–181. doi:10.1017/S0022112086001404.
Peakall, J., McCaffrey, W.D., Kneller, B.C., 2000. A process model for the evolution, morphology and architecture of sinuous submarine channels. J. Sediment Res. 70, 434–448. doi:10.1306/2DC4091C-0E47-11D7-8643000102C1865D.
Pedocchi, F., García, M.H., 2012. Acoustic measurement of suspended sediment con- centration profiles in an oscillatory boundary layer. Cont. Shelf Res. 46, 87–95. doi:10.1016/j.csr.2011.05.013.
Rice, H.P., Fairweather, M., Hunter, T.N., Mahmoud, B., Biggs, S., Peakall, J., 2014. Measuring particle concentration in multiphase pipe flow using acoustic backscatter: generalization of the dual-frequency inversion method. J Acoust Soc Am 136 (1), 156–169. doi:10.1121/1.4883376.
Rice, H.P., Fairweather, M., Peakall, J., Hunter, T.N., Mahmoud, B., Biggs, S.R., 2015. Particle concentration measurement and flow regime identification in multi- phase pipe flow using a generalised dual-frequency inversion method. Procedia Eng. 102, 986–995. doi:10.1016/j.proeng.2015.01.221.
Samothrakis, P., Cotel, A.J., 2006. Finite volume gravity currents impinging on a stratified interface. Exp. Fluids 41, 911–1003. doi:10.1007/s00348-006-0222-x.
Schleiss, A.J., Franca, M.J., Jiménez, C.J., De Cesare, G., 2016. Reservoir sedimentation.
J. Hydraul. Res. 54 (6), 314–595. doi:10.1080/00221686.2016.1225320.
Sequeiros, O.E., Spinewine, B., Beaubouef, R.T., Sun, T., García, M.H., Parker, G., 2010. Characteristics of Velocity and Excess Density Profiles of Saline Underflows and Turbidity Currents Flowing over a Mobile Bed. Journal of Hydraulic Engineering 136, 412–433. doi:10.1061/(ASCE)HY.1943-7900.0000200.
Shi, X., Tan, C., Dong, F., Murai, Y., 2019. Oil-gas-water three-phase flow characteri- zation and velocity measurement based on time-frequency decomposition. Int.
J. Multiphas. Flow 111, 219–231. doi:10.1016/j.ijmultiphaseflow.2018.11.006. Simmons, S.M., Azpiroz-Zabala, M., Cartigny, M.J.B., Clare, M.A., Cooper, C., Par-
sons, D.R., Pope, E.L., Sumner, E.J., Talling, P.J., 2020. Novel acoustic method pro- vides first detailed measurements of sediment concentration structure within submarine turbidity currents. J Geophys Res-Oceans doi:10.1029/2019jc015904, e2019JC015904.
Su, Q., Chao, T., Feng, D., 2017. Mechanism modeling for phase fraction measurement with ultrasound attenuation in oil–water two-phase flow. Meas. Sci. Tech. 28 (3), 035304. doi:10.1088/1361-6501/aa58dc.
Takeda, Y., 1995. Velocity profile measurement by ultrasonic Doppler method. Exp.
Therm. Fluid Sci. 10 (4), 444–453. doi:10.1016/0894-1777(94)00124-Q.
Theiler, Q., Franca, M.J., 2016. Contained density currents with high volume of re- lease. Sedimentology 63 (6), 1820–1842. doi:10.1111/sed.12295.
Thomas, L.P., Dalziel, S.B., Marino, B.M., 2003. The structure of the head of an iner- tial gravity current determined by particle-tracking velocimetry. Experiments in Fluids 34, 708716. doi:10.1007/s00348-003-0611-3.
Xu, J., Swarzenski, P., Noble, M., Li, A.C., 2010. Event-driven sediment flux in Huen- eme and Mugu submarine canyons, southern California. Marine Geology 269, 74–88. doi:10.1016/j.margeo.2009.12.007.
Xu, J., 2010. Normalized velocity profiles of field-measured turbidity currents. Geol- ogy 38 (6), 563–566. doi:10.1130/G30582.