Experimental Study of Tsunami-Like Waves Generated with a Vertical Release Technique on Dry and Wet Beds

Experimental Study of Tsunami-Like Waves Generated with a Vertical Release Technique on Dry and Wet Beds

Davide Wüthrich1; Michael Pfister2; Ioan Nistor, M.ASCE3; and Anton J. Schleiss, M.ASCE4

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Abstract: Tsunamis, impulse waves, and dam failures are disasters that challenge humanity, often leading to massive casualties and extreme economic losses. The highly unsteady flow conditions generated by such events are often in the form of turbulent bores. The pur- pose of this study was to investigate and validate a new generation system for bores propagating over dry and wet bed conditions. There are multiple techniques to generate such waves experimentally, and the study focused on the generation of tsunami-like inundation condi- tions through the vertical release of a water volume. A detailed methodology to characterize the generated waves hydraulically, in terms of their wave heights and flow velocities, is presented, and good agreement with the classical dam-break case for both dry bed surges and wet bed bores was demonstrated. Because of the importance of estimating the impact forces induced by such waves, particular attention was given to the wavefront celerity and the velocity profiles measured behind the wavefront; these were found in agreement with Prandtl’s power law for open channel flows, and in-depth measurements allowed for the definition of an expression to estimate flow decel- eration behind the wavefront. Along with considerations of the Froude number and momentum, this paper provides relevant information to assist engineers in designing safer infrastructures in areas prone to such extreme loading. DOI: 10.1061/(ASCE)WW.1943- 5460.0000447. © 2018 American Society of Civil Engineers.

Author keywords: Dam break; Tsunami; Dry bed surge; Wet bed bore; Velocity profiles; Momentum.

Introduction

Relevance

Tsunamis, impulse waves, and dam-break waves are rare phenom- ena. Therefore, visual observations of prototype events are rare and often difficult to assess during their occurrence. Nevertheless, some recent episodes, such as the 2004 Indian Ocean tsunami and the 2011 Tōhoku tsunami in Japan, allowed for the comparison of theo- retical solutions with posttsunami data collected through postevent field surveys and forensic engineering surveys (Chanson 2006; Chock et al. 2013). Most of the recent studies focused on the tsu- nami inundation depths and velocities (Dias et al. 2006; Matsutomi et al. 2006; Rossetto et al. 2007; Fritz et al. 2012; Jaffe et al. 2012) and showed a wide range of magnitudes, with maximum velocities

1Doctoral Student, Laboratory of Hydraulic Constructions (LCH), School of Architecture, Civil and Environment Engineering (ENAC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Station 18, 1015 Lausanne, Switzerland (corresponding author). E-mail: davide.wuthrich@ epfl.ch

2Professor, Civil Engineering Dept., Haute Ecole d'Ing´enierie et d'Architecture de Fribourg (HEIA-FR, HES-SO), 1700 Fribourg, Switzerland. E-mail: michael.pfister@hefr.ch

3Professor, Dept. of Civil Engineering, Univ. of Ottawa, 161 Louis- Pasteur, A110, Ottawa, ON, Canada K1N 6N5. E-mail: inistor@ uottawa.ca

4Professor, Laboratory of Hydraulic Constructions (LCH), School of Architecture, Civil and Environment Engineering (ENAC), Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Station 18, 1015 Lausanne, Switzerland. E-mail: anton.schleiss@epfl.ch

Note. This manuscript was submitted on March 21, 2017; approved on December 11, 2017; published online on April 23, 2018. Discussion pe- riod open until September 23, 2018; separate discussions must be submit- ted for individual papers. This paper is part of the Journal of Waterway, Port, Coastal, and Ocean Engineering, © ASCE, ISSN 0733-950X.

up to 13 m/s near the Sendai Airport (Jaffe et al. 2012) and inunda- tion depths of more than 15 m in the City of Onagawa (Suppasri et al. 2013).

In mountain areas, landslide-induced waves are characterized by short wavelengths and great impulsiveness. Such was the case of the Vajont Dam (Italy) event, where a landslide into the reservoir generated a sudden overflow of the dam crest by a wave as high as 245 m (Kilburna and Petleyb 2003). The released discharge fell into the narrow downstream valley, resulting in a massive wave that caused the death of more than 2,000 people, leaving the dam almost undamaged, as shown in Fig. 1.

In addition, storm surges, tidal bores, or collapse of artificial and natural dams or dikes can generate flows with similarly drastic con- sequences. The diversity and heterogeneity are reflected in the sev- eral generation techniques used to reproduce these flows in a labora- tory environment, including wave pistons, landslide generators, pump-driven generators, vertical releases, and dam-break gates (vertical lift or swing type).

In this study, a controlled vertical release technique was used such that a water volume dropped from an upper reservoir into a lower one resulted in the formation of a turbulent bore. Similar tech- niques were previously used by Chanson et al. (2002, 2003), Meile (2007), and Meile et al. (2008, 2011). The main advantage of the vertical release technique used in the present study was its flexibility in controlling both the volume and the released discharge, allowing for reproduction of surges and bores with different flow depths and propagation velocities.

Independently of the generating mechanism, the main hydrody- namic properties of the propagating bore and surge were affected by the dry or wet bed conditions of the channel. The difference in behavior between dry and wet surfaces was shown experimentally by Lauber and Hager (1998), Ramsden (1993), and Nouri et al. (2010), among others. A wave propagating on a dry bed is com- monly called a surge; whereas, because of its turbulent and an aer- ated appearance, a wave on a wet bed is termed a bore. An example

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‌Fig. 1. Vajont Dam located in northwest Italy, 53 years after the impulse wave which occurred in October 1963. (Image by Davide Wüthrich, September 2016.)‌

in nature of this difference can be observed in Fig. 2, which shows the case of a tidal bore propagating upstream in the Garonne River in France on both dry and wet bed conditions.

Long-Wave Generation Techniques

Various techniques can be used to reproduce surges and bores in models. A comprehensive literature review of these techniques was presented by Liu et al. (2008). Previous experimental studies used mostly solitary waves to reproduce tsunami and impulse waves; these were obtained through piston-type wave generators. The use of solitary waves was criticized by Madsen et al. (2008) because of the short wavelength and period compared with real tsunami waves. The transition between solitary waves and overland flow was addressed by Fuchs and Hager (2015).

Currently, the use of dam-break waves generated through the

sudden release of water impounded behind a vertical wall is con- sidered a more appropriate method to reproduce the inundation generated by tsunamis and impulse waves (Chanson 2005, 2006). The dam-break technique was used by several authors, including Cross (1967), Yeh et al. (1989), Arnason et al. (2009), Nistor et al. (2009), and O'Donoghue et al. (2010), among others. The sudden opening can be achieved through vertical lift gates (Lauber and Hager 1998) or swing gates (Goseberg et al. 2017). This approach was based on the theory of Ritter (1892), and it assumed a semifinite reservoir, ideal fluid conditions, and a wave propagating on a smooth horizontal channel. At the tip of the wave, friction became nonnegligible (Chanson 2005), and a modified dam-break theory was developed by Whitham (1955) and Chanson (2009).

Landslide-generated waves were often reproduced through the

sudden drop of a solid, granular, or liquid body into the water, producing a wave traveling away from the generation location. This technique was particularly suitable to reproduce impulse

Fig. 2. Tidal bore at Podensac (France) on the Garonne River. The pic- ture shows an example of the difference in behavior for a bore propagat- ing over dry bed (left side, over the bank) and over wet bed (right side, near the surfer). (Image by Davide Wüthrich, October 2015.)

waves. A landslide generator can function either manually, by dropping a solid block inside the water (Thusyanthan and Madabhushi 2008), or with a more sophisticated mechanism, such as a pneumatic landslide generator (Fritz 2002). The drop of a granular body inside the reservoir was previously used by Huber (1980), Fritz (2002), and Heller (2007), among others. Goseberg et al. (2013) introduced the concept of a pump-driven long-wave generation technique as an alternative approach to generate long-period waves in the laboratory. Furthermore, posi- tive surges and bores in rivers and artificial channels can be repro- duced through the sudden closure of a downstream gate (Koch and Chanson 2009; Leng and Chanson 2017b).

A vertical release through the sudden drop of a volume of water was also used to generate tsunami-like waves (Chanson et al. 2002, 2003; Meile 2007; Rossetto et al. 2011). At present, some of the newest large-scale facilities apply a similar concept to reproduce controlled long-period waves using pneumatic tsunami simulators (Allsop et al. 2014; Chandler et al. 2016).

Objective, Novelty of the Study, and Outline

The main objectives of this research were as follows:

• To present and discuss the hydraulic behavior of dry bed surges and wet bed bores generated using the vertical release technique;
• To compare the generated surges and bores with existing theo- ries developed for classical dam-break waves;
• To provide insights on the hydrodynamic behaviors of surges and bores in terms of front celerity, velocity profiles, and deceleration behind the wavefront; and
• To present and discuss the temporal behavior of the Froude number and the momentum flux per unit width for both surges and bores.

The outline of the paper is as follows: After an explanation of the wave-generation technique and instrumentation used, tests performed and the methodology followed throughout the study are described. The next section focuses on the longitudinal pro- files of the produced waves before the explanations of the veloc- ities, Froude number, and momentum flux. The “Discussion” and “Conclusions” sections describe the key findings of this study.

Experimental Setup and Acquisition System

Tests were performed at the Laboratory of Hydraulic Constructions (LCH) at Ecole Polytechnique F´ed´erale de Lausanne (EPFL) in Switzerland. A vertical release technique was used to generate surges propagating over a dry bed and bores propagating over a wet bed. This experimental facility implemented the setup previously used by Meile (2007) and Meile et al. (2008, 2011). Compared to the previous studies cited, the released discharge was higher for this study, and a new downstream channel was built; nevertheless, the upstream and downstream reservoirs were the same as those in the previous work.

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Vertical Release Generation Technique

× ×

A 2.1 3.0 1.0-m upper reservoir with a total storage volume of 7.08 m3 was connected to a water-filled lower reservoir through three newly installed, identical, and independent PVC pipes, each with an internal diameter of 315 mm (Fig. 3). The pipes were symmetrical to the central axis of the channel with a transversal distance of 0.45 m between adjacent pipes [Fig. 3(a)]. Each pipe was independently fitted with a valve, and the sudden

water release was achieved through a system of pulleys and Vectran-fiber ropes with a diameter of 0.01 m and a maximum elastic extension of less than 1%. All ropes were connected to the same handle, thus ensuring a synchronized opening of all valves [Fig. 3(b)]. The release mechanism is shown in Fig. 3(b). The total difference in the head between the upstream and the down- stream reservoir, DH, was 2.1 m.

When the generation system was activated (i.e., the ropes were released and valves opened), a difference in the head between the upper and lower reservoir was established [Fig. 4(b)], resulting into a gravitational flow through the pipes. Since the lower basin was completely filled with water, the incoming discharge resulted in an upward flow at the channel inlet, and subsequently, a free-surface wave formed and propagated downstream in the flume. A schematic of the release mechanism and the resulting flow in the lower reser- voir is presented in Fig. 4. All waves propagated over a smooth hor- izontal channel with a length of 15.5 m and a width of 1.4 m. On average, the Darcy-Weisbach friction factor of the channel, f, was measured to be 0.021 using steady-state experiments under various flow conditions. This factor corresponded to an average roughness, ks of 0.66 mm, which was consistent with the values suggested by

‌Fig. 3. Experimental set-up and instrumentation used in the present study: (a) upper reservoir with pipes; (b) release mechanism and handle; (c) chan- nel (upstream view) (Images by Davide Wüthrich.)

‌CLOSED

Lower basin

Upper reservoir

H0

OPEN

Upper reservoir

Lower basin

H0

H

Upper reservoir

OPEN

U

Lower basin

T < 0 T = 0 T > 0

Fig. 4. Release mechanism and flow behavior before (T < 0), during (T = 0), and after (T > 0) the opening of the gates

Henderson (1966). The water was evacuated at the downstream end of the flume, thus avoiding any backwater effect. For the generation of wet bed bores, an initial still water depth, h0, on the flume (wet bed condition) was ensured using a vertical sill located at the down- stream end of the channel.

Instrumentation and Acquisition System

The flow depth of the propagating waves was measured using seven ultrasonic distance sensors (USs), type UNAM 30I6103 from Baumer (Frauenfeld, Switzerland), with a measuring range between 100 and 1,000 mm. The USs were located along the channel at x of 2, 10.10, 12.10, 13.10, 13.35, 13.60, and 13.85 m from the flume inlet (Fig. 3), which was the origin of the system of coordinates, and sampled at an acquisition frequency of

12.5 Hz with an accuracy of 0.5 mm and a response time of less than 80 ms. The arrangement of sensors from US4 to US7 was chosen to ensure a higher measurement density between x of 13.1 and 13.85 m, thus providing a more precise description of the shape of the propagating wave. The minimal required distance between two adjacent sensors to avoid interference was conserva- tively respected. An additional sensor (US0) from the Baumer UNAM 50 series with an extended measuring range (250– 4,000 mm) was installed in the upper reservoir to ensure the accu- rate recording of the opening time of the system (t = 0 s). For all tests, the opening time was selected when a decrease of 0.01 m was observed in the upper reservoir. A shifted time based on the surge or bore arrival time was defined as T = t – t0.

Flow velocities were investigated using an ultrasound velocity profiler (UVP-DUO) produced by Met-Flow (Lausanne, Switzerland); this instrument provided instantaneous flow velocity profiles along the transducer axis by detecting the Doppler shift frequency of echoed ultrasound as a function of time. The chosen transducer had an emitting frequency of 2 MHz, was installed within the channel bottom pointing in the upstream direction with an incli-

acquisition frequencies ranging between 12.5 and 55 Hz, correspond- ing to measurement durations of 80–18 ms and to an accuracy of approximately 10 mm/s throughout the entire water column. The acoustic scattering was enhanced by means of a hydrogen-bubble- generation technique similarly to Blanckaert and Lemmin (2006) and Meile et al. (2008). The hydrogen bubbles were produced through electrolysis at a distance of 1.5 m from the channel inlet, to ensure sufficient mixing for a uniform distribution in the vertical direction. High speed photos and videos were used to record the time and spa- tial development of the waves.

+

All data were acquired by means of the LabVIEW data-acquisition system. All USs were directly connected to the LabVIEW master pro- gram, and the synchronization with the UVP-DUO unit was achieved through a transistor-transistor logic (TTL)–level ( 5 V, minimum 20 ns) trigger signal, sent when the measure was launched from the main panel. This synchronization time was estimated to be less than 3 ms, which is short compared to the measurement duration of both instruments. This method allowed for the same time reference to be initially set for both instruments, ensuring that every velocity profile was associated to the corresponding flow depth.

Analogy with Dam-Break Waves

‌Preliminary tests showed the key role of the initial discharge, Q0, released into the channel for the definition of the main hydrody- namic properties of the produced wave. The use of 1, 2, or 3 pipes, denoted as n, for the sudden release of water allowed for the control of the initial discharge Q0, producing surges and bores with differ- ent values of wave height, h, and front celerity, U. A comparison with the theoretical solution proposed by Ritter (1892) for dam- break waves was conducted. Similar to what was discussed by Chanson et al. (2002), through the initial discharge Q0, an equiva- lent impoundment depth, d0, was obtained as

9 Q2 !1/3

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nation of 20° with respect to the vertical, and was located at a hor- izontal distance, x, of 13.85 m from the channel inlet (Fig. 3). One UVP per cross section was used, and measurements were taken in

d0 = 4

  0  

gB2

(1)

the transducer axis direction, then projected in the main flow direction (x-axis). Velocity components in the vertical and transver- sal directions were not considered. A sensitivity analysis of the main parameters involved in the UVP acquisition system was performed by Wüthrich et al. (2016a). As a result, the number of repetitions per profile (within the same measure) was selected as 128, leading to

where g = gravity constant; B = channel width; and Q0 = initial dis- charge released into the channel. From Eq. (1), d0 was calculated as the outflow discharge from the upper reservoir, obtained as a func- tion of dH/dt, where H is the water depth measured by US0 (Fig. 4). The graphs obtained for all three scenarios (one, two, and three pipes) are shown in Fig. 5(a) and the computed values of Q0 are

‌1.2‌

1.0

0.8

H/H0

0.6

0.4

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0.2

0.7

d0 = 0.40 m d0 = 0.63 m d0 = 0.82 m

Q0 (d0 = 0.40 m) Q0 (d0 = 0.63 m) Q0 (d0 = 0.82 m) H/H0 = 0.20

T*

h/d0 = 4/9

1 Pipe - d0 = 0.40 m

1. Pipes - d0 = 0.63 m
2. Pipes - d0 = 0.82 m

0.6

0.5

h/d0

0.4

0.3

0.2

0.1

0.0

-10 10 30 50 70 90 110

t·(g/d0)0.5

(a) (b)

0

-10 10 30 50 70 90 110

(t-t0)·(g/d0)0.5

Fig. 5. Measurements of the water depth for three dry bed surges generated with the vertical release technique using one, two, and three pipes in Tests 3, 2, and 1, respectively: (a) upstream reservoir; (b) channel inlet (x = 0 m) (Note: the values of the released discharges are presented in Table 1)

Table 1. Equivalent Impoundment Depths Obtained for the Vertical Release Technique through the Progressive Use of One, Two, and Three Pipes

= pffiffiffiffiffi(ffiffiffiffiffiffiffiffiffiffi—ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi)ffi

presented in Table 1. Given the nonlinear behavior of the reservoir- emptying process, the chosen values showed good agreement dur- ing the initial time, leading to some error in the later phases of the test. Thus, T* was defined as the dimensionless time after which the hypothesis of a continuously released discharge was no longer ac- ceptable (H/H0 = 0.2). These initial discharges were also success- fully compared with the theoretical values using the continuity equation Q0 = AP · VP, where AP is the pipe surface and VP is the

= · pffiffiffiffiffiffiffiffiffiffiffiffi

velocity through the pipes, VP 2g DH j DH . The head loss at the inlet of the pipes, j , was assumed to be 0.5. If the friction losses through the PVC pipes and those in the trajectory between the pipes and the channel inlet are neglected, then the initial dis-

charge is Q0 AP 2gDH (Table 1).

For a constant volume in the upper reservoir, a smaller released discharge allowed for a longer time before the sudden reduction took place, resulting in waves with a longer duration. Higher dis- charges were associated with shorter durations, and the generated waves were characterized by an impulse behavior.

Measurements of the water depth at the channel inlet (x =0 m) were made to validate the comparison to the theory of Ritter (1892). The use of an additional US at x = 0 m allowed for the cap- ture of the oscillating behavior of the flow around a h/d0 value of 4/9, as shown in Fig. 5, for the scenarios with one, two, and three pipes. These findings are similar to what was predicted by Ritter (1892) for an infinite reservoir, implying close similarity between surges and bores produced with the classical dam-break and with the vertical release techniques. Fig. 5(b) shows that, after a certain time, the measured flow depth in the channel suddenly decreased as a consequence of the emptying of the upstream reservoir [Fig. 5(a)].

Experimental Methodology

The purpose of this study was to characterize the generation and propagation of experimentally generated bores and surges in terms of depth and velocity. The main experimental parameters varied were the initial discharge Q0 (the equivalent impoundment depth d0) and the initial still water depth h0. Thirty-eight tests were conducted in this study, as listed in Table 2. For the wet bed bores, all tests were performed for values of h0/d0 less than 0.13, implying that the influence of the initial still water depth, h0, was minimal.

The Reynolds number was defined as R = Vm·DH/ , where Vm is the depth-averaged profile velocity (“Velocity Profiles” section) and DH is the hydraulic diameter. Values of 105 < R < 106 were obtained for all waves, which implied that a sufficient level of turbu- lence was ensured for both surges and bores, thus minimizing scale

effects (Pfister and Chanson 2012). Similar results were presented by Wüthrich et al. (2016b).

The time origin was set as the opening time of the pipes, identi- fied when a reduction in water elevation in the upper reservoir was measured. The wave arrival time at a specific location was set when a local wave height, h, greater than 0.01 m was recorded.

The repeatability of both surges and bores was investigated, and the representative results of the wave heights are presented in Fig. 6. For both wet and dry bed scenarios, the flow depth was meas- ured at US7, which was located 13.85 m from the channel inlet. Wave profiles were normalized using the impoundment depth, d0,

·( )

and the dimensionless time, T g/d0 0.5. Results showed similar profiles for all tests, with values of normalized standard deviation,

s/d0, of less than 5% for wet bed bores and less than 3% for dry bed

‌Table 2. Experimental Program and Characteristics of the Performed Tests

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pgffiffiffihffiffiffi0ffi

repetitions

Dry bed surge Min/Max (surge)

Wet bed bore (h0 = 0.05 m) Min/Max (bore)

‌0.40

0.35

0.30

0.25

h/d0

0.20

0.15

0.10

0.05

0.00

-5 0 5 10 15 20 25 30 35

T · (g/d0)0.5

Fig. 6. Repeatability for dry bed surges (three pipes, d0 = 0.82 m, Test 1, eight repetitions) and wet bed bores with three pipes, (three pipes, d0 = 0.82 m, h0 = 0.05 m, Test 11, five repetitions) measured at x of 13.85 m (US7)

surges. These results are similar to those of Shafiei et al. (2016) for bores. Some differences were observed in terms of surface turbu- lence; however, oscillations remained within the same range, and the spectral distribution of oscillating frequencies was similar for all tests (Wüthrich et al. 2016b).

The bidimensionality of both bores and surges was validated by measuring the wave profiles at two locations in the transversal axis of the channel at the same distance, x, of 13.60 m from the channel inlet (not shown). Fig. 7 presents a visual impression of the bidi- mensionality for both surges and bores.

Water Surface Profiles

The main characteristics of dry bed surges and wet bed bores pro- duced with the vertical release technique are discussed in this sec- tion. For both surges and bores, water surface profiles were meas- ured using seven USs located along the longitudinal axis of the channel (Fig. 3). The synchronization of the acquisition system allowed for the combination of all data and for the obtainment of

a spatial-temporal evolution of the depth profile. In the following sections, the surges and bores generated with the vertical release technique are described and compared to the dam-break waves propagating on dry and wed beds in light of some of the relevant literature.

Dry Bed Surges

The propagation of the surge on the dry smooth channel visually appeared as a thin water layer followed by a continuous rise in water depth until a maximum value was reached. Subsequently, the water level started to decrease. The surge front propagated uniformly, and visually, little to no aeration was observed, as shown in Fig. 7.

The temporal development of the height of a specific surge (d0 = 0.82, Test 1) propagating over a dry bed with a flat, smooth surface is presented in nondimensional form in Fig. 8. Each curve corre- sponds to a measurement location, with US7 located farthest down- stream (Fig. 3). A decrease in the maximum depth was observed as the surge propagated along the channel. This decrease was

attributed to the viscous and diffusive behaviors of the flow. The similarity of the profiles farther downstream in the channel (x > 10 m) indicated that the surge was fully developed and that a quasi-uniform condition was reached. The observed surface fluctua- tions were secondary waves attributed to the turbulence of the flow

(Wüthrich et al. 2016b). Some oscillations of the free surface due to the releasing mechanism were observed in the upstream section of

the channel at 0 < x < 2 m. However, they disappeared after the

US7), were obtained for multiple dry bed surges under identical ini- tial release conditions. The seven water depth measurement loca- tions along the channel (Fig. 3) allowed for the obtainment of multi- ple data sets that were compared with the theoretical parabolic profile from Ritter (1892) presented in Eq. (2). The experimental points are shown in Fig. 9 using the nondimensional streamwise dis- placement defined as x/[t · (gd0)0.5].

wave traveled a few meters farther downstream from the channel inlet.

The longitudinal water surface profiles, observed when the surge

h 1 2

= ·

d0 9

   x    2

(2)

— t · ,gffiffiffidffiffi0ffiffi

reached the locations, denoted as x, of 13.60 and 13.85 m (US6 and

‌Although some minor scattering was found in the upstream part of the surge due to water surface fluctuations, good agreement between all tests was observed. A marginal variation occurred in the tip region for scenarios with different d0 values because of the different propagating velocities.

Fig. 10 presents a focus on the tip region, where the higher den- sities of USs allowed for a more precise investigation of the tip shape. The experimental points obtained for multiple surges with different impoundment depths, denoted by d0, measured at various channel locations, were compared with the theoretical solutions of Whitham (1955) in

x — xs f U2

 g 2

∂U/∂t

d0 =— 8 · g · d0 ·

· ln 1

8   h/d0  · ∂U/∂t

8   h/d0  · ∂U/∂t

+ f · U2/(g · d0) g

+ f · U2/(g · d0)

g

(3)

where f = friction factor of 0.021; U = front celerity of 3.56 m/s for a d0 value of 0.82 m; and ∂U/∂t = 0.15 m/s2. The latter was calculated from the linear interpolation of the average velocity profiles obtained from the UVP measurements. Good agreement was also found with the theoretical solution of Chanson (2009) for the same

friction factor (f).

‌h sffifffiffiffiffiffi ffiffiffiffiffiffiffiUffiffiffiffiffiffiffiffi ffiffiffi2ffiffiffiffiffi ffiffiffiffixffiffiffi—ffiffiffiffiffixffiffisffiffi ffiffiffi

(4)

d0 = 4 · ,ffiffigffidffiffi0ffiffi · d0

Fig. 7. (a) Front of the surge propagating over dry bed (3 pipes, d0 = 0.82 m, Test 1); (b) wet bed bore (d0 = 0.82 m, h0 = 0.05 m, Test 11) with its turbulent front. (Images by Davide Wüthrich, May 2014.)

where xs = location of the front. The results are presented in Fig. 10, where good agreement between all data and curves was observed, indicating consistency with the literature. Furthermore, the experimental points were also compared to prototype points

US 1 - x = 2 m US 2 - x = 10.1 m US 3 - x = 12.1 m US 4 - x = 13.1 m

US 5 - x = 13.35 m US 6 - x = 13.6 m US 7 - x = 13.85 m

0.5

0.4

h / d0

0.3

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0.2

0.1

0 0 10 20 30 40 50 60

t · (g/d0)0.5

Fig. 8. Evolution of the surge on dry bed with d0 of 0.82 m for Test 1

Ritter (1892) d0 = 0.63m - x = 13.60m d0 = 0.82m - x = 13.85m d0 = 0.40m - x = 13.85m d0 = 0.82m - x = 13.60m d0 = 0.40m - x = 13.60m d0 = 0.63m - x = 13.85m

‌0.5

0.4

h/d0

0.3

0.2

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0.1

‌0

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

x/[t·(gd0)0.5]

Fig. 9. Longitudinal dimensionless water surface profiles when the wave reached two measurement locations, at x = 13.60 and 13.85 m for US6 and US7, respectively; comparison of all generated surges with d0 values of 0.82, 0.63, and 0.40 m with the theoretical solutions from Ritter (1892)

d0 = 0.82m - US7 Ritter (1892)

d0 = 0.82m - US6 Chanson (2009) d0 = 0.63m - US7 Whitham (1955) d0 = 0.63m - US6 Chanson (2006) d0 = 0.40m - US7

d0 = 0.40m - US6

0.175

0.150

0.125

h / d0

0.100

0.075

0.050

0.025

0.000

-3 -2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0

(x-xs) / d0

Fig. 10. Comparison of the measured longitudinal wave profiles with the theoretical solutions of Ritter (1892), Whitham (1955), Chanson (2009), and prototype data (Chanson 2006) in the wave-tip region where x was 13.85 and 13.60 m for US7 and US6, respectively

derived from a propagating tsunami-induced inundation advanc- ing inland during the 2004 Indian Ocean Tsunami (Chanson 2006). The good agreement observed in Fig. 10 indicates that the dry bed surges generated with the vertical release technique were representative of the overland flow of real tsunamis observed dur- ing such events.

Wet Bed Bores

The difference between dry bed surges and wet bed bores was evi- dent in Fig. 2. On visual appearance, the propagating bore was simi- lar to a turbulent and highly aerated hydraulic jump [Fig. 7(b)] with periodic surface fluctuations in the form of lumps being ejected and with significant air entrainment observed in the front region. Similar observations were described by Leng and Chanson (2015) for positive surges and tidal bores (Fig. 2). According to Yeh and Mok (1990), the front roller was formed by the flow separation initi- ated at the front toe resulting from the streamline divergence caused by the sudden raise in water depth. Furthermore, the same authors observed a generation-advection cycle, suggesting that the eddies formed inside the roller were later advected in the flow where

turbulence stretching in the slanting vertical direction was detected (Yeh and Mok 1990). Air was entrained behind the bore front for a length of Lr, where air bubbles could be observed, whereas farther behind, mainly clear water appeared.

The development of a wet bed bore propagating over a still water depth, h0, was investigated at different locations along the longitudinal axis of the channel, and the time-history of the water surface is presented in Fig. 11 for a specific case (d0 = 0.82 m, h0 = 0.05 m, Test 11). A substantial difference in behavior from dry bed surges was observed for bores because of a sudden rise in water height at the front. For all wet bed bores, a temporal conser- vation of maximum depth was observed during propagation along the channel. This conserved depth resulted in a uniform transla- tion of the bore shape.

The influence of the initial still water depth, h0, on the propagat- ing bore (Fig. 3) was investigated by testing different h0 values ranging between 0.001 and 0.1 m (Table 2), where the lower value represented a bore propagating over a thin water layer remaining from a previous test. Multiple impoundment depths, denoted by d0,

were tested, resulting in ratios of 0.0012 < h0/d0 < 0.1219 (Table 2). Similar to those of Chanson et al. (2003) and Nouri et al. (2010), the

US1 - x = 2m US2 - x = 10.1m US3 - x = 12.1m US4 - x = 13.1m

US5 - x = 13.35m US6 - x = 13.6m US7 - x = 13.85m

‌0.5

0.4

h/d0

0.3

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0.2

0.1

‌0 0 10 20 30 40 50 60

t · (g/d0)0.5

Fig. 11. Time evolution of a bore on wet bed (d0 = 0.82 m, h0 = 0.05 m, Test 11) at different locations along the longitudinal axis of the channel

h0 = 0.10 m h0 = 0.05 m h0 = 0.03 m

h0 = 0.01 m

h0 = 0.001 m

Dry

0.35

0.30

0.25

(h - h0)/d0

0.20

0.15

0.10

0.05

0.00

10 15 20 25 30 35 40 45 50

t · (g/d0)0.5

Fig. 12. Bore profiles for waves with different initial still water depths at x of 13.85 m (US7) for d0 of 0.82 m with all profiles brought down to (h–h0)/d0 for Tests 1, 4, 5, 8, 11, and 14

results showed that, even for a thin still water layer, the properties of the propagating bore were different from those of a dry bed surge. For still water heights greater than 0.03 m, similar profiles were measured, suggesting that beyond this value, h0 had less influence. For decreasing initial still water depths (h0 < 0.03 m), a transitional

bore, with behavior that became more similar to that of a dry bed

surge with milder front steepness, was observed (Fig. 12). The shift in arrival time revealed different bore front celerity magnitudes that depended on the initial still water depth, h0.

As previously discussed by Stoker (1958), the temporal evolu- tion of a dam-break bore propagating over a wet bed can be divided

into four main regions (downstream to upstream): (1) the turbulent

with those of Stoker (1958) for dam-break waves propagating over a wet bed with zero initial velocity in both the upstream and downstream reservoirs. The good agreement observed in Fig. 13 proves that, similar to previously shown surges, the vertical release technique produced bores that were comparable to those of the classical dam-break scenario. The height of the plateau region (h2, horizontal lines in Fig. 13) was predicted using the nu- merical approximation deduced from the continuity and momen- tum equations in Eq. (5) (Chanson et al. 2000) and compared to the experimental points in Fig. 14.

h2 h0 0.371

bore front; (2) a plateau, which is a region with almost constant water height, h2; (3) a far back region where the Ritter (1892) theory

d0 = 0.932 d0

(5)

+

for a surge propagating on a dry bed can be applied; and (4) the upstream reservoir where h is equal to d0. Fig. 13 presents, for all experimental tests, the longitudinal profiles of the water surface (ar- rival time was defined when a threshold of h = h0 0.01 m was reg- istered at US7, x = 13.85). These profiles were also successfully compared with those of Ritter (1892) in the far back region and

Fig. 14 shows that, for all performed tests, the ratio h0/d0 was lower than the critical h0/d0 value of 0.138, implying that the initial discharge, Q0, was independent of the initial water depth, h0.

As shown in Fig. 15, for all tests performed on the wet bed and for all values of h0 and d0, the shape of the bore front was normal- ized using h2 and the roller length, Lr, and good agreement between

0.5

h0 = 0.001 m, US7

h0 = 0.010 m, US7 h0 = 0.030 m, US7 h0 = 0.050 m, US7 h0 = 0.100 m, US7

h0 = 0.001 m, US6 h0 = 0.010 m, US6 h0 = 0.030 m, US6 h0 = 0.050 m, US6 h0 = 0.100 m, US6

Ritter (1892)

h2 (h0 = 0.010 m) - Stoker (1957) h2 (h0 = 0.030 m) - Stoker (1957) h2 (h0 = 0.050 m) - Stoker (1957) h2 (h0 = 0.100 m) - Stoker (1957)

0.4

h/d0

0.3

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0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

(a) x/[t·(gd0)0.5]

0.5

0.4

h/d0

0.3

‌0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

(b) x/[t·(gd0)0.5]

0.5

0.4

h/d0

0.3

0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

(c) x/[t·(gd0)0.5]

Fig. 13. Longitudinal free-surface profile for bores with different initial still water depths, denoted h0, and impoundment depths, denoted d0, com- pared with the theoretical solutions of Ritter (1892) and the plateau heights, denoted h2, obtained with Eq. (5) (Chanson et al. 2000); measurements at US 7 (solid symbols) and US 6 (empty symbols): (a) d0 = 0.82 m; (b) d0 = 0.63 m; (c) d0 = 0.40 m

all curves was observed. Given the differences in front celerity and flow depth, the length of the roller Lr was identified for every profile using the time taken by the bore to reach the plateau height of h2. The roller length Lr was then derived using the bore celerity such that Lr was U·t. The experimental results were successfully com- pared to formulas found in the literature, and the longitudinal

free-surface elevations showed a self-similar profile in the form of Eq. (6). For the present study, the best fit was found with the exponent, N = 0.482 which was located between the N value of

0.441 proposed by Chanson (2011) for hydraulic jumps and the N value of 0.540 suggested by Wang and Chanson (2015). Eq. (6) is written as

‌Flow Velocities

Front Celerity

h — h0 

=

h2 — h0

x — xs N

Lr

(6)

where Dx = distance between two USs; and Dt = difference in the wavefront arrival time. The measurement locations corresponded to the locations of the USs as shown in Fig. 3. The average front celer- ity was considered for each sensor (US2–US7) relative to US1, which was located at an x of 2 m from the channel inlet. The average front celerity obtained for dry bed surges was compared to formulas commonly used in design codes and practice (Fig. 16); these formu- las were mostly derived from physical models at laboratory scale.

Two velocities were analyzed in the present study: (1) the surge and bore front celerity values, denoted U, derived from the spatial- temporal advancement of the wavefront as detected by the USs and

(2) the velocity profiles within the wave as measured using the ultra- sonic velocity profilers (UVP).

‌The average front celerity of the propagating wave was esti- mated using the measurements of the depth profiles over time as follows:

This comparison proved that the waves generated with the proposed vertical release technique had celerity values consistent with other generation mechanisms described in literature. The celer- ity range was confined by values obtained from the FEMA 55 (upper bound) and the City and County of Honolulu (CCH) building code (lower bound) (FEMA 2001; CCH 2000). The ex- perimental results obtained for the present study were between those of Kirkoz (1983) and Iizuka and Matsutomi (2000). Given the Froude similitude, most formulas estimating the velocities

=

U Dx Dt

(7)

‌are expressed as

U = apgffiffiffidffiffi0ffiffi

(8)

0.35

0.30

(h2 - h0) / d0

0.25

0.20

0.15

0.10

0.05

‌0.00

Chanson et al. (2000) Experimental points h0/d0 = 0.138

0 0.025 0.05 0.075 0.1 0.125 0.15

gh0 =

8 · 2 h0 + 1

— 1

(9)

h0 /d0

where a = coefficient for which the values are presented in Table 3. For the present study, the best correlation was found for an a value of 1.25 for dry bed surges (Fig. 16).

For the same release conditions, wet bed bores propagated with a slower front celerity compared to dry bed surges. This difference in behavior can be observed in Fig. 2 for the case of a tidal bore, where the portion of the wave on the dry bed propagated faster than the portion propagating over the wet bed. The front celerity, U, of a bore moving over a wet bed was a function of the initial still water depth, h0, and small values of h0 corresponded to velocities close to those observed for the dry bed condition, which represented the upper limit.

‌The experimental wavefront celerity, U, obtained for the wet bed bores with various values of h0 and d0 was compared with a the- oretical solution derived from the momentum equation [Eq. (9)], as presented by Stoker (1958) and with the empirical approximation of Montes (1998), presented by Chanson (2004) in Eq. (10):

Fig. 14. Comparison of the experimental points of the plateau height,

h2, with the approximation proposed by Chanson et al. (2000) [Eq. (5)]

U tvu

1ffiffiffiffiffiffi"ffiffiffi ffiffiffiffiffiffiffihffiffi2ffiffiffiffiffiffiffiffiffiffi ffiffiffiffi2ffiffiffiffiffiffiffiffiffiffi#ffiffiffi

1.2

1.0

(h-h0) / (h2-h0)

0.8

0.6

0.4

0.2

0.0

d0 = 0.82 m, h0 = 0.100 m d0 = 0.82 m, h0 = 0.050 m d0 = 0.82 m, h0 = 0.030 m d0 = 0.82 m, h0 = 0.010 m d0 = 0.63 m, h0 = 0.050 m d0 = 0.63 m, h0 = 0.030 m d0 = 0.63 m, h0 = 0.010 m

.

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d0 = 0.40 m, h0 = 0.050 m d0 = 0.40 m, h0 = 0.030 m d0 = 0.40 m, h0 = 0.010 m

Present study - N = 0.482 Chanson (2011a) - N = 0.441

Wang and Chanson (2015) - N = 0.540

-2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0

(x-xs) / Lr

Fig. 15. Normalized bore front profiles, for various values of d0 and h0, for comparisons of the experimental data from the proposed vertical release technique with data from the empirical formulas from Chanson (2011) [Eq. (6)] and from Wang and Chanson (2015) for hydraulic jumps

(gd0)0.5             Matsutomi and Okamoto (2010) FEMA 55 (2000) Shafiei et al. (2016)

CCH (2000) Present study ( = 1.25)

Iizuka & Matsutomi (2000) Dry

Kirkoz (1983) Wet

Murty (1977)

Bryant (2001)

‌8‌

Average front celerity U [m/s]

7

6

5

4

3

2

1

0

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

‌Impoundment depth d0 [m]

Fig. 16. Comparison of the measured average front celerity, U, with formulas from the literature for dry bed surges (all values at model scale)

Eq. [9], Stoker (1957)

Chanson (2004)

d0 = 0.82 m d0 = 0.63 m d0 = 0.40 m

 Dry bed

,ffi2ffi

8

U/(gh0)0.5

6

4

‌U 0.63545 + 0.3286

h0 0.65167

d0

2

(10) 0

,gffiffiffihffiffi0ffiffi =

0.00251 +

h0 0.65167

d0

0 0.04 0.08 0.12 0.16

h0/d0

where d0 = initial equivalent impoundment depth; h0 = initial still water depth; and h2 = plateau height obtained from Eq. (5) and shown in Fig. 3. Very good agreement between all formulas can be observed in Fig. 17. This finding shows that, contrary to dry bed surges, for wet bed bores, a precise prediction of the front celerity can be achieved through Eqs. (9) and (10).

Velocity Profiles

In addition to the recent contributions of Leng and Chanson (2017a, b), only a few studies of the in-wave velocity profiles were available. For this reason, a constant vertical velocity profile was commonly assumed (Whitham 1955).

Similar to the process described by Meile et al. (2008, 2011), a UVP probe installed in the channel bottom measured the inter- nal instantaneous velocity profiles of the propagating surge and bore. Some representative velocity profiles are shown in Fig. 18, which presents the typical profiles associated with turbulent open channel flows. A well-defined boundary layer, followed by an upper sector with almost constant velocities were observed. These results confirmed that surges traveled faster than bores.

For all profiles, the depth-averaged velocity, Vm, was com- puted as

Fig. 17. Average bore front celerity, U, as a function of the initial still water depth, h0; experimental results compared to the momentum equa- tion [Eq. (9)] and the numerical approximation proposed by Chanson (2004), shown in Eq. (10), for different impoundment depths: d0 was

0.82 m for Tests 4, 5, 8, 11, and 14; d0 was 0.63 m for Tests 6, 9, and 12; and d0 was 0.40 m for Tests 7, 10, and 13

m = ð

h

V 1 v dh (11)

h

0

where v = local velocity at depth h. The time history of Vm in Fig. 18 was compared to the wavefront celerity U measured with the USs. Looking at the depth-averaged velocity profiles, it is noticed that the largest velocities occurred at the wavefront, which was consist- ent with other reports in the literature. A continuous deceleration occurred behind the wavefront for all configurations until a quasi- steady state was reached (not discussed herein): This was previ- ously reported by Al-Faesly et al. (2012) and Goseberg et al. (2013). Although the observed deceleration behind the wavefront was predicted by the continuity equation because of the increase in water depth, the last part of the curve was influenced by the

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(a)

‌(b)

Fig. 18. Wave height, h, depth-averaged velocity, Vm, and velocity profiles at specific times for (a) dry bed surge with d0 = 0.82 m for Test 1 and

(b) wet bed bore with d0 = 0.82 m and h0 = 0.050 m for Test 11, both measured at x of 13.85 m (US7) from the channel inlet

‌Fig. 19. Normalized velocity profiles and turbulent intensity, Tu, for T·(g/d0)0.5 < 42: (a) dry bed surge (160 profiles Test 1); (b) wet bed bore with

d0 = 0.82 m and h0 = 0.05 m (104 profiles, Test 11)

reduction of the water volume, and implicitly, of the hydraulic head in the upper basin. For these reasons, all data for T greater than T* were not considered.

The lower velocities observed after the passing of the wavefront were in agreement with the findings of Lauber and Hager (1998) and those of Leng and Chanson (2016, 2017b). In Fig. 18, for bores, the experimental data were also compared with the velocity V2 behind the bore front predicted by the following momentum equa- tion (Henderson 1966; Chanson 2004):

U · h0 = (U — V2) · h2 (12)

where U = bore front celerity; h0 = initial still water depth; and h2 = bore height after the turbulent front [Eq. (5)].

All individual velocity profiles were normalized using the meas- ured depth-averaged velocity, Vm, and the wave height of every pro- file, hi. Although the profiles showed some scattering, probably at- tributable to random air bubbles or impurities occurring in the flow, good agreement between all measured profiles for a dry bed surge and a wet bed bore can be observed in Fig. 19. The velocity profiles were successfully compared to Prandtl’s power law with n of 8, obtained with a flow resistance value f of 0.02 (Chanson 2004):

small given the range of Reynolds numbers (R 105–106). The same findings were confirmed by Leng and Chanson (2017a, b) for surges and bores in both steady and unsteady flows. Some scattering in ve- locity measurements was visible in the upper part of the profiles (Fig. 19), which was probably attributable to the fluctuations observed on the flow surface (Wüthrich et al. 2016b). To gain a better insight into the turbulent behavior of the surges and bores, the fluctuations were separated from the mean values and analyzed per horizontal flow layer. This process resulted in a turbulence intensity value, Tu =

≈

qffiffiffiffiffiffi—ffiffiffiffiffiffiffiffiffiffi

(v ¯v)2 /¯v, per layer. The derived Tu distribution is also pre- sented in Fig. 19 and shows a uniform behavior with Tu values less than 0.11 for dry bed surges and less than 0.13 for wet bed bores. Similar results were obtained for other surges and bores with different values of impoundment depth, d0, and initial still water depth, h0.

The depth-averaged velocities, designated by Vm, for 12 dry bed surges and 19 wet bed bores at two measurements locations along the channel (x was 10.20 and 13.85 m) are presented in dimension- less form in Fig. 20, where T = t – t0 is the shifted time, such that T = 0 coincides with the wave arrival time. The profile plotting was stopped when T equaled T* because the assumption of a continuous water discharge, Q0, was no longer valid (Fig. 5). Despite some

h V n

hi = Vm

(13)

scattering, good agreement was observed for all experimental points

for both dry bed surges and wet bed bores. For dry bed surges, the match between the front celerity and depth-averaged velocity was

good, whereas for bores on a wet bed, an underestimation of the ve-

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Although a logarithmic profile, which takes into account the ve- locity reduction close to the bottom due to the presence of the bound- ary layer, is theoretically more appropriate, Fig. 19 shows that the assumption of a uniform constant velocity profile was feasible for

locity magnitude was consistently observed in the wavefront region [T·(g/d0)0.5 < 15, in Fig. 20(b)]. In this region, Vm was equal to the velocity V2, derived from the momentum equation [Eq. (12)] as a

function of h /d . For both surges and bores, the decrease in V

both dry bed surges and wet bed bores. This can be explained by the 0 0 m

significant vertical exchange of momentum across the wave depth due to turbulence. The estimation of the average velocity through a uniform profile works well in the fully developed region, where the

behind the front was best approximated by Eq. (14), which imposed the boundary condition Vm = U at T ·(g/d0)0.5 = 0:

Vm " rffigffiffiffiffi#

height of the flow is sufficient to neglect the effect of the boundary layer. In the tip region, the thickness of the boundary layer is impor-

U = 1 — c · tanh b · T d0

(14)

tant; hence, Vm is slightly underestimated. The existence of a thin boundary layer was previously observed by Lauber and Hager (1998) through particle image velocimetry (PIV) tests; however, this was

where Vm = depth-average profile velocity; U = wavefront celerity; T = shifted time (T = t – t0); g = gravity constant; and d0 = initial impoundment depth. Parameters b and c were derived empirically.

d0 = 0.82 m - US7 d0 = 0.82 m - US2 d0 = 0.63 m - US7

d0 = 0.63 m - US2 d0 = 0.40 m - US7 d0 = 0.40 m - US2

Eq. [14] - c = 0.6, b = 0.039

Eq. [14] - c = 0.6, b = 0.033

Eq. [14] - c = 0.6, b = 0.024

1.0

0.8

Vm/U

0.6

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0.4

0.2

0.0 0 10 20 30 40 50 60 70 80

T · (g/d0)0.5

(a)

‌1.0

d0 = 0.82 m - h0 = 0.100 m d0 = 0.82 m - h0 = 0.050 m d0 = 0.82 m - h0 = 0.030 m d0 = 0.82 m - h0 = 0.010 m d0 = 0.63 m - h0 = 0.050 m

d0 = 0.63 m - h0 = 0.030 m d0 = 0.63 m - h0 = 0.010 m d0 = 0.40 m - h0 = 0.050 m d0 = 0.40 m - h0 = 0.030 m d0 = 0.40 m - h0 = 0.010 m

Eq.[14] - c = 0.6, b = 0.039

Eq.[14] - c = 0.6, b = 0.032

Eq.[14] - c = 0.6, b = 0.023

V2/U = 0.704 (min value)

V2/U = 0.914 (max value)

0.8

Vm/U

0.6

0.4

0.2

0.0 0 10 20 30 40 50 60 70 80

T · (g/d0)0.5

(b)

Fig. 20. (a) Dimensionless depth-averaged velocities, Vm/U, for 12 dry bed surges with different impoundment depths at two different locations at x of 13.85 and 10.20 m for US7 and US2, respectively; (b) dimensionless depth-averaged velocities, Vm, for 19 wet bed bores with different impound- ment depths and initial still water depths at a fixed location, x = 13.85 m

‌For large values of T·(g/d0)0.5, asymptotic behavior toward uniform flow conditions was observed. While the c value of 0.6 was a con- stant for both bores and surges (empirical best fit), b was influenced by the equivalent impoundment depth, d0, and the wave height, h, as shown in Fig. 21 and as follows in Eqs. (15a) and (15b):

where hmax = maximum wave height for a dry bed surge in Eq. (15a); and h2 = plateau height for wet bed bores in Eq. (15b). For the latter, the value of b was implicitly influenced by the initial still water depth h0 through the plateau height h2, which was a function

of the ratio h0/d0 [Eq. (5), Fig. 14]. However, Fig. 21(a) shows that this dependence was minimal, meaning that the main parameter

= ·

Dry bed surge b 0.0124 d0

hmax

— 1 (15a)

‌controlling b was the impoundment depth d0 [horizontal trend shown in Fig. 21(a)]. These findings showed that, within the tested range, the main influence of the initial still water depth, h , was

Wet bed bore b = 0.0124 ·

d0

h2 — h0 — 1

(15b)

0

observed in the reduction of the wavefront celerity, U (“Front Celerity” Section).

dry bed wet bed

d0 = 0.82 m, Dry d0 = 0.82 m, Wet d0 = 0.63 m, Dry d0 = 0.63 m, Wet d0 = 0.40 m, Dry d0 = 0.40 m, Wet

Eq. [16] - R2 = 0.88

‌0.05 0.05

0.04 0.04

b

b

0.03 0.03

0.02 0.02

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0.01 0.01

0

-0.03 0 0.03 0.06 0.09 0.12 0.15

h0/d0

(a) (b)

0 1 2 3 4 5

d0/(h-h0)

Fig. 21. Definition of parameter b in Eq. (15): (a) Eq. (15a) function of h0/d0; (b) Eq. (15b) function of d0/(h−h0), where h equals hmax for surges and

‌h equals h2 for bores (Note: Same legend applies to both panels)

d0 = 0.82 m, Dry, x = 13.85 m d0 = 0.82 m, Dry, x = 10.20 m d0 = 0.63 m, Dry, x = 13.85 m d0 = 0.63 m, Dry, x = 10.20 m d0 = 0.40 m, Dry, x = 13.85 m d0 = 0.40 m, Dry, x = 10.20 m

d0 = 0.82 m, humid

d0 = 0.82 m, h0 = 0.01m d0 = 0.82 m, h0 = 0.03m d0 = 0.82 m, h0 = 0.05m d0 = 0.82 m, h0 = 0.10m

6 6

5 5

4 4

Fr

Fr

3 3

2 2

1

0 0 10 20 30 40 50

T · (g/d0)0.5

(a) (b)

1

0 0 10 20 30 40 50

T · (g/d0)0.5

≈

Fig. 22. Flow Froude number, F, computed for (a) dry bed surges and (b) wet bed bores

Froude Number and Momentum

The Froude number for both dry bed surges and wet bed bores was calcualted using Eq. (16) as follows:

Vm;i   

toward F 1. For wet bed bores, a more constant flow pattern was observed at all times. This between surges and bores difference was more important as h0 increased. The behavior of wet bed bores with smaller initial still water depth, h0, became similar to that of the dry bed surges. This proved, once again, the transition pattern between

F =

,gffiffiffihffiffiiffi

(16)

dry and wet beds. These findings were consistent with the video analysis of Fritz et al. (2012), who estimated Froude number values close to 1 in Kesennuma during the 2011 Tōhoku, Japan, tsunami.

where Vm = individual depth-averaged profile velocity; g = gravity constant; and hi = wave height of every profile. The values obtained are presented in Fig. 22, where a clear difference between bores and surges is shown. The dry bed surge was supercritical in the first part of the propagating wave, followed by an asymptotic decrease

The momentum associated with the moving wave was an impor- tant parameter because it directly controlled the loading exerted during the impact against a free-standing structure. The momentum, M, per unit width was calculated as the product of water density, r , unit discharge, q, and the average profile velocity, Vm, resulting in

‌0.30

d0 = 0.82 m, Dry, US7 d0 = 0.63 m, Dry, US7 d0 = 0.40 m, Dry, US7 d0 = 0.82 m, Dry, US2 d0 = 0.63 m, Dry, US2 d0 = 0.40 m, Dry, US2

d0 = 0.82 m, h0 = 0.10 m d0 = 0.82 m, h0 = 0.05 m d0 = 0.82 m, h0 = 0.03 m d0 = 0.82 m, h0 = 0.01 m

d0 = 0.82 m, Humid

d0 = 0.63 m, h0 = 0.05 m

0.30

d0 = 0.63 m, h0 = 0.03 m d0 = 0.63 m, h0 = 0.01 m d0 = 0.40 m, h0 = 0.05 m d0 = 0.40 m, h0 = 0.03 m d0 = 0.4m, h0 = 0.01 m

0.25 0.25

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2

0.20 0.20

2

M/gd0

M/gd0

0.15 0.15

0.10 0.10

0.05

0.00 0 10 20 30 40 50

T · (g/d0)0.5

(a) (b)

0.05

0.00 0 10 20 30 40 50

T · (g/d0)0.5

m 0

Fig. 23. Momentum, M = r ·h·V 2, computed for (a) dry bed surges and (b) wet bed bores for various impoundment depths, denoted d , and initial still water depths, denoted h0

m

‌M = r · q · Vm = r · h · V2

(17)

1.2

≈

0

The results obtained from all tests are shown in Fig. 23, where a similar pattern between surges and bores can be observed, including the initial part characterized by an increase in momentum, followed by a subsequent decrease. Although some scattering was present, results showed a peak for all configurations around T · (g/d0)0.5 10, for which values of M/rgd 2 between 0.20 and 0.25 were obtained. It is noteworthy that the maximum of the momentum flux per unit width occurred neither when the velocity was maximal nor when the wave height was maximal, which is in agreement with findings previously reported by Yeh (2007) and Chock et al. (2013). For all tested scenarios, the maximum momentum was reached before the maximum flow depth was observed.

A variable hM is introduced as the ratio between the height at which the maximum momentum occurs, h(Mmax), and the maxi- mum wave height, hmax, as

1.0

)/h

max max

0.8

h = h(M

0.6

M

0.4

0.2

=

hM h(Mmax) hmax

(18)



dry surges

d0 = 0.82 m, Dry d0 = 0.63 m, Dry d0 = 0.40 m, Dry d0 = 0.82 m, Wet d0 = 0.63 m, Wet d0 = 0.40 m, Wet

0.67 (Chock 2015)

0.90

0.0

The results for both surges and bores are shown in Fig. 24. These findings were compared to those of Chock (2015), which showed that the maximum momentum occurred when the water level reached 67% of the maximum wave height recorded on the rising limb of the inundating wave. The approach by Chock (2015) is, on average, supported by the results for dry bed surges (h0/d0 = 0). However, discrepancies were observed for the case of wet bed bores; for these, given the sudden water rise of the water depth, the maximum momentum was observed when the water depth was approximately 90% of the maximum wave height. Thus, the chosen value of 67% may not be conservative for some cases and the maxi- mum momentum might occur for higher water depths.

-0.025 0.025 0.075 0.125

h0/d0

Fig. 24. Dimensionless surge and bore heights when maximum mo- mentum occurred compared with existing guidelines (hM = 0.67) by Chock (2015)

Discussion

The present study introduced a novel technique to generate dry bed surges and wet bed bores in a laboratory environment. If a 1:30

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Froude scaling ratio was assumed, surge and bore depths ranged between 3.9 and 7.8 m (prototype scale), with front celerity values between 10.59 and 19.5 m/s. These values were consistent with field data obtained through posttsunami field surveys and observations, in which flow depths between 4 and 7 m were measured in the southern part of Khao Lak, Thailand, during the 2004 Indian Ocean tsunami (Dias et al. 2006) and velocities as high as 10–13 m/s near the Sendai Airport during the 2011 Tōhoku, Japan, tsunami (Jaffe et al. 2012). The generated surges and bores were similar to those produced with the classical dam-break technique (Ritter 1892; Whitham 1955; Stoker 1958), a method that is widely used at pres- ent to reproduce inland tsunami flows. Similarities between experi- mental and prototype data were also pointed out in terms of the shape at the surge front tip. Furthermore, similar Froude numbers between prototype and real tsunami events were presented. Thus, the authors concluded that the vertical released technique generates surges and bores that are consistent with other methods presented in literature and that this mechanism is well suited to simulate tsunami-like waves in laboratories.

Conclusions

Tsunamis, impulse waves, and dam-breaks waves are rare but highly destructive phenomena. Recent catastrophic events have shown that measures need to be taken to reduce casualties and socioeconomic impacts. The diversity of wave transformation and subsequent inland propagation has led researchers to develop several techniques to generate such tsunami-like flows in labora- tories. This comprehensive study focused on the generation of long waves (surges and bores) through the vertical release of a stored water volume. Both surges and bores produced with this vertical release technique were then analyzed in terms of their hydrodynamic behavior and characteristics, and the following conclusions were drawn:

• A comparison with existing literature for the classical dam-break generation mechanisms showed good agreement between the dry bed surges generated by the proposed vertical release method and the analytical solutions of Ritter (1892) and Whitham (1955). For wet bed bores, the generated water surface profiles agreed well with the theory of Stoker (1958).
• The values of wavefront celerity were successfully compared to those found in the existing literature and the current design guidelines and codes. A new expression to compute wave- front celerity was proposed in Eq. (8) with an a coefficient of1.25. For wet bed bores, very good agreement was found with the momentum equation [Eq. (9)] and the numerical approximation of Chanson (2004). The influence of the initial impoundment depth, h0, was observed in the wavefront celer- ity U, whereas bores propagating over smaller initial still water depths, showed behavior similar to that of dry bed surges.
• The use of UVP probes allowed for the measurement of ve-locity profiles of the propagating wave behind the wavefront, which showed velocity profiles close to those observed in open channel flows. Although the normalized profiles indi- cated good agreement with Prandtl’s exponential law, experi- mental results proved that the common assumption of a constant velocity profile over depth was acceptable. Flow deceleration was observed behind the front for all scenarios, and an expression to predict the depth-averaged velocity at a certain time behind the front was proposed in Eq. (14). The latter did not directly depend on the initial still waterdepth, h0; rather, it depended on the equivalent impound- ment depth, d0.≈
• Dry bed surges exhibited higher Froude numbers in the wave tip region, followed by a rapid decrease, whereas wet bed bores showed more constant Froude numbers over time. All tests had a similar shape for the momentum profiles with max- ima occurring at T·(g/d0)0.5 10, which did not correspond to either the maximum wave height or to the maximum flow ve- locity. The maximum momentum occurred at 65–70% of the maximum wave height for dry bed surges and at 90% of the maximum wave height for wet bed bores, something consist- ent with the latest standard recommendations (Chock 2015).

Acknowledgments

The authors thank Professor Hubert Chanson (University of Queensland, Australia) for his advice. The research study was supported by the Swiss National Science Foundation (SNSF) (Grants 200021_149112/1 and 200021_149112/2).

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