Coastal Engineering 58 (2011) 517–527

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Coastal Engineering

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Physical modelling of tsunami using a new pneumatic wave generator

Tiziana Rossetto a,⁎, William Allsop b, Ingrid Charvet a, David I. Robinson b

a Department of Civil, Environmental and Geomatic Engineering, University College London, Gower Street, London, EC1E 6BT, United Kingdomb HR Wallingford, Howbery Park, Wallingford, United Kingdom

⁎ Corresponding author. Tel.: +44 2076794488.E-mail address: t.rossetto@ucl.ac.uk (T. Rossetto).

0378-3839/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.coastaleng.2011.01.012

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 March 2010Received in revised form 14 January 2011Accepted 20 January 2011Available online 9 March 2011

Keywords:TsunamiPhysical modellingLong sine waveSolitary wavesN-wavesTsunami run-up

The physical simulation of tsunami in the laboratory has taken amajor leap forward with the construction andtesting of a newwave generator, capable of recreating scaled tsunami waves. Numerical tools fail to reproducetsunami nearshore and onshore processes well, and physical experiments in large scale hydraulic facilitiesworldwide have been limited to the generation of solitary waves as an (controversial) approximation forevolved forms of tsunami. The new concept in wave generation presented herein is born of collaborationbetween UCL's Earthquake and People Interaction Centre (EPICentre) and HR Wallingford. It allows for thefirst time the stable simulation of extremely long waves led either by a crest or a trough (depressed wave).This paper presents the working concepts behind the new wave generator and the first stages of testing forverifying its capacities and limitations. It is shown that the new wave generator can not only reproducesolitary waves and N-waves with large wavelengths, but also the 2004 Indian Ocean Tsunami as recorded offthe coast of Thailand (“Mercator” trace).

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1. Introduction

Tsunami can be a highly destructive natural hazard. The 2004Indian Ocean Tsunamiwas one of the worst disasters in recent history,with an estimated 275,000 lives lost (Crossley, 2005). Despite clearevidence of past large magnitude tsunamigenic earthquakes havingoccurred along the Sunda Trench (Bondevik, 2008) few communitieswere prepared for the level of devastation caused by the 2004 tsunamito coastlines bounding the Indian Ocean. This event highlighted thelack of tools for onshore impact assessment of tsunami, which arerequired by governments in order to know when and how to act todeliver adequate protection, and where to locate critical facilities oremergency resources to ensure effective post-disaster relief andrecovery. The development of these tools (e.g. risk maps) is hinderedby the rarity of in-situ measurements of tsunami, which lead to a poorunderstanding of the fundamental characteristics of tsunami in thenearshore and onshore regions. Furthermore, current numerical codeshave great difficulties modelling tsunami onshore flows over realtopography and around structures. There is therefore a lack ofknowledge as to how the characteristics of tsunamis affect theirimpact on the environmental and urban fabric of coastal communities.Following the 2004 Indian Ocean Tsunami it was observed that evenin areas of great destruction, a few buildings were still standing(Rossetto et al., 2007). By understanding general rules as to why these

buildings survived such forces, together with up-to-date civilengineering knowledge, engineers have been able to suggest buildingdesigns and/or defence techniques that may limit loss of life (FEMA,2008; Priyadarshi et al., 2005). But accurate and robust ways of testingthese ideas are crucial to their implementation.

Fig. 1 describes the main areas of research targeting tsunami, fromgeneration to impact. In this project we will focus on the nearshoreeffects of tsunami to fill some of the gaps described above. This paperstarts with a description of tsunami and limitations currentlyassociated with their numerical and physical simulations. The paperthen presents an advance in large scale tsunami wave generation thatwill allow new research to improve knowledge on tsunami impactthrough physical testing. The concepts behind the new tsunamigenerator are explained, and validation tests are presented whichshow its ability and limitations in simulating tsunami at scales rangingfrom 1/100 to 1/50, and to generate both crest and trough-led tsunamiwaves.

2. Limitations in tsunami impact simulation

Tsunamis are long gravity waves caused by a rapid displacement ofa large body of water. They may be triggered by an earthquake, alandslide (above or below the ocean), a volcanic eruption, or a majordebris slide. Most tsunamigenic seismic sources create multiplewaves, which propagate outwards from the fault led by either adepression wave (trough) or by a wave crest. When the seismic slip islong, the tsunami waves are strongly directional (Hwang and Divoky,1970; Kulikov and Mendvedev, 2005). In the open ocean, earthquake

Fig. 1. Diagram showing phases of evolution of a typical earthquake-generated tsunami from source to shore.

Fig. 2. Mercator wave recorded during the 2004 tsunami, recorded over a depth of13 m. The boxed data represents the first trough and peak of the tsunami to bereproduced in the experiment. It is possible that the last two waves are moresignificantly modified by reflections from the coast and are travelling in the oppositedirection. Parameters of the main wave (respectively wave height, amplitude andwavelength): H=6.46 m, a=3.69 m, and L=14,416 m.

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generated tsunamis typically travel at high speeds, have small heightsbut can reach hundreds of kilometres in length. Ameanwavelength of500 km and a mean celerity of 200 m/s were recorded by the JASONsatellite during the 2004 event (leading to a mean tsunami period of40 min), in the offshore region (Kulikov and Mendvedev, 2005). Asthe waves enter shallower water, their celerities and wavelengthsdecrease and heights increase. Where a tsunami is characterised by aleading depression wave, the sea is seen to recede approaching thecoastline before the positive crest reaches the shore. At the shoreline,a tsunami can be several metres high and has also been reported toaccelerate (Synolakis and Bernard, 2006). These waves may causeviolent wave impacts on shoreline structures, and the very longwavelengths may lead to extensive inundation inland. Inundationflows can travel at several metres per second. During the 2004 IndianOcean Tsunami, flow velocities have been recorded on video in severalplaces and estimated from field survey e.g. 6–8 m/s in Khao Lak, and3–4 m/s in Kamala Beach, Thailand (Rossetto et al., 2007), with anestimated peak velocity of almost 5 m/s calculated from a video fromAceh, Sumatra (Fritz et al., 2006).

The best nearshore tsunami trace recorded to date derives from anecho-sounder on the Belgian yacht “Mercator”, which was located1.6 km off the coast of South Phuket, Thailand at the time of the IndianOcean event in 2004 (Rabinovich and Thomson, 2007; Siffer, 2005).The sampling interval of the recording instrument was 1 min, whichleads to a suitable sampling rate for such a low frequency wave signal.Moreover, the boat was located over the continental shelf (depth of12–13 m) but in an open area directly exposed to the source. At thisdistance from the coast, the signal does not represent the offshoretsunami anymore but a shoaled up tsunami wave, therefore slower,shorter and higher than the offshore propagating wave previouslymentioned. The celerity of the wave, which is a function of depth forshallow water waves such as tsunami, will decrease as the waveenters progressively shallower waters. The wavelength decreaseslinearly with the celerity, so the Mercator wave, if considered as apure tsunami signal propagating from the source to the continentalshelf, should display a period similar to the offshore tsunami atgeneration. However, the data (Fig. 2) shows a significant decrease inperiod compared to the generated tsunami. Given the very longwavelength of the 2004 tsunami as reported in Kulikov andMendvedev (2005) and the relatively small dimensions of the domainof propagation (for example, 700 km between the source and Phuketand 120 km between the source and the Nicobar islands), complex(3D) interactions between the main wave and the coastlines certainlyoccurred resulting in an alteration of the main signal. This phenom-enon may be explored using numerical models suited to wavepropagation.

Tide gauge records of this tsunami also exist, but these instru-ments are for the most part located in sheltered harbours where thewaves will have undergone reflection and refraction and hence arenot representative of the original incoming signal. Most tide gaugesexposed to the more direct attack either “topped-out” or failed whenhit by the first wave or were simply swept away and the data neverrecovered. For the modelling work described here, the Mercator trace(as shown in Fig. 2) was used to define a specimen tsunami for thedesign and testing of the tsunami generator.

Generation and propagation of tsunami can be simulated numer-ically. Tsunami transformations into coastal margins can be simulated

by many well-known numerical models such as Nonlinear ShallowWater or Boussinesq models e.g. MOST (Titov and Synolakis, 1998)and FUNWAVE (Grilli et al., 2007). Critical gaps in knowledge exist inthe modelling of nearshore and onshore processes. Many numericalmodels can simulate one or more of the key wave or flow processes atlarge or small scale, but without high resolution bathymetries andtopographies these models fail to deliver accurate results in theonshore regions. High resolution bathymetry and topography wouldalso be required in order to reproduce accurately a given tsunamiscenario in the laboratory. However, when both modelling methodsdo not overcome this limitation, hydraulic modelling can reproducethe interactions of tsunami waves and beaches, sediments, coastaldefences and buildings. These are highly complex processes thatnumerical codes cannot model.

Beside the necessity for very accurate bathymetries and topogra-phies, the main issue of numerical models is the grid resolution. Agood example is a numerical study of the inundation of Hilo, Hawaiiduring the 1946 tsunami (Mader, 2004), where the author found thatfor local flooding a grid resolution as small as 10 m should be used.When the grid resolution required to model local flooding isextremely fine, the total number of grid cells covering a given areaof study is much greater and computing times become unacceptable.

In terms of elevation data, the required resolution will bedependent on the slope and overall complexity of the seafloor/beach/back-beach over the nearshore and onshore regions. In lowtidal areas, typical coastal structure near the shoreline will havevertical heights often as small as 2–4 m, so vertical resolutions oforder 0.2 m may be desirable. Unfortunately, the most widelyavailable elevation datasets have a horizontal resolution of 1′ e.g.BODC (2008).

Physical modelling of wave–structure processes is used to analysefluid flow processes and responses for which complexities are toogreat to model analytically or numerically. In the design of any suchphysical model, it is essential to establish which processes are being

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reproduced correctly, and those that are not reproduced or that maybe affected by model/scale effects. Most wave/structure problemsstudied in physical models, such as direct wave loads, armour move-ment etc., are dominated by wave inertia or momentum. The rangesof scales that can be used without significant scale effects (morecorrectly the size of model waves) are relatively well-established(Hughes, 1995) and quite small scales (for example 1/50 to 1/100) canbe used for flow processes and responses that are dominated by waveinertia or momentum. Physical models of wave disturbance have usedscales of 1/120 to 1/150 without significant distortion. Viscous forcesare generally well reproduced in model water depths greater than20 mm. Surface tension effects are generally negligible for modelwave heights greater than 20 mm or wave periods greater than 0.5 s(Kohlhase and Dette, 1980; Sharp and Abdul Khader, 1984). Forsimple flows (as in tsunamiwave run-up), even flow depths of 20 mmor less may be sufficient to reproduce the main effects withoutsignificant error.

For rubble mound structures, larger (model) wave heights (say,Hs≥100 mm) are often used to minimise Reynolds scale effects ininternal flows, although smaller wave heights may be used togetherwith adjusting the scaling of permeable materials to correct forviscous scale effects (Jensen and Klinting, 1983).

A more important complication in the physical modelling of large/long waves is accurate wave generation, especially because fewfacilities have been constructed to deal with such relatively rarephenomena. Many studies havemodelled generation and propagationof large waves, but they have mainly concentrated on idealisedcnoidal and solitary waves (BODC, 2008; Wolters et al., 2009; Goring,1978; Jensen et al., 2003), which have limited similarity to tsunami(Synolakis, 1987).

Conventional piston wave generators can recreate solitary waves(often used to approximate tsunami, Madsen et al., 2008), but simplydo not have the stroke to reproduce realistic tsunami wavelengthsand periods; an immediate limitation. For example, the tsunamifacility at Oregon State University (Yim et al., 2004) can generatewaves which at a scale of 1/50 in the TsunamiWave Basin would havea period of 3.5 s to 71 s, and at a scale of 1/5 in the Long Wave Flumewould have a period of 1.1 s to 22.4 s. For some events this may besufficient, but most tsunamis have typical periods ranging from 2 to200 min (Voit, 1987). For example, the “Mercator” trace (Siffer, 2005)recorded during the 2004 tsunami displayed a main direct wavewhich had a period of approximately 20 min (see Fig. 2). Facilitiesusing piston wave-makers are further limited to reproducing tsunamias long solitary waves (perhaps to a wave “period” of 10 s model)

Fig. 3. Left — tsunami generator and “Offshore 1” probe and right —

(Shimosako et al., 2002), and will have considerable difficulties toreproduce stable trough-led (leading depression) waves that can alsocharacterise tsunami. The only way they could generate a trough-ledwave is for the piston to start part-stroke and then be pulled back inits first cycle. This method has not been shown to produce stable waveforms as highlighted by the experimental results of Schmidt-Koppenhagen et al. (2006).

3. A new tsunami generation facility

A new type of tsunami generating device has been developed withthe ambition to generate tsunami at an appropriate model scale withcharacteristics consistent with earthquake generated events, i.e. longwavelengths and leading depression waves. Researchers from UCLand HR Wallingford collaborated to produce a unique device to gen-erate scaled tsunami within a wave flume. The aim of the study is tomodel the propagation of earthquake-generated tsunami through thesurf zone and to the inundation of buildings behind the shoreline.From observation of these physical experiments the team hopes tobetter quantify tsunami run-up and/or loading regimes on typicalbuildings, providing essential research input for the future up-gradingof structures in areas at risk from tsunami.

The design concept behind the new tsunami generator is basedon a Pneumatic Tide Generator developed originally in the 1950s togenerate tides in large area hydraulic models (Wilkie and Young,1952). A sealed tank sits at one end of a long flume, with a submergedopening facing shorewards. A fan extracts air from the top of the tank,drawing water from the test flume. A valve releases air to generate awave from the tank. Control of the air valve in the top of the tank givesthe desired wave shape. This form of wave generation is ideally suitedto simulating tsunami as it allows the controlled movement of largevolumes of water in a confined space without high discharge waterpumps, which are expensive in both capital and operational costs.Schematics of the tsunami generator in the flume and the tank areshown in Figs. 3 and 4. Fig. 5 shows a photograph and schematic ofthe tank in the flume and identifies its main components.

The tsunami generator tank is made from steel panels boltedtogether in sections (the constructed size is 4.8 m×1.8 m×1.15 m).Modular construction allows easy assembly, removal and storage. Thetank has internal bracing to avoid distortion under the pressuredifferences between inside and outside of the tank. The device wasinstalled in one of HRWallingford's wave flumes (45 m long and 1.2 mwide). The approach bathymetry and shoreline within the flumewereformed by cement mortar overlying compacted fill and were shaped

propagation region, nearshore and onshore instrumented areas.

Fig. 4. Schematic diagram of the tsunami generator close up, with fundamentalequations for its working.

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to represent a coastal slope of 1:20 up to a shoreline, then a horizontalinland inundation area.

Prior to design of the tsunami generator, desk studies wereperformed to estimate its likely performance envelope and character-istics of the tsunami generator before fabrication. The desk studieswere carried out in three phases, starting with relatively simplesimulations.

In Phase 1, the motion of the water surface within the tank wasmodelled (assuming that the air responded with simple harmonicmotion) to confirm that the elasticity of the air trapped within thetank would not allow significant oscillations of the water surface atany point during, or at the end of wave generation.

In Phase 2 of the calculations, the interaction between the pumpand valve control system was calculated for the generation of therequired wave profiles. The calculations recreated those described byWilkie and Young (1952) but using data for the modern pump andtank arrangement, and based on the mass flow conservationequations shown in Fig. 4. By inputting the performance character-istics of the pump, the tank dimensions and the required wave profile,it was possible to determine whether the design was theoretically

Fig. 5. Left — tsunami generator and right — schematic diagram of the generating system. AG: glass window, and H: security valve.

capable of drawing and releasing the water at a sufficient rate togenerate the required waves. The calculation procedure assumes thatthe flow is incompressible, so the volume of flow being pumped out ofthe tank is equal to the sum of the air entering through the valve andthe water entering through the gate opening (0.45 m high), as shownin Fig. 4.

The required wave profile can be used to determine the requiredwater flow rate during a wave cycle (shown as the dashed pink linewithin Fig. 6). If this flow rate is ever greater than the pump'spumping ability (i.e. if the dashed pink line in Fig. 6 ever crosses thesolid dark-blue line) then the wave cannot, in theory, be generated.The required flow through the valve can be calculated by taking oneflow rate away from the other, giving the short-dashed red line inFig. 6. The relationship between flow rate, pressure difference andvalve angle can then be used to estimate the required valve operatingrange and speed.

It was assumed that idealised solitary or N-waves as proposed byTadepalli and Synolakis (Synolakis, 1986; Tadepalli and Synolakis,1994, 1996) would be required as well as the first trough and peak ofthe time series of the Boxing Day Tsunami measured by the Belgianyacht “Mercator” (see Fig. 2). Baffles were placed within the tsunamigenerator to dampen oscillationswithin the tankwithout significantlyreducing the peak flow rates.

Control of the tsunami generator can be achieved either throughan open or closed loop system. With open loop control, the userprescribes a time series for the control valve position during wavegeneration. This gives tighter control on the wave generated, butrequires calibration for each wave profile generated. The closed loopcontrol system uses a proportional integral feedback loop to updatethe valve position based on readings of water level within the tank, orperhaps in the wave flume itself. This method requires no individualwave calibrations, but requires substantial care in the choice of inputparameters, and where and how the comparator water level ismeasured, in order to work reliably. The experiments described in thispaper were carried out using the open loop control only. Initial workwith the feedback loop considered only water levels, but not watervelocities, giving some undesired wave behaviour within the flume. Inthe open loop, it is necessary to monitor the water level within thetank, especially during the generation of a trough, so it does not reachheights greater than 1.7 m. Indeed, when water gets close to the roofof the tank (where the valves and pump are located), water can be

: Wave tank, B: gate, C: “Offshore 1” probe, D: control valve, E: water supply, F: pump,

Fig. 6. Control valve and pump performance according to necessary flow rate for wavegeneration.

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drawn into the pump and irreversibly damage it. It is also important towait several minutes between each test, with the pump on and at theadequate valve position for generation of the next wave, to allow theflume water level to be still and free from the parasitic oscillations ofthe previous test.

4. Capabilities and limitations of the new tsunami generator

The first experiments with the tsunami generator were intendedto gauge its capabilities and limitations. The type and characteristicsof the generated waves for this paper are listed in Table 1, and theresults are presented in the following sections. The location of thewave probes used throughout the experiments is shown in Fig. 7. First,sine waves of various periods and amplitudes were generated toobserve the response of the system to a periodic input and assess theability of the new machine to reproduce effectively simple periodicsignals.

The sine waves modelled here (relative to any realistic tsunami)were also inherently steep. As their steepnesses (height/length) weretherefore relatively large, the surf similarity parameters will havebeen relatively low, as would have been any reflections from theshoreline. Most importantly, sine waves are periodic waves withclosed orbital particle paths therefore they do not transport massforward. Tsunamis on the other hand propagate as bulk flows. Liketranslator waves, they carry mass forward and are essentially depthaveraged. This difference has been confirmed by observations madeduring the first round of experiments: whereas a significant motion ofthe shoreline (runup) could always be detectedwith the solitarywavetests (translator waves), no motion of the shoreline was detected forsine waves regardless of their periods. Sine waves were not thereforeconsidered further in the tsunami generator experiments.

4.1. Sine wave tests

Finite wave trains of sinusoids of different periods were generated.The open loop control allows generation of sine waves of periodsbetween 50 s and 200 s. The parameters of the sine waves testedare listed in Table 1. We can see that the maximum amplitude of0.045 m also corresponds to the maximum wave period of 200 s. Incomparison, during their experimental study of tsunami solitonfission using sine waves (incident wave condition), Matsuyama et al.(2007) generated a wave amplitude of 0.02 m for a maximum periodof 120 s and a maximum wave amplitude of 0.09 m for a period of40 s.

Thewavelengths generated in our experiments in somecases exceedthe flume length, so major reflections would be expected. However,contrary to translator waves such as solitary waves and N-waves, sine

waves are essentially orbital and relatively little wave momentum iscarried forward except in shallow water.

A wide range of waves was generatedwith good sinusoidal shapes.On several occasions an interruption in the regularity of the signalcould be observed and was interpreted indeed as a parasitic reflectiondue to the geometry of the flume.Waves that are not purely sinusoidalhave been flagged ** in Table 1. They correspond mainly to an inputsignal with a period of 50 s which may be a resonance effect of thesystem. Ideal oscillatorywaves do not transportmass but in reality theorbital particle trajectories are open and some forward motion mayoccur. Period outputwas always consistent with the period input fromthe control valve (see Fig. 8). These initial tests confirmed that thegenerator is capable of generating waves in a controlled manner.

4.2. Solitary wave tests

The generator was then tasked to generate solitary waves(Miles, 1980), as described by:

η x;tð Þ = a sech x−ct=Lð Þð Þ2 ð1Þ

where η is the surface elevation (in metres), x is the horizontalcoordinate, t is time (in seconds), a is the wave amplitude (in metres),c is the wave celerity (in metres per second) and L is the length of thewave (in metres).

Solitary waves have been used by many to simulate tsunami inboth numerical and experimental studies e.g. Jensen et al., (2003),Synolakis (1987), Briggs et al. (1995), Borthwick et al. (2006).Composed only of a positive elevation, they can be reproduced inwave flumes equipped with traditional paddle type generators.Recently researchers have argued that they are not truly representa-tive of tsunami (Madsen et al., 2008). In order to reproduce pastexperiments and provide data for numerical modelling of thesewaves, solitary waves were however chosen as a further test case forthe tsunami generator. Solitary waves were reproduced in the flumewith amplitude (a) to water depth (h) ratios ranging from a/h=0.014to 0.20 (as measured in the constant depth propagation region, closeto the tank). This range was mainly limited by the height of thetsunami tank, as wave heights for a given period increase with headdifference between the flume water level and the water level in thetank. (It is however noted that the tank design could simply be alteredin the future if a greater range of a/h ratios were required.) The periodof the waves presented in this paper ranged from 4.2 s to 17.1 s (seeTable 1). The longer wave periods imply much longer wavelengthsand therefore lower wave steepness. These waves have much greatersurf similarity or breaker parameters than the tested sine waves(Borthwick et al., 2006). Moreover, contrary to sine waves, a solitarywave does carry forwardmomentum and hencemuch higher levels ofreflection from the slope are expected. As these reflections affectedthe second half of the solitary wave signal on many occasions, the halfperiod of the waves was estimated first (rising part of the wave). Thiswas done by calculating the total length of time between the rise ofthe water level above 1% of the flume water level and the occurrenceof the peak (maximum amplitude). The period values presented inTable 1 are equivalent to two half periods as defined here. A solitarywave produced in these experiments is compared to a theoreticalwave profile (Miles, 1980) and a paddle generated solitary wave bySynolakis (1986) in Fig. 9. A good fit is observed between the wavegenerated by Synolakis and the theoretical wave shape (Eq. (1)),however the solitary waves generated in the present experiments donot display such a goodmatch. This is very likely due to the generationmethod. Indeed, the tsunami generator has been designed for thegeneration of long waves by increasing the speed of water exchangebetween the tank and the flume, compared to the previous tidegenerator (Wilkie and Young, 1952). Even by using the fastest valvemotion there are however physical limitations on how quickly the

Table 1Table of the initial set of waves tested. (*) The valve time series ID corresponds to the name of the input file to be used at a given depth of operation to reproduce the same wave. Forsine waves, there is an inbuilt function where only wave period and range of valve motion (in motor units) are necessary for wave generation. (**) These waves resulted in a non-sinusoidal signal. This was likely to be an effect of parasitic reflections, or resonance for a particular period. Calculation of period/wavelength: the wave peaks – for all wavesexceeding the effective flume length – are likely to be affected by reflections, especially the second half of the positive amplitude, and represent a composite wave (reflections anddirect signal). Therefore, the period has been calculated: for solitary waves, by assuming symmetry and doubling the first half period and for N-waves, by calculating the full troughperiod and assuming symmetry for the positive part of the wave (resulting in the same calculation as for a solitary wave). (***) The recording of wave 307 is a model wave at anundistorted scale of 1/50 compared to the prototype Mercator (as measured nearshore).

Valve time seriesID*

Wave type Purpose of test Depth(m)

Period(s)

Wavelength(m)

Amplitude(m)

Wave height(m)

a/h(#)

H/L (#)(steepness)

200 s; 0 to 300 Sine Valve operation 0.642 200 501.92 0.045 0.090 0.0701 0.0001875 s; 0 to 300 Sine Valve operation 0.642 75 188.22 0.027 0.054 0.0421 0.00029100 s; 0 to 150 Sine Valve operation 0.642 100 250.96 0.024 0.048 0.0374 0.0001950 s; 0 to 150** Sine Valve operation 0.642 50 125.48 / / / /200 s; 0 to 150 Sine Valve operation 0.642 200 501.92 0.037 0.074 0.0576 0.00015100 s; 50 to 250 Sine Valve operation/profile comparison 0.642 100 250.96 0.022 0.044 0.0343 0.0001850 s; 50 to 250** Sine Valve operation 0.642 50 125.48 / / / /75 s; 50 to 250** Sine Valve operation 0.642 75 188.22 / / / /100 s; 0 to 300 Sine Valve operation 0.642 100 250.96 0.035 0.070 0.0545 0.0002850 s; 0 to 300** Sine Valve operation 0.642 50 125.48 / / / /75 s; 0 to 150 Sine Valve operation 0.642 75 188.22 0.017 0.034 0.0265 0.00018100 s; 0 to 300 Sine Valve operation 0.831 100 285.52 0.024 0.048 0.0289 0.0001750 s; 0 to 300** Sine Valve operation 0.831 50 142.76 / / / /100 s; 0 to 150 Sine Valve operation 0.831 100 285.52 0.016 0.032 0.0193 0.00011135 Solitary Profile comparison 0.46 8.7 18.48 0.120 0.120 0.0138 0.00649133 N Profile comparison 0.53 9.6 21.89 0.029 0.056 0.0547 0.00256149 Solitary Repeatability 0.45 5.5 11.77 0.027 0.027 0.0600 0.00229148 Solitary Repeatability 0.45 5.8 12.19 0.03 0.03 0.0667 0.00246147 Solitary Repeatability 0.45 5.9 12.40 0.037 0.037 0.0822 0.00298146 Solitary Repeatability 0.45 6.4 13.45 0.039 0.039 0.0867 0.00290139 Solitary Repeatability 0.45 6.6 13.87 0.049 0.049 0.1089 0.00353138 Solitary Repeatability 0.45 6.9 14.50 0.052 0.052 0.1156 0.00359137 Solitary Repeatability 0.45 6.9 14.50 0.068 0.068 0.1511 0.00469136 Solitary Repeatability 0.45 7.1 14.92 0.07 0.07 0.1556 0.00469135 Solitary Repeatability 0.45 5.6 11.77 0.092 0.092 0.2044 0.00782174 N Repeatability 0.64 17.8 44.60 0.023 0.052 0.0359 0.00117134 N Repeatability 0.53 7.1 16.19 0.006 0.022 0.0113 0.00136132 N Repeatability 0.53 8.3 18.93 0.036 0.061 0.0679 0.00322130 N Repeatability 0.54 8.4 19.33 0.053 0.074 0.0981 0.00383135 Solitary Runup tests 0.45 9.8 20.59 0.082 0.082 0.1822 0.00398136 Solitary Runup tests/propagation 0.45 6.9 14.50 0.076 0.076 0.1689 0.00524137 Solitary Runup tests 0.45 6.4 13.45 0.065 0.065 0.1444 0.00483138 Solitary Runup tests 0.45 4.5 9.45 0.045 0.045 0.1000 0.00476139 Solitary Runup tests 0.45 6.3 13.24 0.054 0.054 0.1200 0.00408146 Solitary Runup tests 0.45 17.1 35.93 0.042 0.042 0.0931 0.00117148 Solitary Runup tests 0.45 5.7 11.98 0.030 0.030 0.0670 0.00252149 Solitary Runup tests 0.45 5.5 11.56 0.027 0.027 0.0590 0.00230135 Solitary Runup tests 0.517 8.2 18.47 0.076 0.076 0.1461 0.00409136 Solitary Runup tests 0.517 8 18.02 0.07 0.070 0.1354 0.00389137 Solitary Runup tests 0.517 7 15.76 0.067 0.067 0.1296 0.00425138 Solitary Runup tests 0.517 9.3 20.94 0.054 0.054 0.1050 0.00259139 Solitary Runup tests 0.517 6.3 14.19 0.053 0.053 0.1016 0.00370146 Solitary Runup tests 0.517 6.7 15.09 0.039 0.039 0.0762 0.00261147 Solitary Runup tests 0.517 5 11.26 0.032 0.032 0.0621 0.00285148 Solitary Runup tests 0.517 4.2 9.46 0.024 0.024 0.0464 0.00254149 Solitary Runup tests 0.517 6.3 14.19 0.027 0.027 0.0514 0.00187135 Solitary Runup tests 0.571 9 21.30 0.080 0.080 0.1405 0.00377136 Solitary Runup tests 0.571 7.9 18.70 0.072 0.072 0.1265 0.00386137 Solitary Runup tests 0.571 8.4 19.88 0.072 0.072 0.1259 0.00362138 Solitary Runup tests 0.571 8.3 19.64 0.070 0.070 0.1224 0.00356139 Solitary Runup tests 0.571 8.1 19.17 0.048 0.048 0.0845 0.00252146 Solitary Runup tests 0.571 5.2 12.31 0.035 0.035 0.0615 0.00285147 Solitary Runup tests 0.571 5 11.83 0.033 0.033 0.0569 0.00275148 Solitary Runup tests 0.571 4.7 11.12 0.027 0.027 0.0472 0.00242149 Solitary Runup tests 0.571 8.5 20.12 0.028 0.028 0.0492 0.00140113 N Runup tests 0.46 8.6 18.27 0.074 0.097 0.1599 0.00531130 N Runup tests 0.46 7.2 15.29 0.073 0.096 0.1585 0.00628131 N Runup tests 0.46 7.6 16.14 0.073 0.097 0.1580 0.00601132 N Runup tests 0.5 7 15.50 0.048 0.079 0.0960 0.00510133 N Runup tests/propagation 0.53 8 18.24 0.029 0.056 0.0545 0.00307280 N Runup tests 0.55 7.9 18.35 0.016 0.055 0.0285 0.00300113 N Runup tests 0.61 8.6 21.04 0.057 0.081 0.0941 0.00385130 N Runup tests 0.61 7.3 17.86 0.059 0.081 0.0965 0.00454131 N Runup tests 0.61 7.3 17.86 0.056 0.079 0.0922 0.00442132 N Runup tests 0.62 7.2 17.76 0.038 0.066 0.0620 0.00372133 N Runup tests 0.63 8.3 20.63 0.023 0.047 0.0371 0.00228280 N Runup tests 0.64 9.1 22.80 0.014 0.050 0.0224 0.00219113 N Runup tests 0.65 9 22.73 0.067 0.091 0.1032 0.00400

522 T. Rossetto et al. / Coastal Engineering 58 (2011) 517–527

Table 1 (continued)

Valve time seriesID*

Wave type Purpose of test Depth(m)

Period(s)

Wavelength(m)

Amplitude(m)

Wave height(m)

a/h(#)

H/L (#)(steepness)

130 N Runup tests 0.65 7.1 17.93 0.070 0.093 0.1084 0.00519131 N Runup tests 0.65 7.1 17.93 0.063 0.083 0.0976 0.00463132 N Runup tests 0.66 7.1 18.07 0.045 0.073 0.0680 0.00404133 N Runup tests 0.68 8.5 21.95 0.026 0.051 0.0379 0.00232280 N Runup tests 0.69 8 20.81 0.014 0.052 0.0207 0.00250307 Mercator*** Profile comparison 0.61 114.65 280.46 0.073 0.130 0.1194 0.00046

523T. Rossetto et al. / Coastal Engineering 58 (2011) 517–527

water can drop and rise in the tank, due to the time necessary for thepressure inside the tank to reach static equilibrium for each positionof the control valve. The solitary waves generated this way cannotdisplay comparable steepnesses.

Despite these differences, the solitary waves follow a similar trendas Synolakis' solitary wave benchmark data for runup (Synolakis,1987), except that for comparable amplitude the new solitary wavesshow a slightly higher runup (Fig. 10). Synolakis (1987) generated areference series of solitary waves in the laboratory using aconventional wave paddle. He measured run-up of these waves overa 1:19.85 slope and derived run-up relationships for breaking andnonbreaking waves. The dataset produced by Synolakis (1987) hasbeen widely used for physical and numerical modelling testing e.g.Borthwick et al. (2006). Run-up levels on a slope of 1:20 weremeasured for a subset of the solitary waves produced by the newtsunami generator. The new experimental data are compared to thoseof Synolakis (1987) in Fig. 10. Although providing a slightly steepertrend-line, the results in Fig. 10 show that the experiments produced atrend in run-up results comparable to the one of Synolakis (1987).According to Madsen and Fuhrman (2008), the effect of wavesteepness on runup should not be significant for such waves. Thiswould suggest that not thewave steepness, but the total wave volumeor energy may play a role in the determination of run-up, at least forthe range of normalised amplitudes tested here (given the differencein wave profiles shown in Fig. 9). Further investigation is required toverify and explain this. The results also provide confidence in theability of the tsunami generator to reproducewave characteristics andeffects similar to those produced by a conventional wave paddle.

Consistency of wave generation was assessed by investigating therepeatability of waveforms. Excellent reproducibility of solitary waves

Fig. 7. Flume setup and general dimension

was possible over the full range of a/h ratios. Example wave profilesfor three repetitions of tests for nine solitary waves of increasing sizeare shown in Fig. 11a. The solitary wave profiles used were smallerthan some of those used during other sections of the testing, but thisensured that it was possible to investigate a full range of a/h ratios,and so observe repeatability for a range of wave kinematics.

4.3. N-wave tests

N-waves are formed by a depression wave followed or precededby an elevation wave. N-waves have been described by Tadepalli andSynolakis (1994, 1996) to account for the first trough that precedesthe positive part of certain tsunami waves and can be seen as twomirror solitary waves on either side of the mean water level. N-wavescan be isosceles (the positive amplitude is the same as the negativeamplitude); have a small trough and a large peak; or vice versa. Theirleading profile is described by:

η xð Þ = εg⋅H x−X2ð Þsech2 γ x−θð Þð Þ j t=0 ð2Þ

where η(x) is the surface elevation, εgb1 is a scaling parameterdefining the crest amplitude H (for comparison with a solitary waveof same height H), θ=X1+ct, and L=X1−X2 (X1 and X2 are notexplicitly defined by Tadepalli and Synolakis, 1994, 1996); howeverX2 is obviously the x position of the inflexion point of the profile,corresponding to η(x=X2)=0 and X1 is the position of a positivesolitary wave of the same amplitude centred on X=X1 at t=0, asdescribed by Synolakis (1987). c is the celerity of the wave and hasbeen set by the authors in Tadepalli and Synolakis (1994, 1996) to beequal to 1, and γ =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3Hp0 = 4

p, p0 is a steepness parameter. Again, p0

s. The slope of the bathymetry is 1/20.

Fig. 10. Comparison between tsunami generator and Synolakis (Kohlhase and Dette,1980) run-up data (R/h is run-up normalised by depth, and a/h is wave amplitudenormalised by depth).Fig. 8. Comparison between theoretical (dashed line) and experimental (full line) sine

waves. Both elevation (y-axis) and distance (x-axis) have been normalised by depth.The experimental wave represented here corresponds to test 27. Depth and waveparameters for this wave are listed in Table 1.

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is not explicitly defined by the authors in Tadepalli and Synolakis(1994, 1996). In Tadepalli and Synolakis (1996) this parameter is setto 1 for comparison of a range of N-waves to Boussinesq (solitary)profiles and Gaussian profiles. All variables are dimensionless(normalised by depth), according to Tadepalli and Synolakis (1994).We will define the period of an N-wave to be the total length of timecontaining 99% of the shape of the wave (trough and peak).

N-waves, especially leading depression N-waves, have not beenstudied previously in the laboratory as no facility has been able toreproduce stable depression waves. N-waves have however aparticular interest here as they can produce steeper positive wavefronts after the initial depression has passed than solitary waves. Thiscan potentially lead to higher impact forces on any structure in thepath of such a wave.

Due to its novel method of wave generation, the tsunami generatorhas the ability to produce waves with depressed components. N-wavesof different shapes and amplitudes were therefore reproduced in thelaboratory (see Table 1). A good agreement was observed forexperimental N-wave (test ID 133) when compared to the theoretical

Fig. 9. Comparison between a generated solitary wave (blue solid), a solitary wave asgenerated by Synolakis (green dashed), and the Boussinesq profile (red dashed)according to Miles (Schmidt-Koppenhagen et al., 2006). Both elevation (y-axis) anddistance (x-axis) have been normalised by depth. The experimental wave representedhere corresponds to test 321. Depth and wave parameters for this wave are listed inTable 1.

leading profile of N-waves as described by Tadepalli and Synolakis(1996), as shown in Fig. 12. This level of agreement is representative ofthe match obtained for other N-wave profiles.

N-waves with relatively short wave periods (7 s to 17.8 s unscaled,see Table 1, for typical N-waves displaying a/h ratios between 0.011and 0.16) were seen to propagate in the tank with minimaltransformations, as shown in Fig. 13. It should be noted here that allshort period waves will not be representative of real tsunami (such asthe Mercator wave) at a 1:100–1:50 scale. These short waves are anecessary point of comparison with N-wave (Tadepalli and Synolakis,1994, 1996) and solitary wave (Miles, 1980) theories, as well as basereference for comparison with longer waves. The initial form of thewave is preserved until the nearshore effects are realised at thebathymetry. The period of the experimental N-waves tested forpropagation is 8 s, generated over an average depth of 0.53 m (seeTable 1). Therefore, we can deduce the approximate wavelength ofthe laboratory N-waves to be 18.2 m. According to Fig. 7, the distancetravelled by the 18 m long wave in the constant depth region of theflume is 15.2 m. Therefore, it is not possible to know with the presentset-up whether the N-waves produced by the new tsunami generatorwould be stable over longer distances. In the flume, a flat bottompropagation region of two or more wavelengths would be necessaryto assess the change or conservation of the wave shape, which is notavailable for these waves in our current setup. Consistency of wavegeneration was assessed by investigating the repeatability of wave-forms. As in the case of the solitary waves, excellent repeatability wasachieved for N-waves, see Fig. 11b.

4.4. The “Mercator” tests

After successfully generating a range of solitary waves and N-waves,the aim of the study was to recreate a single tsunami: the Mercatortsunami record close to the shore, as described in Section 2. This wasthe only historical tsunami signal we attempted to reproduce in thisstudy, as it was the only high resolution profile of a tsunami recordedrelatively close to the shore available at the time of carrying out theseexperiments. Moreover, it effectively matches the profile of a very longN-wave.

The final test on the performance of the new tsunami generatorwas to recreate the time seriesmeasured by the “Mercator” (Fig. 2). Asthis time series is a very long wave, its offshore profile is rapidlyaffected by reflections from the sloping beach. Even so, as the waveshoals up in the nearshore region, the model wave (scale 1/50) andprototype wave profiles prove to be comparable, Fig. 14. The positiveamplitude possible to generate at this scale was 0.073 m, and thenegative amplitude −0.062 m, for a period of 114.6 s. According to

Fig. 11. Repeatability of solitary and N-waves: (a) the profiles obtained from three tests for each of nine different solitary wave heights and (b) the profiles obtained for three tests forfour different N-waves. The experimental waves represented here correspond to tests 192 to 229 for solitary waves, and 230 to 244 for N-waves. Wave parameters for these wavesare listed in Table 1.

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Froude scaling, it is expected that in the same wave at a scale of 1/100the possible period to generate for the Mercator would be about 81 s,its positive amplitude would be 0.036 m and negative amplitudewould be −0.031 m.

Because this wave, even at model scale 1/50, is very long (almost300 m) compared to the propagation length of the flume (about30 m), it is acceptable to compare model and prototype profilesanywhere along the flume.

From Fig. 14 it can be seen that the principal wave characteristics,especially the long trough preceding the tsunami peak, werereproduced well up until the point at which the leading edge wavereturned to the generator. A longer flume would allow waves withgreater periods to propagate without being affected by reflections inthe offshore region. An improved control system might also removethe reflected component and produce waves at a larger scale.

5. Conclusions

The paper has described the evolution of a new facility that wascreated with the aim of generating a nearshore tsunami at scalesbetween 1/100 and 1/50 within a wave flume (using Froude scaling).

Fig. 12. Comparison of a generated N wave and the corresponding theoretical N wave.Both elevation (y-axis) and distance (x-axis) have been normalised by depth. Theexperimental wave represented here corresponds to test 341. Depth and waveparameters for this wave are listed in Table 1.

Through testing, it has been shown that the tsunami generator cangenerate several well-known wave profiles (including a real tsunamias recorded close to the shore) to reasonable accuracies at scales of upto 1/50. The paper also identifies aspects of the current set-up thatneed to be addressed during future research.

Sine waves have been generated with consistent repeatability, forwave periods between 50 s and 200 s. Solitary waves have beengenerated with a/h values of 0.014 to 0.20, and for wave periodsbetween 4.2 s and 17.1 s. The profiles for these solitary waves wereless close to theory than the generated sine waves (a general issuewith steepness was found with the generator, discussed later), butwave run-up levels compared well with published data, and so gaveconfidence in the general wave kinematics. Trough-led N-waves weregenerated to a reasonable level of accuracy for a/h ratios between0.011 and 0.16 for periods ranging between 7 s and 17.8 s (a uniqueachievement for a wave generator). The tsunami generator was alsoshown to reasonably reproduce the wave profile of a major tsunami ata realistic scale. The maximum wavelength corresponding to theMercator recording (2004 tsunami) that was reproduced here was14 km at a scale of 1/50. Table 1 shows the range of a/h ratios andsteepnesses achieved throughout these tests: 26 out 74waves have ana/h ratio of the same order of magnitude as the prototype Mercatorwave (i.e. a/h=0.28), the other waves being one order of magnitudesmaller. All waves have a steepness of the same order of magnitude asthe Mercator wave (i.e. h/L=0.0009). These are promising resultsgiven the purpose of the generator, which is to reproduce tsunamiwaves nearshore and very close to the coast. However, for the longwaves relevant for tsunami in Table 1, only a very small portion of thegenerated wave is contained in the flume which has an effectivelength (depending on the operating depth) of about 30 m only.

A number of areas for improvement in the current set-up andgeneration technique need to form part of future work to beperformed with the tsunami generator. The main issue highlightedwith these tests is the flume length, which should be significantlyincreased to allow the shortest waves to propagate over at least twowavelengths.

These tests found maximum wave height that could be achievedusing the generator. Results suggested that these were limited by thehead of water that could be held within the tank during generation.Increasing the height of the tank (and maybe the performance of thepump) might solve these problems.

Fig. 13. Propagation of a typical short N-wave in the constant depth region. All the recording offshore probes were separated by approximately 1 m. The experimental waverepresented here corresponds to test 341. Wave parameters for this wave are listed in Table 1.

526 T. Rossetto et al. / Coastal Engineering 58 (2011) 517–527

The tank can presently only generate waves of useful accuracywhen operated with an open control system. This can make wavegeneration quite cumbersome if a range of wave profiles need to beinvestigated. In order to perfect the closed loop control system, amethod needs to be developed to measure and interpret water levelvelocities.

So far no comprehensive measurements of the velocity profilebeneath the water surface have been taken for the generated wave.The wave profiles have shown to be reasonably accurate, but greaterconfidence in the wave kinematics (which is essential for accuratewave propagation) cannot be gained without also studying thevelocity profile.

The current wave generation technique also contains no capacityfor wave absorption at the generation point. This inevitably limits thewave length (and so the size and scale) of the waves that can begenerated. Furthermore, general waves have been produced andconsideration of tsunami transformed from deep ocean to nearshorewould require numerical modelling. It is proposed that in a futureversion of the experiments a numerical model be created toaccompany the experiments and closed loop control system designed,using input on size and velocity of any reflected waves to compensatefor reflections within the wave generation. It is proposed to designthis simultaneous generation and absorption by running a much

Fig. 14. Comparisons between a generated short N wave and Mercator (solid) withtheoretical and measured profiles (dashed). The longest wave is affected by reflectionsfrom the slope. The experimental waves represented here correspond to test 133 for theshort N-wave, and test 307 for the Mercator. Wave parameters for these waves arelisted in Table 1.

larger numerical experiment with the location of the experimentalwave-maker embedded within the numerical domain. In this way thenumerical output can be interrogated to determine the necessarybehaviour of the wave-maker. Iteration will be required betweenpredictions from the numerical scheme and experimental runs in thephysical flume to achieve satisfactory results.

Generally speaking, the limitations that have been found are notfunctions of the generation technique per se, but of the specificgeometry and properties of the set-up being used. A taller tank, or alonger flume, would enable longer waves with greater wave heightsto be generated. The current tsunami generator has been shown togenerate reasonably accurate wave profiles for wave periods in excessof 25 s, which is unique within the wave generation community.Many other facilities exist that can create larger waves at bigger scales(the Delta flume in the Netherlands, GWK in Hannover and CIEM inUPC Barcelona), as well as facilities that generate long-period waves(Oregon State University and Port and Airport Research Institute,Yokosuka) but none exists that can produce such long period ortrough-led waves.

Acknowledgements

The experimental work described in this paper has been supportedby EPSRC, HRWallingford and Arup. Pierre-Henri Bazin (Ecole Centralede Lyon), Mervyn Littlewood and Clive Rayfield (HR Wallingford) andDr Tristan Robinson and Tristan Lloyd (UCL) are also thanked for theircontribution to the tsunami generator experiments.

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