Wave characteristic and morphologic effects on the onshore hydrodynamic response of tsunamis

While the destruction caused by a tsunami can vary significantly owing to near- and onshore controls, we have only a limited quantitative understanding of how different local parameters influence the onshore response of tsunamis. Here, a numerical model based on the non-linear shallow water equations is first shown to agree well with analytical expressions developed for periodic long waves inundating over planar slopes. More than 13,000 simulations are then conducted to examine the effects variations in the wave characteristics, bed slopes, and bottom roughness have on maximum tsunami run-up and water velocity at the still water shoreline. While deviations from periodic waves and planar slopes affect the onshore dynamics, the details of these effects depend on a combination of factors. In general, the effects differ for breaking and non-breaking waves, and are related to the relative shift of the waves along the breaking–non-breaking wave continuum. Variations that shift waves toward increased breaking, such as steeper wave fronts, tend to increase the onshore impact of non-breaking waves, but decrease the impact of already breaking waves. The onshore impact of a tsunami composed of multiple waves can be different from that of a single wave tsunami, with the largest difference occurring on long, shallow onshore topographies. These results demonstrate that the onshore response of a tsunami is complex, and that using analytical expressions derived from simplified conditions may not always be appropriate.     

Run-Up of a Solitary Tsunami Wave on a Sloping Coast

Within the framework of the nonlinear theory of long waves, we perform the numerical analysis of the one-dimensional run-up of solitary tsunami waves upon a plane sloping coast. We study the dependences of the run-up heights on the parameters of waves at the entrance of the shelf zone and on the slope of the coast. The run-up heights of tsunami waves are estimated for the bottom topography typical of the south coast of the Crimean Peninsula. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 11–18, July–August, 2005.     

Kinematics of breaking tsunami wavefronts: A data set from large scale laboratory experiments

This paper provides an overview of a new large scale laboratory data set on the kinematics of breaking tsunami wavefronts. The aim of the experiments was to provide an open access data set for model testing, calibration and verification, with particular emphasis on fluid kinematics in the wave breaking and run-up (swash) zones. The experiments were performed over a composite slope in the tsunami wave basin at the O. H. Hinsdale Wave Research Laboratory at Oregon State University. Data for ten different wave conditions were collected, including non-breaking and breaking waves, and both shore breaks and fully developed long bores.Surface elevation and fluid kinematics were measured with a closely spaced array of surface piercing wave gauges, non-contact ultrasonic wave gauges and four 3-D side-looking Acoustic Doppler Velocimeters. The array was traversed from the nearshore (depth = 0.2 m) to the middle and upper run-up zone, providing kinematic data at 30 cross-shore locations. Video was also recorded from 4 cameras covering the propagation, breaking and run-up zones. Surface elevation, flow velocities and the wave maker displacement were also recorded to provide offshore boundary conditions.The experiments include conditions with wave heights up to 0.55 m, notional wave periods up to 20 s and run-up lengths of up to 15.2 m on a 1/30 slope. In terms of the slope in the shoaling and breaker zones, the data correspond to Iribarren numbers in the range of 0.26–5.6. Raw, calibrated and processed data are stored with open access within the OSU Tsunami Wave Basin Experiment Notebook, which provides full access to all the wave maker control signals, data, instrument coordinates, and processing and plotting software. This paper serves as an introduction to the data set, demonstrates data quality and provides an initial analysis of some key parameters that govern the impact of tsunami events, including run-up versus offshore wave conditions and nearshore bore height, the maximum inundation depths at the original shoreline position, and the time to maximum inundation depth and flow reversal. Examples of temporal and convective accelerations and turbulent flow components are also presented to illustrate further details of the kinematics.     

On the run-up and back-wash processes of single and double solitary waves — An experimental study

The run-up and back-wash processes of single and double solitary waves on a slope were studied experimentally. Experiments were conducted in three different wave flumes with four different slopes. For single solitary wave, new experimental data were acquired and, based on the theoretical breaking criterion, a new surf parameter specifically for breaking solitary waves was proposed. An equation to estimate maximum fractional run-up height on a given slope was also proposed. For double solitary waves, new experiments were performed by using two successive solitary waves with equal wave heights; these waves were separated by various durations. The run-up heights of the second wave were found to vary with respect to the separation time. Particle image velocimetry measurements revealed that the intensity of the back-wash flow generated by the first wave strongly affected the run-up height of the second wave. Showing trends similar to that of the second wave run-up heights, both the back-wash breaking process of the first wave and the reflected waves were strongly affected by the wave–wave interaction. Empirical run-up formula for the second solitary wave was also introduced.     

Relatioship between the intensity of tsunami and the location of the epicentre of underwater earthquakes near the continental slope of the South Coast of Crimea

Within the framework of the nonlinear theory of one-dimensional long waves, we performed the numerical analysis of the dependence of the intensity of tsunami on the shelf of the South Coast of Crimea on the location of the epicentre of underwater earthquakes near the continental slope of the basin. The calculations were carried out for the parameters of the model corresponding to the Yalta tsunami of September 12, 1927. It is shown that, for the same magnitude of the earthquake, the smaller the distance from its epicentre to the coastal line, the lower tsunami waves in the coastal zone and the smaller their vertical run-up. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Numerical investigation of tsunami-like wave hydrodynamic characteristics and its comparison with solitary wave

Solitary waves have been commonly used as an initial condition in the experimental and numerical modelling of tsunamis for decades. However, the main component of a tsunami waves acts at completely different spatial and temporal scales than solitary waves. Thus, use of solitary waves as approximation of a tsunami wave may not yield realistic model results, especially in the coastal region where the shoaling effect restrains the development of the tsunami wave. Alternatively, N-shaped waves may be used to give a more realistic approximation of the tsunami wave profile. Based on the superposition of the sech²(*) waves, the observed tsunami wave profile could be approximated with the N-shaped wave method, and this paper presents numerical simulation results based on the tsunami-like wave generated based on the observed tsunami wave profile measured in the Tohoku tsunami. This tsunami-like wave was numerically generated with an internal wave source method based on the two-phase incompressible flow model with a Volume of Fluid (VOF) method to capture the free surface, and a finite volume scheme was used to solve all the governing equations. The model is first validated for the case of a solitary wave propagating within a straight channel, by comparing its analytical solutions to model results. Further, model comparisons between the solitary and tsunami-like wave are then made for (a) the simulation of wave run-up on shore and (b) wave transport over breakwater. Comparisons show that use of these largely different waveform shapes as inputs produces significant differences in overall wave evolution, hydrodynamic load characteristics as well as velocity and vortex fields. Further, it was found that the solitary wave uses underestimated the total energy and hence underestimated the run-up distance.     

Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

珠江三角洲快速客船船行波模拟及其爬高研究

采用不规则波生波技术模拟珠江三角洲快速客船实测船行波,分别在波浪水槽和波浪水池中进行了船行波模拟试验研究。确定了不同波要素、不同入射角以及不同护岸坡比、平台宽窄、护面层结构等对船行波在斜坡护岸上的爬高影响,取得了船行波在斜坡式护岸上爬高的经验关系式。为珠江三角洲内河航道快速客船船行波作用下护坡的设计提供参考依据。     

Flow fields in reflected waves at a sloped sea wall

Wave run-up, and flow visualization experiments were conducted with a 1:2 sloped sea wall model. The visualization experiments gave an overview of flow fields in reflected, non-breaking conditions. Maximum particle velocities were found to be significantly smaller than suggested in the literature. Downrush produced a fast sheet flow, extending down to the toe of the sea wall. This created a ‘reverse’ breaker during the retreat of the initially non-breaking wave, which explains the high-energy dissipation rates for non-breaking waves reported in the literature. Embankments may therefore be exposed to wave impact pressures in areas up to 1.18H₀ below MWL.     

Tsunami generation,propagation, and run-up with a high-order Boussinesq model

In this work we extend a high-order Boussinesq-type (finite difference) model, capable of simulating waves out to wavenumber times depth kh < 25, to include a moving sea-bed, for the simulation of earthquake- and landslide-induced tsunamis. The extension is straight forward, requiring only an additional term within the kinematic bottom condition. As first test cases we simulate linear and nonlinear surface waves generated from both positive and negative impulsive bottom movements. The computed results compare well against earlier theoretical, numerical, and experimental values. Additionally, we show that the long-time (fully nonlinear) evolution of waves resulting from an upthrusted bottom can eventually result in true solitary waves, consistent with theoretical predictions. It is stressed, however, that the nonlinearity used far exceeds that typical of geophysical tsunamis in the open ocean. The Boussinesq-type model is then used to simulate numerous tsunami-type events generated from submerged landslides, in both one and two horizontal dimensions. The results again compare well against previous experiments and/or numerical simulations. The new extension compliments recently developed run-up capabilities within this approach, and as demonstrated, the model can therefore treat tsunami events from their initial generation, through their later propagation, and final run-up phases. The developed model is shown to maintain reasonable computational efficiency, and is therefore attractive for the simulation of such events, especially in cases where dispersion is important.     

Historical tsunami in the Makran Subduction Zone off the southern coasts of Iran and Pakistan and results of numerical modeling

Tsunami hazard in the Makran Subduction Zone (MSZ), off the southern coasts of Iran and Pakistan, was studied by numerical modeling of historical tsunami in this region. Although the MSZ triggered the second deadliest tsunami in the Indian Ocean, among those known, the tsunami hazard in this region has yet to be analyzed in detail. This paper reports the results of a risk analysis using five scenario events based on the historic records, and identifies a seismic gap area in western Makran off the southern coast of Iran. This is a possible site for a future large earthquake and tsunami. In addition, we performed numerical modeling to explain some ambiguities in the historical reports. Based on the modeling results, we conclude that either the extreme run-up of 12–15 m assigned for the 1945 Makran tsunami in the historical record was produced by a submarine landslide triggered by the parent earthquake, or that these reports are exaggerated. The other possibility could be the generation of the huge run-up heights by large displacements on splay faults. The results of run-up modeling reveal that a large earthquake and tsunami in the MSZ is capable of producing considerable run-up heights in the far field. Therefore, it is possible that the MSZ was the source of the tsunami encountered by a Portuguese fleet in Dabhul in 1524.     

The influence of seaward boundary conditions on swash zone hydrodynamics

The influence of the seaward boundary condition on the internal swash hydrodynamics is investigated. New numerical solutions of the characteristics form of the nonlinear shallow-water equations are presented and applied to describe the swash hydrodynamics forced by breaking wave run-up on a plane beach. The solutions depend on the specification of characteristic variables on the seaward boundary of the swash zone, equivalent to prescribing the flow depth or the flow velocity. It is shown that the analytical solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. J. Fluid Mech. 16, 113–125] is a special case of the many possible solutions that can describe the swash flow, but one that does not appear appropriate for practical application for real waves. The physical significance of the boundary conditions is shown by writing the volume and momentum fluxes in terms of the characteristic variables. Results are presented that illustrate the dependence of internal flow depth and velocity on the boundary condition. This implies that the internal swash hydrodynamics depend on the shape and wavelength of the incident bore, which differs from the hydrodynamic similarity inherent in the analytical solution. A solution appropriate for long bores is compared to laboratory data to illustrate the difference from the analytical solution. The results are important in terms of determining overwash flows, flow forces and sediment dynamics in the run-up zone.     

The role of bottom friction in models of nonbreaking tsunami wave runup on the shore

The role of bottom friction in the runup of nonbreaking long waves on the shore is analyzed. The case of the normal incidence of monochromatic waves is considered. The relief of the model region consists of an even horizontal bottom area conjugated with a flat slope. The energy dissipation is estimated as the work of bottom friction forces over the wave field obtained using the known analytical solution based on the Carrier-Greenspan transforms. Estimates of energy losses for waves whose periods are typical for tsunami waves have been obtained. The energy dissipation is shown to be not concentrated in the shore line area as a rule. The question about the practicability of using partially reflecting boundary conditions on the coast to take into account the bottom friction in large-scale models of tsunami propagation is considered.     

Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model

This paper presents CCHE2D-NHWAVE, a depth-integrated non-hydrostatic finite element model for simulating nearshore wave processes. The governing equations are a depth-integrated vertical momentum equation and the shallow water equations including extra non-hydrostatic pressure terms, which enable the model to simulate relatively short wave motions, where both frequency dispersion and nonlinear effects play important roles. A special type of finite element method, which was previously developed for a well-validated depth-integrated free surface flow model CCHE2D, is used to solve the governing equations on a partially staggered grid using a pressure projection method. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed based on the partially staggered grid. In addition, a simple and efficient wetting and drying algorithm is implemented to deal with the moving shoreline. The model is first verified by analytical solutions, and then validated by a series of laboratory experiments. The comparison shows that the developed wave model without the use of any empirical parameters is capable of accurately simulating a wide range of nearshore wave processes, including propagation, breaking, and run-up of nonlinear dispersive waves and transformation and inundation of tsunami waves.     

植被斜坡岸滩海啸波消减数值模拟研究

An explicit one-dimensional model based on the shallow water equations(SWEs) was established in this work to simulate tsunami wave propagation on a vegetated beach. This model adopted the finite-volume method(FVM)for maintaining the mass balance of these equations. The resistance force caused by vegetation was taken into account as a source term in the momentum equation. The Harten–Lax–van Leer(HLL) approximate Riemann solver was applied to evaluate the interface fluxes for tracing the wet/dry transition boundary. This proposed model was used to simulate solitary wave run-up and long-periodic wave propagation on a sloping beach. The calibration process suitably compared the calculated results with the measured data. The tsunami waves were also simulated to discuss the water depth, tsunami force, as well as the current speed in absence of and in presence of forest domain. The results indicated that forest growth at the beach reduced wave energy loss caused by tsunamis. A series of sensitivity analyses were conducted with respect to variable parameters(such as vegetation densities, wave heights, wave periods, bed resistance, and beach slopes) to identify important influences on mitigating tsunami damage on coastal forest beach.     

Correlation between the intensity of tsunami in the Black Sea and the magnitude of underwater earthquakes

We perform the analysis of tsunami waves in the shelf zone of the Crimean peninsula generated by underwater earthquakes whose epicentres are located near the lower boundary of the continental slope. For this purpose, we use a one-dimensional nonlinear dissipative numerical model of long waves. The investigated distributions of the depth of the basin correspond to four points of the south coast of the Crimean peninsula. We use the empirical dependences of parameters of the sources of tsunami waves on the magnitude of the earthquake obtained earlier for the Pacific Ocean. It is shown that the height, vertical climb, and duration of tsunami waves increase with the magnitude of the earthquake. For equal magnitudes of the earthquake, the highest tsunamis on the south coast of the Crimea are observed between Alushta and Yalta. We also deduced a generalized regression dependence of the height of tsunami waves near the coast on the magnitude of the earthquake. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Equilibrium beach profiles under breaking and non-breaking waves

Simple theoretical models to determine the equilibrium profile shape under breaking and non-breaking waves are presented. For the case of breaking waves, it is assumed that the seaward transport in the undertow is locally balanced by a net vertical sedimentation, so that no bottom changes occur at equilibrium. The parameterization of the water and sediment flux in the surf zone yields a power curve for the equilibrium profile with a power of 2/3, which is in agreement with previous field investigations on surf zone profile shapes. Three different models were developed to derive the profile shape under non-breaking waves, namely (1) a variational formulation where the wave energy dissipation in the bottom boundary layer is minimized over the part of the profile affected by non-breaking waves, (2) an integration of a small-scale sediment transport formula over a wave period where the slope conditions that yield zero net transport determine equilibrium, and (3) a conceptual formulation of mechanisms for onshore and offshore sediment transport where a balance between the mechanisms defines equilibrium conditions. All three models produced equilibrium profile shapes of power-type with the power typically in the range 0.15–0.30. Comparison with field data supported the results obtained indicating different powers for the equilibrium profile shape under breaking and non-breaking waves.     

海堤坡角变化对海啸波传播过程影响数值分析

针对近岸海域极端海况的防灾减灾问题,准确模拟追踪海啸波传播过程,再现液面局部射流、崩破波等波面湍动现象。建立SPH数值水槽,边界条件基于固壁粒子法,减少海堤坡角改变对计算域精度的影响,讨论粒子间距设置对模拟精度的影响。模拟7种不同海堤坡角下波浪的爬高与衰减情况,讨论了海堤坡角变化对消波系数的影响。当粒子间距设置为0.002 m时,模型能准确地捕捉海啸波的强非线性现象。随着海堤坡角增大,海啸波峰值爬升率增大,波浪越堤后因崩破波的产生,波能衰减进一步加剧。当坡角较小时,消波系数随坡角的增大提升明显,而后趋于缓慢增长。     

Laboratory-scale generation of tsunami and long waves

Physical modeling of long waves in laboratories is still a valuable and trustworthy option to study long wave propagation, run-up and near-shore dynamics, and complex nonlinear interactions of approaching wave and macroroughness elements on the shore. Yet, problems develop if full-scale measured time series of real tsunami or numerically derived time series are to be adequately modeled in a timewise meaningful and scaled experiment. Hence, an in-depth review of the state-of-the-art long wave generation methods in laboratory wave flumes and basins is conducted. The study reveals that improved laboratory techniques could significantly contribute to enhance the accuracy and applicability of experimental tests. This would give important information on the interaction between the shoreline and infrastructures on land in order to deduce valuable information on the topic of tsunami inundation processes or wave-induced impacts on houses. In this light, a novel wave generation technique using high-capacity pipe pumps under some control and a loop-feedback control is meticulously developed and discussed. The wave generation facility is successfully tested for single sinusoidal leading depression waves as well as for prolonged solitary and leading depression N-waves of varying duration. The long wave generation technique is further assessed in terms of its capability to generate long waves abstracted from prototype conditions. The influence of controller settings on the resulting waves is discussed.