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Landslides and landslide-generated tsunami waves arbitrarily happen and cause tremendous hazards to human lives worldwide. Among the recent landslide tsunami events, the rigid submarine landslide sources are becoming more and more concerned due to their mysteries. Dynamical properties of rigid submarine landslides (e.g., velocity) play an important role in the generated tsunami waves. In this study, an empirical velocity profile of rigid submarine landslide-generated waves on an inclined plane is proposed. This new velocity profile is suggested from the velocity profile in a physical experiment of the horizontal rigid submarine landslidegenerated waves. A new FLOW-3D HYDRO package is employed to conduct the rigid submarine landslidegenerated waves experiment. We first verified the chosen numerical model to the experimental data of rigid submarine landslides moving horizontally. Following the rigid velocity profile on the horizontal plane, we propose a new method to apply it on the inclined plane. The error norm technique is used to find out the empirical velocity profile among 10 critical velocity profiles applied. The novel empirical velocity profile of the critical case of m = 3 as well as critical velocity value of Vc = 0.82 m/s is used to generate tsunami waves, which are in good agreement with the experimental data and better than those of other similar three-dimensional numerical models. [ABSTRACT FROM AUTHOR]

The urgent necessity to fortify coastal regions and safeguard both the natural environment and key coastal infrastructure underscores the significance of structural measures in coastal engineering. Among these, the seawall reigns as the primary fortification method. This study aims to elucidate the impact of a stepped structure on the propagation and overtopping of solitary waves when they encounter an impermeable seawall. The investigation has been conducted using ANSYS Fluent, a widely recognized commercial software. Although previous researchers have extensively used the two-dimensional volume of fluid (VOF) model, based on the Reynolds-Averaged Navier-Stokes (RANS) equations and the k-e turbulence closure solver, this study fills the gap in the understanding of the stepped structure's effect. It shows a commendable agreement with experimental results, proving its reliability. Simulations were executed with varied configurations of stepped structures (Step width Sw=0.6 m, 1.2 m, 1.8 m, and Step height Sh=0.3 m, 0.6 m, 0.9 m), emulating tsunami waves of constant wave height and water depth over a stepped structure on a 1:20 sloped beach. Initially, the accuracy of the results was substantiated by comparing them with experimental and numerical data of the free surface and the distribution of the pressure field on the seawall. Numerical simulations, incorporating varying wave heights, water depths, and step heights, were performed to scrutinize the evolution of waves and the pressure exerted by waves impacting the seawall. [ABSTRACT FROM AUTHOR]

Mangroves are crucial for protecting coastal areas against extreme disasters such as tsunamis and storm surges. An experimental study was conducted to determine how mangroves can mitigate the tsunami wave propagation. The test was performed in a flume, where mangrove models were installed on a slope, and dam-burst waves were used to simulate tsunami waves. To study how mangrove forests reduce the impact of tsunamis, this paper measured the heights of the incoming waves under different initial conditions (tsunami wave intensity and initial water depth) and plant factors (arrangement and distribution density) and described the reduction process. The results show that, after passing through the mangrove, the tsunami bore height will decrease within a certain range as the initial water depth increases. However, there is no correlation between the increase of inundation level and the drop of water level. The bore height attenuation is more significant at higher density of mangroves, but after tsunami passing through the mangroves, the relative bore height will decrease. When the distribution density of mangroves is constant, the wave attenuation at different locations (before, on and after the slope) shows different relationships with the initial water depth and wave height for different models. The transmission coefficient (Ki) shows a parabolic correlation with its density. The proportion of the energy loss caused by the mangrove resistance to the total energy (Eb) is defined as Cm2. The variation trend of Cm2 corresponds to the tsunami wave energy attenuation rate (Ca) and Ki. [ABSTRACT FROM AUTHOR]

To study the mechanism of tsunami wave forces on round-ended piers and the force calculation method, a series of round-ended piers with different ratios of length to width (L/D , D is the diameter of the semicircle at both ends, L is the rectangular length between two end semicircles) are taken as the research object of this study. Firstly, a series of tsunami waves are experimentally generated over dry-bed and wet-beds with different water depths in a dam-break flume. Secondly, the pressure time histories on the outer sides of the round-ended piers are presented and explored. After that, the characteristics of the resultant force and moment at the pier bottom, the maximum force and moment as well as the force and moment in the quasi-steady stage, are obtained and analyzed successively, to explore the influence of L/D. Furthermore, the influences of L/D to the mechanism of tsunami wave forces on round-ended piers are exhaustively investigated. The study indicates that, with the increase of L/D , almost unaffected pressure time histories on front side, obvious time delay in the impulsive stage and a slight increase in amplitude in the quasi-steady stage on the back side, are observed, accordingly L/D has a significant influence on the generated force and moment on round-ended piers. Finally, the calculation method of the maximum tsunami wave forces on round-ended piers and the corresponding coefficients are provided. This study can contribute to the safety design of round-ended piers in tsunami-prone areas. • he pressure time histories on the front side and back side of round-ended piers are obtained and analyzed. • The time histories of forces and moments as well as the corresponding dimensionless coefficients are presented and explored. • The calculation methods for maximum force and moment on round-ended piers are proposed and related coefficients are suggested. [ABSTRACT FROM AUTHOR]

This article presents an algorithm for registering the arrival of tsunami waves based on the operational data of sea level measurements. The algorithm was developed using the fuzzy mathematics approach and implies an expert assessment while the procedure of adjustment and tuning. Its adaptive capabilities allow to function in accordance with the current preceding the arrival of a tsunami wave. The presented algorithm tends to be a universal tool that can be used for detecting the restructuring of processes according to measurements of their characteristics in time. [ABSTRACT FROM AUTHOR]

This article presents a methodology for calculating extreme loads (positive and negative) acting on an object during the direct impact of a tsunami wave. The methodology is based on an analysis of the results of physical modeling of the interaction of long tsunami-type waves with a storage unit of compressed natural gas for various parameters of the object and external influence being studied. [ABSTRACT FROM AUTHOR]

This companion paper presents the results of a series of numerical experiments examining the effects of a mitigation canal on the hydrodynamics of a tsunami-like turbulent bore proceeding over a horizontal bed. The hydraulic bores were generated by a dam-break setup which employed impoundment depths of do = 0.20 m, 0.30 m, and 0.40 m. The bore propagated downstream of the impoundments in the flume and interacted with a canal with varying geometry located downstream. The bore then left the flume through a drain located further downstream of the canal. In this study, the effect of the canal depth on the specific momentum and specific energy of hydraulic bores passing over a rectangular canal is numerically studied. The canal width was kept constant, at w = 0.6 m, while the canal depths were varied as follows: d = 0.05 m, 0.10 m, and 0.15 m. The time history of mean flow energy during the bore's passing over the mitigation canal indicates that the jet stream of the maximum mean flow energy is controlled by the canal depth. The time required to dissipate the jet stream of the maximum vorticity, the turbulent kinetic energy, and the energy dissipation rate all increased as the canal depth decreased. The effect of canal orientation on the bore hydrodynamics was also numerically investigated, and it was found that the impulsive momentum and specific energy reached the highest values for canal orientations of 45 and 60 degrees. For the same canal depth, the highest peak specific momentum occurred with the highest degree of canal orientation (θ = 60°). [ABSTRACT FROM AUTHOR]

This companion paper investigates the hydrodynamics of turbulent bores that propagate on a horizontal plane and have a striking resemblance to dam break waves and tsunami-like hydraulic bores. The focus of this paper is on the propagation of a turbulent bore over a mitigation canal using both laboratory experiments and numerical simulations. In the first part of this paper, the effects of canal depth on the time histories of wave height and velocity were experimentally investigated, and the experimental results were used for the validation of the numerical model. The rapid release of water from an impoundment reservoir at depths of do = 0.30 m and 0.40 m generated bores analogous to tsunami-induced inundations. The time histories of the wave heights and velocities were measured at 0.2 m upstream and at 0.2 m and 0.58 m downstream of the canal to study the energy dissipation effect of the mitigation canal. The recorded time series of the water surface levels and velocities were compared with simulation outputs, and good agreement was found between the experimental and numerical water surface profiles, with a Root Mean Square Error (RMSE) of less than 6.7% and a relative error of less than 8.4%. Three turbulence models, including the standard k-ε, Realizable k-ε, and RNG k-ε, were tested, and it was found that all these models performed well, with the standard k-ε model providing the highest accuracy. The velocity contour plots of the mitigation canal with different depths showed jet streams of different sizes in the shallow, medium-depth, and deep canals. The energy dissipation and air bubble entrainment of the bore as it plunged downward into the canal increased as the canal depth increased, and the jet stream of the maximum bore velocity decreased as the canal depth increased. It was found that the eye of the vortex created by the bore in the canal moved in the downstream direction and plunged downward in the middle of the canal, where it then began to separate into two smaller vortices. [ABSTRACT FROM AUTHOR]

This study delves into the intricate dynamics of tsunami wave run-up, with a specific focus on nonlinear wave behavior. Leveraging the self-manipulated interFoam solver, we scrutinized various factors influencing run-up, including surf-similarity, wave non-linearity and beach slope. The variation in run-up height with surf-similarity follows a consistent pattern for waves of different non-linearity: an initial increase followed by a decrease as surf-similarity intensifies. Low surf-similarity waves tend to exhibit intensive run-up with wave breaking, while high surf-similarity waves display gentler and prolonged run-up and run-down processes. Under fixed surf-similarity, tsunamis on mild slopes break more easily, yielding lower run-up heights compared to steep slopes. Furthermore, waves with higher non-linearity are more prone to breaking compared to waves with similar surf-similarity but lower non-linearity. We calibrate Madsen & Schäffer (2010)'s analytical solution and introduce semi-empirical methods for conservative estimation of run-up height and velocity, along with an empirical formula for estimating swash periods. This approach utilizes wave data along a sloping beach, eliminating the need for arbitrary input from the beach's toe or offshore areas. Notably, our methods demonstrate feasibility on run-up height estimation for waves with non-linearity up to 1.3, indicating its applicability across a wide range of conditions. Despite inherent limitations, the proposed methods and formula signify potential additions to the toolkit for tsunami forecasts and hazard assessment, providing insights and alternative avenues for further exploration in this intricate field. • A systematic exploration of tsunami waves covering a broad range of surf-similarity, wave non-linearity and slope. • A self-manipulated interFoam solver to generate strongly nonlinear waves. • Under fixed surf-similarity, the beach slope significantly impacts wave run-up. • Empirical methods are proposed for estimations of run-up height, velocity and swash period. • The methods allow applying wave data at various locations along a sloping beach. [ABSTRACT FROM AUTHOR]

We present a narrative of the eruptive events culminating in the cataclysmic January 15, 2022 eruption of Hunga Tonga-Hunga Ha'apai Volcano by synthesizing diverse preliminary seismic, volcanological, sound wave, and lightning data available within the first few weeks after the eruption occurred. The first hour of eruptive activity produced fast-propagating tsunami waves, long-period seismic waves, loud audible sound waves, infrasonic waves, exceptionally intense volcanic lightning and an unsteady volcanic plume that transiently reached—at 58 ​km—the Earth's mesosphere. Energetic seismic signals were recorded worldwide and the globally stacked seismogram showed episodic seismic events within the most intense periods of phreatoplinian activity, and they correlated well with the infrasound pressure waveform recorded in Fiji. Gravity wave signals were strong enough to be observed over the entire planet in just the first few hours, with some circling the Earth multiple times subsequently. These large-amplitude, long-wavelength atmospheric disturbances come from the Earth's atmosphere being forced by the magmatic mixture of tephra, melt and gasses emitted by the unsteady but quasi-continuous eruption from 0402±1–1800 UTC on January 15, 2022. Atmospheric forcing lasted much longer than rupturing from large earthquakes recorded on modern instruments, producing a type of shock wave that originated from the interaction between compressed air and ambient (wavy) sea surface. This scenario differs from conventional ideas of earthquake slip, landslides, or caldera collapse-generated tsunami waves because of the enormous (∼1000x) volumetric change due to the supercritical nature of volatiles associated with the hot, volatile-rich phreatoplinian plume. The time series of plume altitude can be translated to volumetric discharge and mass flow rate. For an eruption duration of ∼12 ​h, the eruptive volume and mass are estimated at 1.9 ​km3 and ∼2 900 ​Tg, respectively, corresponding to a VEI of 5–6 for this event. The high frequency and intensity of lightning was enhanced by the production of fine ash due to magma—seawater interaction with concomitant high charge per unit mass and the high pre-eruptive concentration of dissolved volatiles. Analysis of lightning flash frequencies provides a rapid metric for plume activity and eruption magnitude. Many aspects of this eruption await further investigation by multidisciplinary teams. It represents a unique opportunity for fundamental research regarding the complex, non-linear behavior of high energetic volcanic eruptions and attendant phenomena, with critical implications for hazard mitigation, volcano forecasting, and first-response efforts in future disasters.

In this paper, we study a dissipation of solitary wave due to mangrove forest by using numerical simulation. Here, the solitary wave is chosen to represent tsunami wave form. To simulate the wave dynamic, we use the non-dispersive Nonlinear Shallow Water Equations (NSWE). The model is implemented numerically by using finite volume method in a momentum conservative staggered grid. By using the proposed numerical scheme, the numerical code is able to simulate solitary wave breaking phenomenon. Wave dissipation due to mangrove forest is modelled as bottom roughness with an approximate value of manning roughness, which is derived from the classical Morisson’s formula. To test the modelled dissipation by mangrove forest, we reconstruct a physical experiment in hydrodynamic laboratory where a solitary wave propagates above a sloping bottom, which has a parameterized mangrove in the shallower part. Two cases are performed to test the performance of the numerical implementation, i.e. the non-breaking and breaking solitary waves. Results of simulation agree quite well with the measurement data. The results of simulation are also analyzed quantitatively by calculating errors as well as correlation with the measurement data. Moreover, to investigate effects of wave steepness on solitary wave, to the reduction of wave energy, we perform numerical investigation. Various solitary waves with different wave steepness are simulated to see their effects on amplitude and energy reduction due to mangrove forest.

This companion paper investigates the hydrodynamics of turbulent bores that propagate on a horizontal plane and have a striking resemblance to dam break waves and tsunami-like hydraulic bores. The focus of this paper is on the propagation of a turbulent bore over a mitigation canal using both laboratory experiments and numerical simulations. In the first part of this paper, the effects of canal depth on the time histories of wave height and velocity were experimentally investigated, and the experimental results were used for the validation of the numerical model. The rapid release of water from an impoundment reservoir at depths of do = 0.30 m and 0.40 m generated bores analogous to tsunami-induced inundations. The time histories of the wave heights and velocities were measured at 0.2 m upstream and at 0.2 m and 0.58 m downstream of the canal to study the energy dissipation effect of the mitigation canal. The recorded time series of the water surface levels and velocities were compared with simulation outputs, and good agreement was found between the experimental and numerical water surface profiles, with a Root Mean Square Error (RMSE) of less than 6.7% and a relative error of less than 8.4%. Three turbulence models, including the standard k-ε, Realizable k-ε, and RNG k-ε, were tested, and it was found that all these models performed well, with the standard k-ε model providing the highest accuracy. The velocity contour plots of the mitigation canal with different depths showed jet streams of different sizes in the shallow, medium-depth, and deep canals. The energy dissipation and air bubble entrainment of the bore as it plunged downward into the canal increased as the canal depth increased, and the jet stream of the maximum bore velocity decreased as the canal depth increased. It was found that the eye of the vortex created by the bore in the canal moved in the downstream direction and plunged downward in the middle of the canal, where it then began to separate into two smaller vortices.

This companion paper presents the results of a series of numerical experiments examining the effects of a mitigation canal on the hydrodynamics of a tsunami-like turbulent bore proceeding over a horizontal bed. The hydraulic bores were generated by a dam-break setup which employed impoundment depths of do = 0.20 m, 0.30 m, and 0.40 m. The bore propagated downstream of the impoundments in the flume and interacted with a canal with varying geometry located downstream. The bore then left the flume through a drain located further downstream of the canal. In this study, the effect of the canal depth on the specific momentum and specific energy of hydraulic bores passing over a rectangular canal is numerically studied. The canal width was kept constant, at w = 0.6 m, while the canal depths were varied as follows: d = 0.05 m, 0.10 m, and 0.15 m. The time history of mean flow energy during the bore’s passing over the mitigation canal indicates that the jet stream of the maximum mean flow energy is controlled by the canal depth. The time required to dissipate the jet stream of the maximum vorticity, the turbulent kinetic energy, and the energy dissipation rate all increased as the canal depth decreased. The effect of canal orientation on the bore hydrodynamics was also numerically investigated, and it was found that the impulsive momentum and specific energy reached the highest values for canal orientations of 45 and 60 degrees. For the same canal depth, the highest peak specific momentum occurred with the highest degree of canal orientation (θ = 60°).

Submarine volcanic eruptions have the potential to generate tsunamis, which can cause destruction well beyond the range of the eruption itself. Here, we present a series of underwater eruption experiments in which a non‐condensing gas was injected into a water tank with a range of water depths and applied pressures. This study proposes an effective scaled water depth and categorizes underwater eruptions into three types: deep‐water eruptions, intermediate‐water eruptions, and shallow‐water eruptions. In deep‐water eruptions, most of the energy is dissipated within the water column before the plume reaches the surface, and negligible waves are generated. In intermediate‐water eruptions, reductions in water depth reduce the loss of energy to the water column, leaving more energy available for wave generation. This causes an increase in wave heights as water shallows, up to a point. In sufficiently shallow‐water cases, the water depth is so small that almost all of the energy from the eruptive jet or plume passes through the water and is dissipated into the air, so there is only small wave‐making potential, even with relatively intense source strength. Therefore, there exists a critical water depth at which an eruption with a given source intensity will generate the largest waves. That depth lies at the boundary between the intermediate‐ and shallow‐depth regimes, where the energy available for wave generation is at a maximum. This research reveals fundamental wave generation mechanisms related to underwater gas eruptions, thereby extending our understanding of submarine volcanic tsunami generation and providing a foundation for future hazard assessment. Plain Language Summary: Tsunamis are most often generated by seafloor motion due to earthquakes. However, tsunamis generated by underwater volcanic eruptions are less common and are often underestimated by researchers. In order to study the waves generated by short‐lived underwater volcanic eruptions, we injected compressed air from a submerged vent into a tank filled with water in the laboratory. We find that for an eruption of a given source intensity, the maximum wave heights first increase and then decrease as water depths increase from shallow to deep. This is because the ejected jet passes through the free surface and its energy is lost in air in shallow‐water depths, while most of the energy is lost underwater during the plume motion in deep‐water depths. Therefore, there is an optimal depth where an eruption with a given source intensity can generate the largest waves. These results are significant because they show the most dangerous conditions in tsunamis generated by submarine volcanic eruptions. The riskiest conditions need to be better accounted for in the future tsunami risk assessments. Key Points: We present new physical experiments to model waves generated by underwater gas eruptionsBased on an effective scaled depth, underwater eruptions are divided into three types: deep‐, intermediate‐, and shallow‐water eruptionsWe hypothesize that there is a critical water depth at which a subaqueous eruption of a given intensity will generate the largest waves [ABSTRACT FROM AUTHOR]

In this study, taking the reclamation engineering in the South China Sea as the background, several wave flume experiments (geometrical similarity scale is set as 1:10) are performed to study the dynamics and the stability of a reclaimed calcareous sand foundation and the breakwater built on it, under the impacting of tsunami wave. Tsunami wave is similarly simulated by N wave in the wave flume. It is shown by the experimental results that the revetment breakwater has no visible displacement, and there is no significant deformation in the reclaimed coral sand foundation, regardless the foundation is in dense or loose state under tsunami wave attacking. Furthermore, there is indeed excess pore pressure generated in the reclaimed coral foundation with a maximum magnitude of 1.5 kPa, caused by the water overtopping or the seepage. It is found that the excess pore pressure has not caused liquefaction in the reclaimed calcareous sand foundation due to the fact that there is only one peak impacting for the tsunami wave-induced load, rather than a cyclic one. Finally, it is concluded that the reclaimed calcareous sand foundation and the breakwater built on it are basically stable under tsunami wave impacting. However, the excessive water overtopping would be a potential threat for the vegetation behind the breakwater, as well as for the underground desalinated water in the reclaimed lands. [ABSTRACT FROM AUTHOR]

Scale or dimension is critical for all physical laws, and different scales might result in distinct and sometimes contradicting laws for the same phenomenon. In this study, the idea of the two-scale fractal is utilized to model the time-fractional tsunami wave traveling on an unsmooth surface. Mass and momentum conservation equations are established in a fractal space. To covert the considered fractional model into a differential equation, the fractional complex transform is used, then He’s variational iteration method is adopted to solve the resultant equation. The fractal model helps in studying the dynamic behavior of tsunami wave and their prevention through boundary control. The present study sheds new light on two-scale fluid mechanics. [ABSTRACT FROM AUTHOR]

This study addresses the possibility of application of the discrete mathematical analysis (DMA) methods to develop algorithms for registration of tsunami occurrences on the basis of routine data of sea level measurements. The algorithms are based on the relationship between the regression derivative and the trend of the record: areas of positive (negative) derivatives correspond to increasing (decreasing) trends. Boundaries between these areas are extremums. The article describes three DMA-algorithms for tsunami registration, and performs a comparative analysis. [ABSTRACT FROM AUTHOR]

Modelling of tides and tsunami waves propagation is important problem for the hydraulic engineering practice since it allows to predict characteristics of these phenomena (load, values of run up and flooding zones, propagation times to structures and so on) and to make reasonable choice of design solution for coastal structures. Numerical modeling is effective way to simulate tides and tsunami waves propagation. Results of simulations of tides and tsunami waves propagation on the basis of shallow water model are presented and analyzed in the article. It was considered explicit and implicit numerical scheme for solution of shallow water model equations, which were verified on the number of experimental results including experimental data on distribution of dam-break wave propagation on a dry and sloping bottom. It is shown that the numerical data of tides in Persian Gulf are well co-ordinated with the data of tidal tables, both on time and on level of tides in various points. Numerical results of tsunami waves propagation in the Krasheninnikov Bay and Kozmino Bay are presented at various angles of tsunami at open boundary of computed area. Numerical results of tide currents for Krasheninnikov Bay are presented for various velocities of a wind. Developed programs may be used, particular, for numerical calculations of impact characteristics of tsunami waves on structures in coastal and offshore zones according requirements of Russian normative documents.

The purpose of this experimental study was to investigate the effects of a rectangular canal on the hydrodynamics of turbulent surges before and after the canal by implementing a series of physical experiments. A dam-break wave model was used to simulate the tsunami-like turbulent waves passing over a smooth and horizontal surface, in the presence and absence of a canal. Three canal depths of d = 0. 0 5 , 0.10 and 0.15 m were used to model shallow, moderate and deep conditions and three canal widths of w = 0. 6 0 , 1.60 and 3.0 m were selected to model narrow to wide canals. The front velocity of the dam-break induced surges were controlled by rapidly releasing upstream impounded set volumes of water with depths of d o = 0. 2 0 , 0.30 and 0.40 m. The dam-break wave propagation over a horizontal, dry and smooth bed revealed four regimes describing the variations of surge height with time. The arrival time to reach the maximum surge height and the quasi steady-state regime was correlated with each impoundment depth and an empirical formulation was proposed to estimate the onset of the quasi steady-state flow. The maximum surge heights measured before and after the mitigation canal location were compared with those recorded in the corresponding tests without the presence of the canal. It was found that the peak surge height upstream of the canal could increase up to 40% compared to the test without the presence of the canal in relatively small impoundment depth and in presence of a narrow canal due to momentum dissipation. The wave height downstream of the canal increased between 10% and 50% of the wave height without the presence of the canal and the minimum change in the wave height occurred for the canal width to depth ratio of 20. The time-history of surge velocity after the mitigation canal indicated a significant decay of between 40% and 60% in the presence of a canal due to the bed friction changes and momentum dissipation. [ABSTRACT FROM AUTHOR]

We consider a transformation of long linear waves in an ocean with a variable depth. We calculate the transformation coefficients (the coefficients of transmission and reflection) as the functions of frequency and the total depth drop for three typical models of bottom profile variation: (i) piecewise-linear, (ii) piecewise-quadratic, and (iii) hyperbolic tangent profiles. For all these cases, exact solutions are obtained, analysed and graphically illustrated. This allows us to derive the transformation coefficients in the analytic form for the subsequent comparison with the results of approximate, numerical, or experimental study. We show that the results obtained are in agreement with both the energy flux conservation and Lamb's formulae in the limiting case of zero frequency. We also study wave transformation on the underwater barriers and trenches of different shapes and compare the results obtained. [ABSTRACT FROM AUTHOR]

In order to evaluate the impact of tsunami wave climbing along the sloping breakwater, the solitary wave was produced in the absorbing wave maker tank to simulation the interaction between the tsunami and the slop breakwater. The maximum tsunami wave run-up height was analyzed, the experimental data of three kinds of protective structures, i.e. the accropode armour, the barrier board and the stone at slope 1:1.5 and 1:2 were obtained. Compared with the empirical formula with other relevant studies, and considering the influence of roughness of different armour, a new formula of the maximum tsunami run-up height along the sloping breakwater was proposed. The results show the good correlation between the new empirical formula and a large number of measured data. [ABSTRACT FROM AUTHOR]

This study focuses on the hydrodynamic interaction between tsunami waves and bridge girder. Firstly, a series of tsunami waves were experimentally generated by dam-break waves under various initial water depths, the wave front profiles and their evolution were obtained accordingly. Then, experimental studies on hydrodynamic interaction between these tsunami waves and a plate-girder as well as a T-girder were carried out systematically, and the characteristics of the whole interaction process were analyzed successively. After that, the pressure time histories on the front side, back side, upper side and downward side of the bridge girder were obtained, and the obvious differences in pressure time histories at different positions were compared and analyzed in detail. Furthermore, the horizontal impact peak force, vertical impact peak force and impact peak moment on the two bridge girders, as well as the forces and moments in the quasi-stationary stage, ware presented, and their evolution with initial water depth, incoming wave height and girder elevation are revealed elaborately. Finally, based on the findings of this study and considering the variation of tsunami wave front profile and girder elevation, the calculation formulas for the impact peak forces and moment, as well as the forces and moment in the quasi-stationary stage, are proposed for the plate-girder and T-girder, and related coefficients are suggested from the experimental results of this study. This study could deepen the insight of the hydrodynamic interaction between tsunami waves and bridge girders, and provides a new rapid calculation method for the forces and moment on plate-girder and T-girder. • The pressure time histories on the outer sides of T-girder and plate-girder are obtained and analyzed. • The forces and moments in impulse stage and quasi-stationary stages and their evolution with tsunami wave and girder elevation are presented and explored. • The calculation formulas for the forces and moments in impulse stage and quasi-stationary stage are proposed and related coefficients are suggested. [ABSTRACT FROM AUTHOR]

Novel tsunami prediction models based on deep learning technique are used for tsunami wave prediction. The Long Short-Term Memory (LSTM) model and its variants are compared with numerical models and observation data. Three different types of tsunami prediction, namely single tsunami prediction at the same location, single tsunami prediction at different locations, and different tsunami prediction at different locations are considered. Different input–output ratios are examined. The error indicators are utilized to evaluate the reliability and accuracy. It is found that the input–output ratio 2:1 is most suitable for tsunami prediction. However, more inputs may not bring better prediction results under the same input–output ratio. Results show that our proposed Bidirectional Long Short-Term Memory (Bi-LSTM) and Convolutional Neural Networks–Long Short-Term Memory(CNN–LSTM) models are superior to the National Oceanic and Atmospheric Administration (NOAA) numerical model in prediction. This may be because the observed tsunami data contains rich information, and the deep learning model can better grasp various information hidden in the data, thus giving excellent prediction results. • New tsunami wave prediction approach is established. • Accurate prediction of tsunami wave is achieved. • The input–output ratio is discussed. [ABSTRACT FROM AUTHOR]

Events of a seismic nature followed by catastrophic floods caused by tsunami waves (the incidence of which has increased in recent decades) have an important impact on the populations of littoral regions. On the coast of Japan and Kamchatka, it takes nearly 20 min for tsunami waves to approach the nearest dry land after an offshore seismic event. This paper addresses an important question of fast simulation of tsunami wave propagation by mapping the algorithms in use in field-programmable gate arrays (FPGAs) with the help of high-level synthesis (HLS). Wave propagation is described by the shallow water system, and for numerical treatment the MacCormack scheme is used. The MacCormack algorithm is a direct difference scheme at a three-point stencil of a “cross” type; it happens to be appropriate for FPGA-based parallel implementation. A specialized calculator was designed. The developed software was tested for precision and performance. Numerical tests computing wave fronts show very good agreement with the available exact solutions (for two particular cases of the sea bed topography) and with the reference code. As the result, it takes just 17.06 s to simulate 1600 s (3200 time steps) of the wave propagation using a 3000 × 3200 computation grid with a VC709 board. The step length of the computational grid was chosen to display the simulation results in sufficient detail along the coastline. At the same time, the size of data arrays should provide their free placement in the memory of FPGA chips. The rather high performance achieved shows that tsunami danger could be correctly evaluated in a few minutes after seismic events.