Numerical investigation on tsunami wave mitigation on forest sloping beach

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.

A mathematical model of calculating local tsunami wave source constraints and propagation

This paper presents a local tsunami simulation, including the initial displacement field model of tsunami source and tsunami wave propagation model. We deduced the tsunami wave equation; applied the matching of interior and exterior solutions method and water mass method to determine the initial displacement field in different bottom topography. Tsunami wave propagation model was based on the Boussinesq equation. Difference format was based on the ADI method which discretized in alternating direction in the form of implicit scheme. The open boundary of ADI had been revised considering the influence of wave propagation in the equation of motion. The local tsunami mathematical model was used in the simulation of 2011 Japan tsunami, and the results and the observation data match well.

Experimental study on the mitigation effect of mangroves during tsunami wave propagation

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(K_(i)) shows a parabolic correlation with its density. The proportion of the energy loss caused by the mangrove resistance to the total energy(E_(b)) is defined as C_(m2). The variation trend of C_(m2) corresponds to the tsunami wave energy attenuation rate(C_(a)) and K_(i).

Numerical Studies on the Generation and Propagation of Tsunami Waves Based on the High-Order Spectral Method

An effective numerical model for wave propagation over three-dimensional(3D)bathymetry was developed based on the High-Order Spectral(HOS)method and combined with a moving bottom boundary.Based on this model,tsunami waves caused by various mechanisms were simulated and analyzed.Two-dimensional bed upthrust and the effect of the uplift velocity of the bathymetry on the wave profiles of tsunami waves were studied.Next,tsunami waves caused by 3D submarine slides were generated and the effects of the slide velocity,slide dimension and water depth on the tsunami waves were analyzed.Based on wavelet analysis,the properties of the tsunami wave propagation were investigated.The results show that the bottom movement can significantly affect the generation and propagation of tsunami waves and the studies could help understand the mechanisms of tsunamis caused by a moving bottom boundary.

Propagation Mechanisms of Incident Tsunami Wave in Jiangsu Coastal Area,Caused by Eastern Japan Earthquake on March 11,2011

At 13：46 on March 11, 2011（Beijing time）, an earthquake of Mw=9.0 occurred in Japan. By comparing the tsunami data from Guanhekou marine station with other tsunami wave observation gathered from southeast coastal area of China, it was evident that, only in Guanhekou, the position of the maximum wave height appeared in the middle part rather than in the front of the tsunami wave train. A numerical model of tsunami propagation based on 2-D nonlinear shallow water equations was built to study the impact range and main causes of the special tsunami waveform discovered in Jiangsu coastal area. The results showed that nearly three-quarters of the Jiangsu coastal area, mainly comprised the part north of the radial sand ridges, reached its maximum tsunami wave height in the middle part of the wave train. The main cause of the special waveform was the special underwater topography condition of the Yellow Sea and the East China Sea area, which influenced the tsunami propagation and waveform significantly. Although land boundary reflection brought an effect on the position of the maximum wave height to a certain extent, as the limits of the incident waveform and distances between the observation points and shore, it was not the dominant influence factor of the special waveform. Coriolis force＇s impact on the tsunami waves was so weak that it was not the main cause for the special phenomenon in Jiangsu coastal area. The study reminds us that the most destructive wave might not appear in the first one in tsunami wave train.

Evolvement of tsunami waves on the continental shelves with gentle slope in the China Seas

Potential tsunami generated in the Okinawa Trench or the Manila Trench may attack the southeast coast of China. The continental shelves with extremely gentle slope in the China Seas affect the evolvement of tsunami waves. In this paper, we carry out the simulation of tsunami propagation based on the fully nonlinear and highly dispersive Boussinesq model, which could describe the nonlinearity and dispersion of water waves quite well. So the undulation characters could be well presented. In terms of the real topographies of the East China Sea and the South China Sea, we take some typical profiles to simulate the hypothetical tsunamis generated in the Okinawa Trench and the Manila Trench. Different waveforms in the near shore regions are obtained. The N-shape tsunami waves will evolve into long wave trains, undular bores or solitons near the coastal area. The numerical results of the near shore waveform provide essential conditions for the further studies of tsunami runup and inundation.

Identification of Forerunners and Transmission of Energy to Tsunami Waves Generated by Instanteneous Ground Motion on a Non-Uniformly Sloping Beach

The problem of generation and propagation of tsunami waves is mainly focused on plane beach, there are very few analytical works where wave generation is considered on non-uniformly sloping beach and as a result those works might have failed to capture important facts which are influenced by bottom-slope of the beach. Some researchers provided solution to the forced long linear waves but on a beach with uniform slope while the importance of including variable bottom topography is mentioned by few researchers but they also stayed away from considering continuous variability of the ocean bed as they were studying runup problem. This paper analyzes tsunami waves which are generated by instantaneous bottom dislocation on a ocean floor with variable slope of the form y=-qxr, q > 0, r > 0. Attempts are made to find analytical solution of the problem and along the way tsunami forerunners are identified while investigating the short time wave behavior, not found even with constant slope beaches. In our study a rather significant phenomenon with regard to energy transmission to the waves at steady-state are observed with some notable features.

Kinematic dynamo by large scale tsunami waves in open ocean

Kinematic dynamo problem is studied with tsunami motion in open oceans. Using long wave approximation, a series solution of the dynamo problem is established with fast convergent rate based on a small parameter relating water wave dispersive effects. Taking solitary wave and single wave as typical tsunami wave models, the magnitude of tsunami induced magnetic field is estimated at the order of 10 nano Tesla （nT） just over sea level and 1 nT at altitudes of several hundreds kilometers, respectively, depending on the wave parameters as well as earth magnetic field. The space and time behavior of the magnetic field predicted by present model shows fairly similarity with the field data at Easter Island during 2010 Chile tsunami.

Converting Tsunami Wave Heights to Earthquake Magnitudes

There is a fairly strict relation between maximum tsunami wave heights and causation earthquake magnitudes. This provides a new tool for estimating the magnitude of past earthquakes from the observed wave heights of related paleo-tsunami events. The method is subjected to a test versus two paleoseismic events with multiple independent estimates of corresponding earthquake magnitude. The agreement to the tsunami wave height conversion is good, confirming very high magnitudes of M 8.5 - 9.0 and M 8.4 - 8.5. Applying the same method to two Late Holocene events of methane venting tectonics indicates a ground shaking of forces equivalent to a M 8.0 earthquake, seriously changing previous long-term crustal hazard assessments.

Mathematical modeling of tsunami wave propagation at mid ocean and its amplification and run-up on shore

The paper deals with the study of the mathematical model of tsunami wave propagation along a coast-line of an ocean.The model is based on shallow-water assumption which is represented by a system of non-linear partial differential equations.In this study,we employ the Elzaki Adomian Decomposition Method(EADM)to successfully obtain the solution for the proposed model for different coastal slopes and ocean depths.How tsunami wave velocity and run-up height are affected by the coast slope and sea depth are demonstrated.The Adomian Decomposition Method together with Elzaki transform allows for solutions,without the need of any linearization or perturbation,in the form of rapidly converging series.The obtained numerical results for tsunami wave height and velocity are very close match to the real physical phenomenon of tsunami.

Tsunami wave propagation model:A fractional approach

This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model.The present model has been studied on the shallow-water assumption.It is represented by a time-fractional coupled system of non-linear partial differential equations.Solutions to the proposed model for different coastal slopes and ocean depths have been obtained.Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different ordersα.The obtained results are compared with Elzaki Adomian Decomposition Method(EADM)to validate the proposed method for an orderα=1.

Will oscillating wave surge converters survive tsunamis?

With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter （OWSC） could withstand the force of an incoming tsunami. Several tools are used to provide an answer： an analytical 3D model developed within the framework of linear theory, a numerical model based on the non-linear shallow water equations and empirical formulas. Numerical results show that run-up and draw-down can be amplified under some circumstances, leading to an OWSC lying on dry ground t

Modeling of Tsunami Generation and Propagation by a Spreading Curvilinear Seismic Faulting in Linearized Shallow-Water Wave Theory

The processes of tsunami evolution during its generation in search for possible amplification mechanisms resulting from unilateral spreading of the sea floor uplift is investigated. We study the nature of the tsunami build up and propagation during and after realistic curvilinear source models represented by a slowly uplift faulting and a spreading slip-fault model. The models are used to study the tsunami amplitude amplification as a function of the spreading velocity and rise time. Tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the movable source models. We analyzed the normalized peak amplitude as a function of the propagated uplift length, width and the average depth of the ocean along the propagation path.

Generation and Propagation of Tsunami by a Moving Realistic Curvilinear Slide Shape with Variable Velocities in Linearized Shallow-Water Wave Theory

The process of tsunami evolution during its generation under the effect of the variable velocities of realistic submarine landslides based on a two-dimensional curvilinear slide model is investigated. Tsunami generation from submarine gravity mass flows is described in three stages. The first stage represented by a rapid curvilinear down and uplift faulting with rise time. The second stage represented by a unilaterally propagation in the positive x direction to a significant length to produce curvilinear two-dimensional models represented by a depression slump, and a displaced accumulation slide model. The last stage represented by the time variation in the velocity of the accumulation slide (block slide). By using transforms method, Laplace in time and Fourier in space, tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically for the movable source model. Effect of the water depths on the amplification factor of the tsunami generation by the submarine slump and slide for different propagation lengths and widths has been studied and the results are plotted. Comparison of tsunami peak amplitudes is discussed for different propagation lengths, widths and water depths. In addition, we demonstrated the tsunami propagation waveforms after the slide stops moving at different propagation times.

Under the surface:Pressure-induced planetary-scale waves,volcanic lightning,and gaseous clouds caused by the submarine eruption of Hunga Tonga-Hunga Ha'apai volcano

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 58km-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 quasicontinuous 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 km^(3) 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.

Mutual Influence of the Atmosphere and the Ocean under Wave Processes

The article solves the problem of surface gravitational waves using the theory of tangential discontinuity between media: air-water. Using the improved equation of mass continuity and taking into account the atmosphere inhomogeneity in the gravitational field of the Earth, it is shown that during wave processes, these two media mutually influence each other, which explains the reason for the formation of a stormy condition over the ocean and the drop in atmospheric pressure before the storm. The mechanism of the formation of the “killer wave” has been established and thus the “greatest mystery of nature” has been solved. The scale of wind and tsunami wavelengths has been established.

Modelling Solitary Waves and Its Impact on Coastal Houses with SPH Method

The interaction between solid structures and free-surface flows is investigated in this study. A Smoothed Particle Hy- drodynamics （SPH） model is used in the investigation and is verified against analytical solutions and experimental obser- vations. The main aim is to examine the effectiveness of a tsunami-resistant house design by predicting the wave loads on it. To achieve this, the solitary wave generation and ran-up are studied first. The solitary wave is generated by allowing a heavily weighted block to penetrate into a tank of water at one end, and the near-shore seabed is modelled by an inclined section with a constant slope. Then, the SPH model is applied to simulate the three-dimensional flows around different types of houses under the action of a solitary wave. It has been found that the tsunami-resistant house design reduces the impact force by a factor of three.

夏威夷ALEUTIAN海啸的NEOWAVES数值模拟

夏威夷群岛因其特殊的地理位置及周围海底地形,长期遭受太平洋地震带和近岸地震带产生的海啸影响,如何准确地确定夏威夷群岛沿岸的海啸爬高对海洋结构设计具有重大意义。基于非线性浅水方程建立的NEOWAVES模型包含非线性静水压力项和垂向动量方程,用于描述海底的动态变形和弱频散波的传播过程,它能够模拟海啸的整个生命过程,包括产生、传播、爬高和淹没。以对夏威夷地区影响比较严重的1946年Aleutian历史海啸为例,采用NEOWAVES模型模拟其产生、传播以及在夏威夷欧胡岛沿岸地带的爬高。计算结果表明,NEOWAVES模型计算得到的欧胡岛沿岸(北部、西部和南部)的爬高与历史记录的爬高数据接近,验证了NEOWAVES模型的合理性和可靠性,同时也为夏威夷地区海洋结构物的设计提供合理的参考意见。

Laboratory Generation of Solitary Waves:An Inversion Technique to Improve Available Methods

Solitary waves are often used in laboratory experiments to study tsunamis propagation and interaction with coasts. However, the experimental shape of the waves may differ from the theoretical one. In this paper, a correction technique aiming at minimizing the discrepancies between the two profiles is presented. Laboratory experiments reveal their effectiveness in correcting the experimental shape of solitary waves, mainly for low nonlinearities.

Inundation Studies Along the East Coast of India due to Tsunamigenic Earthquakes in North-Andaman and Car Nicobar Subduction zone

The Sumatra-Andaman arc is an active subduction zone and had generated several destructive Tsunamis in the past.In this paper we have analyzed two historical Tsunamigenic earthquakes from this region. One of the historical earthquake is the earthquake of 26th June 1941 in the North Andaman region,which was one of the strongest in the Andaman Sea and Bay of Bengal of magnitude M_w=7.7.This earthquake had triggered tsunami which affected the east coast of India.The other is the earthquake in Car Nicobar region on 31 st December 1881 of magnitude M_w=7.9. This submarine earthquake beneath the