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.

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 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.

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.

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.

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.

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.

Characteristics of wave amplitude and currents in South China Sea induced by a virtual extreme tsunami

This paper investigates the potential extreme tsunami hazards of the worst case scenario of the magnitude M_w=9.30 in South China Sea（SCS）as the Manila Trench is becoming one of the most hazardous tsunami source regions.Using nonlinear shallow water equations model,the time series of surface elevation,arrival time,spatial distributions of maximum wave amplitude and velocity distribution are presented.The characteristics of wave and currents are analyzed.The numerical results indicate that most of the energy of tsunami wave distributes in central and north part of SCS.The offshore regions around SCS will be influenced significantly by the tsunami currents generated by an earthquake in the Manila subduction zone.The maximum wave amplitude near Guangdong Province,Hainan Island,and Taiwan Island exceeds 4 m and velocities at the majority of measured locations near coast exceeds 2 m/s.Nested grid with high resolution is used to study the impacts of the tsunami on Hainan Island,Taiwan Island,and Lingding Bay.The regions with high hazard risk due to strong currents are identified.Finally,a fast tsunami warning method in SCS is developed and discussed,which can provide tsunami warning information in 5 min.

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.

150 Years(1872-2022)of research on deep-water processes,deposits,settings,triggers,and deformation:A difficult domain of progress,dichotomy,diversion,omission,and groupthink

In capturing a snapshot of 150 years(1872-2022)of research on deep-water processes,deposits,settings,triggers,and deformation,the following 22 topics are selected:(1)H.M.S.Challenger expedition(1872-1876):The discovering of the“Challenger Deep”by the H.M.S.Challenger in the Mariana Trench has been the single most important achievement in deep-water research.(2)Five pioneers amid 50 notable contributors:R.A.Bagnold,J.E.Sanders,G.D.Klein,F.P.Shepard,and C.D.Hollister.(3)Mass transport:Mass-transport deposits(MTD)are the most important deep-water facies in terms of volume,geohazards,and petroleum reservoirs.(4)Gravity flows:There are six basic types,namely(a)hyperpycnal flows,(b)turbidity currents,(c)debris flows,(d)liquefied/fluidized flows,(e)grain flows,and(f)thermohaline contour currents.Sandy debrites are the most important petroleum reservoir facies.Despite their popularity,turbidites are not an important reservoir facies.(5)Kelvin-Helmholtz(KH)waves:Turbidites,related to KH waves,with internal hiatus are not qualified to function as predictive facies models;nor are they fit for stratigraphic correlations.(6)High-density turbidity currents(HDTC):Misclassification of density-stratified gravity flows with laminar debris flows and turbulent turbidity currents as HDTC is flawed.Experimental generation of density-stratified gravity flows in flume studies has debunked the concept of HDTC.(7)Classification of turbidites:Contrary to the popular groupthink,turbidites are exclusive deposits of turbidity currents.(8)Bottom currents:The four basic types of deep-marine bottom currents are:(a)thermohaline-induced geotropic contour currents,(b)wind-driven bottom currents,(c)tide-driven bottom currents(mostly in submarine canyons),and(d)internal wave/tide-driven baroclinic currents.(9)Classification of contourites:Contrary to the popular groupthink,contourites are the exclusive deposits of thermohaline-induced geotropic contour currents.(10)Tidal currents in submarine canyons:Their velocity measurements have been the single most important achievement in deep-water process sedimentology.(11)Modern and ancient systems:There is a dichotomy between rare observations of turbidity currents in modern settings and overwhelming cases of interpretations of ancient turbidites in outcrops and cores.The reason is that turbidity currents are truly rare in nature,but the omnipotent presence of turbidites in the ancient rock record is the manifestation of groupthink induced by the turbidite facies model(i.e.,the Bouma Sequence).(12)Internal waves and tides:Despite their ubiquitous documentation in modern oceans,their ancient counterparts in outcrops are extremely rare.This is another dichotomy.(13)Hybrid flows:They are commonly developed by intersecting of down-slope gravity flows with along-slope contour currents.However,they are often misapplied to down-slope flow transformation of gravity flows.(14)Density(sediment)plumes:Deflected sediment plumes by wind forcing are common.Despite their importance in provenance studies,they are not adequately studied.(15)Hyperpycnal flows:They occur near the shoreline,next to the plunge point;but are of no relevance in deep-water environments.However,their importance in deep-marine settings is overhyped in recent literature.(16)Omission of erosional contact and internal hiatus:In order to promote genetic facies models that must not contain internal hiatuses,some researchers selectively omit internal hiatuses observed by the original authors.(17)Triggers of sediment failures:There are 22 types,but short-term triggers,such as earthquakes and meteorite impacts are more important than the conventional long-term trigger known as Eustasy.(18)Tsunami waves:Despite their sedimentologic importance,there are no reliable criteria for recognizing tsunami deposits in the ancient rock record.(19)Soft-Sediment Deformation Structures(SSDS):Although most SSDS are routinely interpreted as seismites,not all SSDS are caused by earthquakes.There are 10 other mechanisms,such as sediment loading,which can trigger liquefaction that can develop SSDS.(20)The Jackfork Group,Pennsylvanian,Ouachita Mountains,USA:Our reinterpretation of this classic North American flysch turbidites as MTD and bottomcurrent reworked sands has resulted in the longest academic debate with 42 printed pages in the AAPG Bulletin history since its founding in 1917.(21)Basin-floor fan model,Tertiary,North Sea:Our examination of nearly 12,000 ft(3658 m)of conventional core from Paleogene and Cretaceous deep-water sandstone reservoirs cored in 50 wells in 10 different areas or fields in the North Sea and Norwegian Sea reveals that these reservoirs are predominantly composed of MTDs,mainly sandy slumps and sandy debrites,and bottom-current reworked sands.Our core-seismic calibration debunked the conventional wisdom(groupthink)that basin-floor fans are composed of sandy turbidites in a sequence-stratigraphic framework.(22)Turbidite groupthink:A case study in illustrating how turbidite groupthink functions,without sound scientific methods,on the basis of published information on modern turbidity currents in Bute Inlet(fjord and estuary),British Columbia,Canada.This compendium is hybrid in composition between an atlas(with 108 figures)and a review article(with 348 references).The author admonishes scientists against deep-sea groupthink and provides a roadmap for future researchers by identifying potential topics for research involving density plumes,internal waves,tidal currents,tsunami waves,sediment deformation,and lowstand braid deltas.

AN EXPERIMENTAL OBSERVATION OF A SOLITARY WAVE IMPINGE-MENT,RUN-UP AND OVERTOPPING ON A SEAWALL

A sequence of laboratory experiments using solitary waves was performed to model the effect of leading form of three types of tsunamis（a bore,an impinging wave and an overtopping wave）on a seawall on a sloping beach.The wave evolution process,impinging pressure along the seawall surface,total overtopping discharge behind the seawall and the maximum run-up height on the rear slope were measured and compared.Laboratory data were employed to re-examine relevant empirical formulae in the literature.The effect of the presence of the seawall in reducing maximum run-up height using the present setup was briefly discussed.The present data can be used for calibrating numerical and mathematical models.

Efficient numerical scheme based on the method of lines for the shallow water equations

In this paper,a nonlinear shallow-water model of tsunami wave propagation at different points along a coastline of an ocean has been numerically simulated using method of lines.The simulation is carried out for various coastal slopes and the ocean depths.The effects of the coast slope and sea depth on the tsunami wave run-up height and velocity are illustrated.The accuracy of the mathematical model is verified by solving a classical test problem with known analytic solution.The computed run-up height and velocity show satisfactory agreement with the tsunami wave physics.