Generation and propagation of nonlinear tsunamis in shallow water by a moving topography

Abou-Dina, M. S.; Hassan, F. M.

doi:10.1016/j.amc.2005.11.033

Cited by 13 publications

(8 citation statements)

References 13 publications

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“…The massive destruction and loss of life associated with the recent tsunamis has underscored the need to develop and implement tsunami hazard mitigation measures. In recent years, significant advances have been made in developing mathematical models to describe the entire process of tsunami event generated by seismic seafloor deformation caused by an underwater earthquake; see [1][2][3]. Numerical models based on the nondispersive shallow-water equations are often used to simulate tsunami propagation and run-up (e.g., [4,5]).…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Allam

Omar

Ramadan

2014

ISRN Applied Mathematics

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Tsunami generation and propagation caused by stochastic seismic fault driven by two Gaussian white noises in the x- and y-directions are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading uplift length and rise times of the three-dimensional stochastic fault source model. 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). The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to the geometric spreading and also due to dispersion. The maximum amplitude amplification is proportional to the propagation length of the stochastic source model and inversely proportional to the water depth. The increase of the normalized noise intensities on the bottom topography leads to an increase in oscillations and amplitude in the free surface elevation. We derived and analyzed the mean and variance of the random tsunami waves as a function of the propagated uplift length, noise intensities, and the average depth of the ocean along the generation and propagation path.

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Section: Introductionmentioning

confidence: 99%

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Allam

Omar

Ramadan

2014

ISRN Applied Mathematics

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“…Several types of finite difference schemes, within the frame of the shallow water approximations, have been developed for such initial boundary value problems [19,20].…”

Section: Introductionmentioning

confidence: 99%

Boundary integral method applied to the propagation of non-linear gravity waves generated by a moving bottom

Hassan

2009

Applied Mathematical Modelling

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A numerical procedure is applied for the solution of the non-linear problem of propagation of waves generated in a homogeneous fluid, occupying an infinite channel, by the bounded motion of the bottom. For the sake of comparison, the analytical solution of the corresponding linearized problem is also given. The obtained results show that for sufficiently small amplitude of the bottom's motion, the predictions of the linear theory are in good agreement with those of the nonlinear theory only in some starting time interval, this interval being longer for smaller amplitudes. In the course of time, a growing oscillatory divergence is found to exist between the two theories. This divergence increases significantly with the increase of the amplitude of the bottom's motion. Numerical results are presented and discussed. Unlike results of other publications, the numerical scheme given here proves numerical stability for the considered cases.

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“…Laplace and Fourier transform can now be applied to the bed motion described by (18) and (19). First, beginning with the uplift faulting (18) for 0 ≤ t≤ t 1 where…”

Section: Solution Of the Problemmentioning

confidence: 99%

“…In their experiments, they found that the inclusion of a dissipative term was more important than the inclusion of nonlinearity, although the inclusion of nonlinearity was undoubtedly beneficial in describing the observations. Abo Dina et al [18] have adopted a nonlinear theory and constructed a numerical model of tsunami generation and propagation which permits a variable bed displacement with an arbitrary water depth to be included in the model. In this model, he considered nonlinearities and omitted the linear effects of frequency dispersion; hence, no insight into the possible importance of the interaction of nonlinear and linear effects in the far field was possible, see also [19,20].…”

Section: Introductionmentioning

confidence: 99%

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

Hassan¹,

Ramadan²,

Hanna³

2010

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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.

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Generation and propagation of nonlinear tsunamis in shallow water by a moving topography

Cited by 13 publications

References 13 publications

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Boundary integral method applied to the propagation of non-linear gravity waves generated by a moving bottom

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

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