Energy of tsunami waves generated by bottom motion

Dutykh, Denys; Dias, Frédéric

doi:10.1098/rspa.2008.0332

Cited by 57 publications

(54 citation statements)

References 30 publications

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“…Figure 3 shows that the region r < 7 cm contains most of the kinetic energy during the bottom deformation. As shown in figure 4 (inset), the kinetic energy within this volume, E K , captures also the main temporal features of the motion (see also [44]). The bottom uplift induces an intense first maximum of E K .…”

Section: Results and Discussion (A) Velocity Fieldmentioning

confidence: 99%

Experiments on generation of surface waves by an underwater moving bottom

et al. 2015

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We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal highpass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

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Section: Results and Discussion (A) Velocity Fieldmentioning

confidence: 99%

Experiments on generation of surface waves by an underwater moving bottom

et al. 2015

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“…Better results could be obtained if the resolutions are increased. As discussed by Dutykh and Dias, 33 neglecting vertical velocity may underestimate the kinetic energy in the framework of shallow water approximation, therefore destroys the total energy conservation. In Eq.…”

Section: A Leading-depression N-wave With γ =mentioning

confidence: 99%

Characteristics of tsunami motion and energy budget during runup and rundown processes over a plane beach

2012

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Motions of tsunami waves during runup and rundown processes on the uniform sloping beach are studied numerically by the fully nonlinear and highly dispersive Boussinesq equations. We first study the leading-depression N-wave defined by solitary theory. The shoreline movement and its moving speed are analyzed during the wave approaching the coastal area. Details on the flow field and the energy transformation are obtained in terms of the reconstruction of the full velocity field by Boussinesq equations. In addition, solitary wave is studied as a comparison. The different energy budget explains the phenomenon that the N-wave leads much larger runup than the solitary wave in some specific situations. The investigation is then extended to the patterns of the energy transformation of N-shape waves, hump-like waves, and sinusoidal long waves. These waves are of the same order in scale with the recent giant tsunamis. The results show that the potential energy of the N-shape tsunami waves nearly reaches the maximum while that of the hump-like tsunami waves does not reach the maximum at the maximum runup, meanwhile the kinetic energy of both waves does not go to zero. For the sinusoidal wave train, however, its potential energy reaches the maximum and its kinetic energy goes to zero exactly at the maximum runup. To understand the responses caused by the variation of the waveforms, effects of the nonlinearity and the dispersion on the energy budget are studied in the geophysical tsunamis order. Moreover, the regularities of the energy budget of some general cases including the leading-depression N-waves (LDNs), the leading-elevation N-wave, and generalized LDNs are investigated extensively. The mechanism of the energy budget of these waves is quite different as just considering the potential energy at the maximum runup. C 2012 American Institute of Physics. [http://dx

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“…One can easily check, after computing the variations, that the Hamiltonian (2.20) yields 22) which are equivalent to the system (2.10)-(2.11) after introduction of the auxiliary variables u andv defined in (2.14) and (2.15).…”

Section: Properties Of the New Modelmentioning

confidence: 99%

“…This quantity is traditionally associated to the wave energy propagation speed [22,54]. Recall, that in the classical linearized shallow water theory, the phase c and group c g velocities are equal [54]:…”

Section: Group Velocitymentioning

confidence: 99%

Modified shallow water equations for significantly varying seabeds

Dutykh

Clamond²

2016

Applied Mathematical Modelling

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Abstract. In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive non-hydrostatic extension of the classical Saint-Venant equations. A key feature of the new model is that, like the classical NSWE, it is hyperbolic and thus similar numerical methods can be used. We also propose a finite volume discretisation of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modelling are also discussed.

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Energy of tsunami waves generated by bottom motion

Cited by 57 publications

References 30 publications

Experiments on generation of surface waves by an underwater moving bottom

Experiments on generation of surface waves by an underwater moving bottom

Characteristics of tsunami motion and energy budget during runup and rundown processes over a plane beach

Modified shallow water equations for significantly varying seabeds

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