Water waves generated by a moving bottom

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.

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“…Some of these parameters are shown in figure 1. More details can be found in [4] for example. A value of 90…”

Section: Physical Problem Descriptionmentioning

confidence: 99%

Comparison between three-dimensional linear and nonlinear tsunami generation models

Kervella

Dutykh

Dias

2007

Theor. Comput. Fluid Dyn.

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“…In general the tsunami wave at the source can be either a wave of depression, or of elevation, or a combination of these, see the recent assessments by Dutykh and Dias (2007), Arcas and Segur (2012) and Dias et al (2014). As the wave propagates shorewards over the continental slope and shelf, and finally impacting the shoreline, the increasing effect of nonlinearity will lead to quite different set of behaviours depending on the wave polarity, see Carrier et al (2003) and Fernando et al (2008) for instance.…”

Section: Introductionmentioning

confidence: 99%

“…This configuration was observed in the Sumatra tsunami of 2004, see Ioulalen et al (2007) and Grilli et al (2007), and that in Tohoku in 2011 see Mori et al (2013), and was examined in experiments by Klettner et al (2012) motivated in part by these observations. Such a structure depends of course on the shape of the co-seismic bottom displacements, see the theoretical analysis by Dutykh and Dias (2007) for instance. Shallow water theory implies that the elevation will travel faster with a speed difference c ∼ √ g h, and then after a time t * ∼ L 0 / c the waves undergo a transition.…”

Section: Introductionmentioning

confidence: 99%

Changing forms and sudden smooth transitions of tsunami waves

Grimshaw

Hunt

Chow

2014

J. Ocean Eng. Mar. Energy

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In some tsunami waves travelling over the ocean, such as the one approaching the eastern coast of Japan in 2011, the sea surface of the ocean is depressed by a small metre-scale displacement over a multi-kilometre horizontal length scale, lying in front of a positive elevation of comparable magnitude and length, which together constitute a down-up wave. Shallow water theory shows that the latter travels faster than the former, leading to an interaction, whose description is the issue addressed in this paper, using model equations of the Korteweg-de Vries type. First, we re-examine the undular bore solutions of the Korteweg-de Vries equation which describe how an initial depression wave deforms into a depression rarefaction wave followed by an undular bore of large elevation waves riding on this depression. Then we develop a new extended Korteweg-de Vries equation some of whose solutions can be used to describe the interaction of an elevation wave chasing a depression wave. These show that the two waves coincide at a given position and time producing a maximum elevation. Typically this amplitude is larger than the initial displacement magnitude by a factor which can be as large as two, which may explain anomalous elevations of tsunamis at particular positions along their trajectories. It is physically significant that for these small amplitude waves, no wave breaking occurs and there is no excess dissipation. Then, following the transition, the elevation wave moves ahead of the depression wave and the distance between them increases either linearly or

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“…The function T (t) provides us a complete information on the dynamics of the bottom motion. In tsunami wave literature, it is called a dynamic scenario [21,33,37]. Obviously, other choices of the time dependence are possible.…”

Section: Wave Generation By Sudden Bottom Upliftmentioning

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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Water waves generated by a moving bottom

Cited by 68 publications

References 34 publications

Comparison between three-dimensional linear and nonlinear tsunami generation models

Comparison between three-dimensional linear and nonlinear tsunami generation models

Changing forms and sudden smooth transitions of tsunami waves

Modified shallow water equations for significantly varying seabeds

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