Water waves over a rough bottom in the shallow water regime
نویسندگان
چکیده
منابع مشابه
Water Waves over a Rough Bottom in the Shallow Water Regime
This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem of homogenization theory. In this setting we derive a new model system of equations, consisting of the classical shallow water equations coupled with nonloca...
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The traditional shallow water model for waves propagating over varying bathymetry depends for its derivation on the asymptotic analysis of a Dirichlet-Neumann operator. This analysis however is restricted to smoothly varying topographies. We propose an adaptation to one dimensional polygonal bottoms using the conformal mapping idea of Hamilton and Nachbin. The asymptotic analysis of the Dirichl...
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The propagation of surface water waves over rough topographical bottoms is investigated by the multiple scattering theory. It is shown that the waves can be localized spatially through the process of multiple scattering and wave interference, a peculiar wave phenomenon which has been previously discussed for frozen light in optical systems [Nature 390, 661 (1997)]]. This paper demonstrates that...
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This paper is a study of the problem of nonlinear wave motion of the free surface of a body of fluid with a periodically varying bottom. The object is to describe the character of wave propagation in a long-wave asymptotic regime, extending the results of R. Rosales & G. Papanicolaou (1983 Stud. Appl. Math. 68, 89–102) on periodic bottoms for two-dimensional flows. We take the point of view of ...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2012
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2011.10.004