Long wave expansions for water waves over random topography
نویسندگان
چکیده
منابع مشابه
Long Wave Expansions for Water Waves over Random Topography
In this paper, we study the motion of the free surface of a body of fluid over a variable bottom, in a long wave asymptotic regime. We assume that the bottom of the fluid region can be described by a stationary random process β(x, ω) whose variations take place on short length scales and which are decorrelated on the length scale of the long waves. This is a question of homogenization theory in...
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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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The deformation of a nonlinear pulse traveling in a dispersive random medium can be studied with asymptotic analysis based on separation of scales when the propagation distance is large compared to the correlation length of the random medium. We consider shallow water waves with a spatially random depth. We use a formulation in terms of a terrain-following Boussinesq system. We compute the effe...
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We consider whether small-amplitude topography in a two-dimensional ocean may contain internal wave attractors. These are closed orbits formed by the characteristics (or wave beam paths) of the linear, inviscid, steady-state Boussinesq equations, and their existence may imply enhanced scattering and energy decay for the internal tide when dissipation is present. We develop a numerical code to d...
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Abstract. We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously co...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2008
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/21/9/014