Asymptotics of surface waves over random bathymetry

Rays , Waves and Asymptotics

Asymptotics of random contractions

In this paper we discuss the asymptotic behaviour of random contractions X = RS, where R, with distribution function F , is a positive random variable independent of S ∈ (0, 1). Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of X assuming that F is in the max-domain of attraction of an extreme value distributio...

Cloaking of a vertical cylinder in waves using variable bathymetry

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Exponential Asymptotics and Capillary Waves

Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The ampli...

Effective Behavior of Solitary Waves over Random Topography

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...