Journal of Fluid Mechanics

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Particle dispersion by random waves in rotating shallow water

OLIVER BÜHLERa1 and MIRANDA HOLMES-CERFONa1 c1

a1 Center for Atmosphere Ocean Science at the Courant Institute of Mathematical Sciences New York University, New York, NY 10012, USA

Abstract

We present a theoretical and numerical study of wave-induced particle dispersion due to random waves in the rotating shallow-water system, as part of an ongoing study of particle dispersion in the ocean. Specifically, the effective particle diffusivities in the sense of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, p. 196) are computed for a small-amplitude wave field modelled as a stationary homogeneous isotropic Gaussian random field whose frequency spectrum is bounded away from zero. In this case, the leading-order diffusivity depends crucially on the nonlinear, second-order corrections to the linear velocity field, which can be computed using the methods of wave–mean interaction theory. A closed-form analytic expression for the effective diffusivity is derived and carefully tested against numerical Monte Carlo simulations. The main conclusions are that Coriolis forces in shallow water invariably decrease the effective particle diffusivity and that there is a peculiar choking effect for the second-order particle flow in the limit of strong rotation.

(Received March 05 2009)

(Revised July 01 2009)

(Accepted July 02 2009)

Correspondence:

c1 Email address for correspondence: holmes@cims.nyu.edu

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