Preprint A500/2007
The eddy viscosity for gravity waves propagating over turbulent surfaces
Josselin Garnier | André Nachbin
Keywords: water waves | Random media | eddy viscosity

This paper analyses (one-dimensional) nonlinear wave propagation over a disordered fluid body having a small viscosity. The lower boundary is disordered and modelled by a random process. As a pulse shaped nonlinear wave propagates over this turbulent boundary, the velocity and wave elevation are viewed as random fields. Starting from first principles the eddy viscosity is characterized and shown to depend on different scales. This is captured as the leading order pseudo-differential operator resulting from the asymptotic analysis of stochastic differential equations. A discussion is provided showing that mean-field theory would have not captured the correct attenuation rate for the large scale object. Numerical results are provided illustrating the accuracy of the eddy viscosity expression.