Citation
Knobloch, Edgar and Martel, Carlos and Vega de Prada, José Manuel
(2002).
Coupled Mean Flow-Amplitude Equations for Nearly Inviscid Parametrically Driven Surface Waves.
"Annals of the New York Academy of Sciences", v. 974
;
pp. 201-219.
ISSN 1749-6632.
https://doi.org/10.1111/j.1749-6632.2002.tb05909.x.
Abstract
Nearly inviscid parametrically excited surface gravity-capillary waves in two-dimensional periodic domains of finite depth and both small and large aspect ratio are considered. Coupled equations describing the evolution of the amplitudes of resonant left- and right-traveling waves and their interaction with a mean flow in the bulk are derived, and the conditions for their validity established. In general the mean flow consists of an inviscid part together with a viscous streaming flow driven by a tangential stress due to an oscillating viscous boundary layer near the free surface and a tangential velocity due to a bottom boundary layer. These forcing mechanisms are important even in the limit of vanishing viscosity, and provide boundary conditions for the Navier-Stokes equation satisfied by the mean flow in the bulk. The streaming flow is responsible for several instabilities leading to pattern drift.