Coupled mean flow-amplitude equations for nearly inviscid parametrically driven surface waves.
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.
Knobloch
Edgar
E
Department of Physics, University of California, Berkeley, California 94720, USA. knobloch@physics.berkeley.edu
Martel
Carlos
C
Vega
José M
JM