Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio

Nearly inviscid parametrically excited surface gravity-capillary waves in t wo-dimensional domains of finite depth and large aspect ratio are considere d. 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. Un der suitable conditions the mean flow consists of an inviscid part together with a viscous mean flow driven by a tangential stress due to an oscillato ry viscous boundary layer near the free surface and a tangential velocity d ue to a bottom boundary layer, These forcing mechanisms are important even in the limit of vanishing viscosity, and provide boundary conditions for th e Navier-Stokes equation satisfied by the mean flow in the bulk. For modera tely large aspect ratio domains the amplitude equations are nonlocal but de couple from the equations describing the interaction of the slow spatial ph ase and the viscous mean flow. Two cases are considered in detail, gravity- capillary waves and capillary waves in a microgravity environment. (C) 2001 Elsevier Science B.V. All rights reserved.