A numerical analysis of the influence of the liquid depth on two dimensional Faraday waves

Abstract

In this work a numerical analysis of two-dimensional Faraday waves is presented. This study is based on direct numerical simulation of Navier-Stokes and continuity equations with appropriate boundary conditions. Stability maps on the (F-α) plane for viscous liquid layers with equilibrium depths between 5×10−5 m and 10−5 m are presented; comparisons are made with the linear stability predictions obtained with Benjamin and Ursell?s model for an inviscid fluid and with Kumar and Tuckerman?s model for a viscous fluid. Regions in which time-periodic solutions are no longer obtained and nonlinear effects are relevant, and are also delimited and analyzed: in these zones the disintegration of the free surface into drops may take place.