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

SEBASTIÁN UBAL; MARÍA D. GIAVEDONI; FERNANDO A. SAITA

PHYSICS OF FLUIDS

AMER INST PHYSICS

Año: 2003 vol. 15 p. 3099 - 3113

1070-6631

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-alpha) plane for viscous liquid layers with equilibrium depths between 5x10^-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.