Scaling of the transition to parametrically driven surface waves in highly dissipative systems

We present an experimental study of the onset of the Faraday instability in highly dissipative fluids. In this regime of high viscosity and shallow fluid depth, we find that the critical acceleration for the transition to parametrically excited surface waves scales as a function of two dimensionless parameters corresponding to the ratios of the critical driving amplitude height and viscous boundary layer depth to the fluid depth. This scaling, which exists over a wide range of fluid parameters, identifies the proper characteristic scales and indicates that a Rayleigh-Taylor type mechanism drives the instability in this regime.