Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability

Abstract

Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show low-frequency modulations corresponding to the motion of phase defects, while theory predicts a stationary transverse amplitude modulation (TAM). (2) High-nu fluids destabilize first to stripes. Stripes then show an oscillatory TAM whose frequency is incommensurate with the driving frequency. At higher a, the TAM undergoes a phase instability. At still higher a, edge dislocations form and fluid droplets are ejected. (3) Intermediate-nu fluids show a complex coexistence of squares and stripes, as well as stationary and oscillatory TAM instabilities of the stripes.