Signature of elasticity in the Faraday instability

We investigate the onset of the Faraday instability in a vertically vibrated wormlike micelle solution. In this strongly viscoelastic fluid, the critical acceleration and wave number are shown to present oscillations as a function of driving frequency and fluid height. This effect, unseen in either in simple fluids or in previous experiments on polymeric fluids, is interpreted in terms of standing elastic waves between the disturbed surface and the container bottom. It is shown that the model of Kumar [Phys. Rev. E 65, 026305 (2002)] for a viscoelastic fluid accounts qualitatively for our experimental observations. Explanations for quantitative discrepancies are proposed, such as the influence of the nonlinear rheological behavior of this complex fluid.