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 wavenumber are shown to present oscillations as a function of driving frequency and fluid height. This effect, unseen neither in simple fluids nor 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 S. Kumar [Phys. Rev. E, {\bf 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 behaviour of this complex fluid.