Streaming patterns in Faraday waves

Abstract

Waves patterns in the Faraday instability have been studied for decades. Besides therich dynamics that can be observed on the waves at the interface, Faraday waves hidebeneath them an elusive range of flow patterns —or streaming patterns— which havenot been studied in detail until now. The streaming patterns are responsible for a netcirculation in the flow which are reminiscent of convection cells. In this article, we analysethese streaming flows by conducting experiments in a Faraday-wave setup. To visualizethe flows, tracers are used to generate both trajectory maps and to probe the streamingvelocity field via Particle Image Velocimetry (PIV). We identify three types of patternsand experimentally show that identical Faraday waves can mask streaming patterns thatare qualitatively very different. Next we propose a three-dimensional model that explainsstreaming flows in quasi-inviscid fluids. We show that the streaming inside the fluid arisesfrom a complex coupling between the bulk and the boundary layers. This coupling canbe taken into account by applying modified boundary conditions in a three-dimensionalNavier-Stokes formulation for the streaming in the bulk. Numerical simulations basedon this theoretical framework show good qualitative and quantitative agreement withexperimental results. They also highlight the relevance of three-dimensional effects inthe streaming patterns. Our simulations reveal that the variety of experimental patternsis deeply linked to the boundary condition at the top interface, which may be stronglyaffected by the presence of contaminants along the surface.