Streaming patterns in Faraday waves

Abstract

Wave patterns in the Faraday instability have been studied for decades. Besides the rich wave dynamics observed at the interface, Faraday waves hide elusive flow patterns in the bulk - streaming patterns - which have not been studied experimentally. The streaming patterns are responsible for a net circulation in the flow, which is reminiscent of the circulation in convection cells. In this article, we analyse these streaming flows by conducting experiments in a Faraday-wave set-up using particle image velocimetry. To visualise the flows, we perform stroboscopic measurements to both generate trajectory maps and probe the streaming velocity field. We identify three types of patterns and experimentally show that identical Faraday waves can mask streaming patterns that are qualitatively very different. Next, we consider a three-dimensional model for streaming flows in quasi-inviscid fluids, whose key is the complex coupling occurring at all of the viscous boundary layers. This coupling yields modified boundary conditions in a three-dimensional Navier-Stokes formulation of the streaming flow. Numerical simulations based on this framework show reasonably good agreement, both qualitative and quantitative, with the velocity fields of our experiments. The model highlights the relevance of three-dimensional effects in the streaming patterns. Our simulations also reveal that the variety of streaming patterns is deeply linked to the boundary condition at the top interface, which may be strongly affected by the presence of contaminants.