Streaming patterns in Faraday waves

Abstract

Waves patterns in the Faraday instability have been studied for decades. Besides the rich dynamics that can be observed on the waves at the interface, Faraday waves hide beneath them an elusive range of flow patterns -or streaming patterns-which have not been studied in detail until now. The streaming patterns are responsible for a net circulation in the flow which are reminiscent of convection cells. In this article, we analyse these streaming flows by conducting experiments in a Faraday-wave setup. To visualize the flows, tracers are used to generate both trajectory maps and to probe the streaming velocity field via Particle Image Velocimetry (PIV). We identify three types of patterns and experimentally show that identical Faraday waves can mask streaming patterns that are qualitatively very different. Next we propose a three-dimensional model that explains streaming flows in quasi-inviscid fluids. We show that the streaming inside the fluid arises from a complex coupling between the bulk and the boundary layers. This coupling can be taken into account by applying modified boundary conditions in a three-dimensional Navier-Stokes formulation for the streaming in the bulk. Numerical simulations based on this theoretical framework show good qualitative and quantitative agreement with experimental results. They also highlight the relevance of three-dimensional effects in the streaming patterns. Our simulations reveal that the variety of experimental patterns is deeply linked to the boundary condition at the top interface, which may be strongly affected by the presence of contaminants along the surface.

Localized Faraday patterns under heterogeneous parametric excitation

“…The relation between the experiment quantities and the dimensionless parameters ν, µ, γ, as well as the envelope ψ and the time, are given in detail in Refs. [27,36,37]. For our experiments, it can be shown that |ψ| 2 ∼ 10 −3 , µ ∼ 10 −2 , ν ∼ 10 −1 and γ ∼ 10 −1 .…”

Mean flow produced by small-amplitude vibrations of a liquid bridge with its free surface covered with an insoluble surfactant

“…The case of Faraday waves in a rectangular container was considered in Ref. [39], where no specific surfactant was added. In this study, surface contamination was seemingly present due to the use of tap water, which is easily contaminated.…”

Counter-rotation in an orbitally shaken glass of beer

“…Nontrivial surface flows in orbital shaking strikingly illustrates the critical influence of surface contamination in wave-induced flow generation [9][10][11][12][13]. We show here that the reversal in the floating raft rotation results from a complex interplay between transport by the rotating sloshing wave, friction with the container wall, and internal stress in the viscoelastic raft [14].…”

“…We measure the mean motion of the surface covering averaged over the wave period with a camera located above the cylinder. In order to filter out the large-amplitude wave motion and measure only the second order mean flow, the image acquisition is synchronized with the forcing [4,12]. This stroboscopic measurement is sensitive to the total (Lagrangian) mass transport, which includes the (Eulerian) steady streaming contribution and the Stokes drift contribution.…”