Three dimensional flows beneath a thin layer of 2D turbulence induced by Faraday waves

Abstract

Faraday waves occur on a fluid being subject to vertical shaking. Although it is well known that form and shape of the wave pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow. This flow exhibits attributes of two-dimensional turbulence and is replicated in this study. Despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional (2D) systems, little is known about the velocity fields developing beneath the fluid surface. In this study, planar velocity fields are measured by means of particle image velocimetry with high spatio-temporal resolution on the water surface and at different depths below it. A sudden drop in velocity and turbulent kinetic energy is observed at half a Faraday wavelength below the surface revealing that the surface flow is the main source of turbulent fluid motion. The flow structures below the surface comprise much larger spatial scales than those on the surface leading to very long-tailed temporal and spatial velocity (auto-) correlation functions. The three-dimensionality of the flow is estimated by the compressibility, which increases strongly with depth while the divergence changes its appearance from intermittent and single events to a large scale pattern resembling 2D cut-planes of convection rolls. Our findings demonstrate that the overall fluid flow beneath the surface is highly three-dimensional and that an inverse cascade and aspects of a confined 2D turbulence can coexist with a three-dimensional flow. Graphic abstract

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“…The vibration of the SurferBot establishes a surface flow field accompanying the radiating capillary wavefield. To visualize the flow field, buoyant hollow glass microspheres of diameter approximately 70 µm (Fibreglast Part #22) were suspended at the air-water interface and used as tracer particles [25]. To avoid clumping, the particles were stirred before each experimental trial.…”