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
Highlights
IntroductionFaraday waves (Faraday 1831) are subject to studies for a large variety of applications, ranging from bio-medicine to material sciences (e.g. controlled pattern formation, walking and orbiting of droplets) (Saylor and Kinard 2005; Couder et al 2005)
Faraday waves (Faraday 1831) are subject to studies for a large variety of applications, ranging from bio-medicine to material sciences (Saylor and Kinard 2005; Couder et al 2005)
For a thick layer of 3 cm liquid height the system is by no means shallow in comparison to the typical scale of energy injection and, as we show in this study, pronounced three dimensional flows occur in the bulk
Summary
Faraday waves (Faraday 1831) are subject to studies for a large variety of applications, ranging from bio-medicine to material sciences (e.g. controlled pattern formation, walking and orbiting of droplets) (Saylor and Kinard 2005; Couder et al 2005). The presence of an inverse energy cascade in 2D turbulence has been theoretically predicted (Kraichnan 1971) and was observed in both numerical and experimental results for different fluid flows (von Kameke et al 2011; Farazmand et al 2011; Boffetta and Ecke 2012; Liao and Ouellette 2013; Francois et al 2013) and references therein). Energy is introduced at intermediate forcing scales and transferred upwards to larger scales, resulting in a net inverse energy flux Under particular conditions, this phenomenon can even lead to energy condensation, by which large and ordered flow structures emerge from the seemingly disordered motion at small scales (Xia et al 2009; Musacchio and Boffetta 2019; Shats et al 2014)
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