Nonlinear Generation of Vorticity by Surface Waves

The mass-transport induced by crossed surface waves consists of the Stokes and Euler contributions which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and it is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced masstransport theoretically and experimentally and demonstrate that both contributions have different time scales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution instantly tracks the wave pattern and therefore it evolves faster due to the additional wave damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film presented on the fluid surface with the compression modulus being the only non-zero rheological parameter of the film. Then the Euler contribution into the mass-transport becomes larger and the evolution of the Stokes contribution becomes faster as compared to the free surface case. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.

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“…2. The result is in agreement with earlier measurements [5,17], see also the discussion of these papers in Ref.…”

Section: Discussionsupporting

confidence: 94%

“…VI.A]. We have calculated both these quantities (4) and (5) and found that the obtained value of the film compression modulus ε leads to the values which are in a reasonable agreement with the experimental data, see Fig. 5.…”

Section: Discussionsupporting

confidence: 77%

Formation and decay of eddy currents generated by crossed surface waves

et al. 2019

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“…This results in a small displacement of the particle in the direction of the wave propagation when a wave cycle is completed. Note that the physics of the Lagrangian circular drift revealed here is intrinsically different from a recent Eulerian theory of vorticity generation on a surface perturbed by waves, which considers bulk viscosity as the essential ingredient of the mechanism 22 .…”

Section: Resultscontrasting

confidence: 58%

Wave-based liquid-interface metamaterials

et al. 2017

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The control of matter motion at liquid–gas interfaces opens an opportunity to create two-dimensional materials with remotely tunable properties. In analogy with optical lattices used in ultra-cold atom physics, such materials can be created by a wave field capable of dynamically guiding matter into periodic spatial structures. Here we show experimentally that such structures can be realized at the macroscopic scale on a liquid surface by using rotating waves. The wave angular momentum is transferred to floating micro-particles, guiding them along closed trajectories. These orbits form stable spatially periodic patterns, the unit cells of a two-dimensional wave-based material. Such dynamic patterns, a mirror image of the concept of metamaterials, are scalable and biocompatible. They can be used in assembly applications, conversion of wave energy into mean two-dimensional flows and for organising motion of active swimmers.

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“…58 Several nonlinear models based on potential or viscous flows near a free surface have been proposed. 52,55,[59][60][61] An interesting path could be related to the Stokes drift induced by the variation of the temporal phase of 2D quasi-standing waves as shown in Fig. 9(b).…”

Section: D Turbulence In Faraday Wavesmentioning

confidence: 99%

Two-dimensional turbulence in three-dimensional flows

Xia

Nicolas

2017

Physics of Fluids

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This paper presents a review of experiments performed in three-dimensional flows that show behaviour associated with two-dimensional turbulence. Experiments reveal the presence of the inverse energy cascade in two different systems, namely, flows in thick fluid layers driven electromagnetically and the Faraday wave driven flows. In thick fluid layers, large-scale coherent structures can shear off the vertical eddies and reinforce the planarity of the flow. Such structures are either self-generated or externally imposed. In the Faraday wave driven flows, a seemingly three-dimensional flow is shown to be actually two-dimensional when it is averaged over several Faraday wave periods. In this system, a coupling between the wave motion and 2D hydrodynamic turbulence is uncovered.

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Nonlinear Generation of Vorticity by Surface Waves

Cited by 56 publications

References 8 publications

Formation and decay of eddy currents generated by crossed surface waves

Formation and decay of eddy currents generated by crossed surface waves

Wave-based liquid-interface metamaterials

Two-dimensional turbulence in three-dimensional flows

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