Generation of vortices by gravity waves on a water surface

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%

“…Next, we consider the formation and decay of the vortex motion for the same experimental conditions in more detail and compare the results with analytical predictions (14) and (17), which are reasonable because t E ≈ 125 s is significantly longer than t S ≈ 10 s, see Fig. 3.…”

Section: Methodsmentioning

confidence: 69%

Formation and decay of eddy currents generated by crossed surface waves

et al. 2019

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“…The dependence Ω L ∝ sin ψ stated in equation (28) that the generation of eddy currents is a nonlinear second order effect, which was proved experimentally in papers [4,5,10], and that the vortices' centers (where the vorticity is maximized) are located in the nodes of the wave pattern, which was also demonstrated experimentally in papers [4][5][6]. Indeed, averaging over time of product of two monochromatic phase-shifted functions must be proportional to sin(ψ + α), where ψ is the phase shift and α is some possible correction, and therefore Ω L ∝ sin(ψ + α).…”

Section: B Eddy Currents On the Fluid Surface And In The Bulkmentioning

confidence: 83%

“…Next we turn to the nonlinear analysis and here motivated by recent experiments [4][5][6] we consider two monochromatic orthogonal standing waves propagating perpendicular to each other h = H 1 cos(ωt) cos(kx) + H 2 cos(ωt + ψ) cos(ky).…”

Section: B Eddy Currents On the Fluid Surface And In The Bulkmentioning

confidence: 99%

“…The interest to the progressive wave is justified by almost unidirectional wave spectrum excited by a wind in the ocean. In the laboratory, surface waves can be excited by the wavemakers and this promoted expansion of the interest onto crossed monochromatic plane waves as the simplest nontrivial example [4][5][6]. In the experiments, the eddy laminar horizontal currents induced by crossed waves were observed by analysing the velocity of floating particles by PIV-method.…”

Section: Introductionmentioning

confidence: 99%

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Influence of a thin compressible insoluble liquid film on the eddy currents generated by interacting surface waves

Parfenyev

Vergeles

2018

Phys. Rev. Fluids

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Recently the generation of eddy currents by interacting surface waves was observed experimentally. The phenomenon provides the possibility for manipulation of particles which are immersed in the fluid. The analysis shows that the amplitude of the established eddy currents produced by stationary surface waves does not depend on the fluid viscosity in the free surface case. The currents become parametrically larger being inversely proportional to the square root of the fluid viscosity in the case when the fluid surface is covered by an almost incompressible thin liquid (i.e. shear elasticity is zero) film formed by an insoluble agent with negligible internal viscous losses as compared to the dissipation in the fluid bulk. Here we extend the theory for a thin insoluble film with zero shear elasticity and small shear and dilational viscosities on the case of an arbitrary elastic compression modulus. We find both contributions into the Lagrangian motion of passive tracers, which are the advection by the Eulerian vertical vorticity and the Stokes drift. Whereas the Stokes drift contribution preserves its value for the free surface case outside a thin viscous sublayer, the Eulerian vertical vorticity strongly depends on the fluid viscosity at high values of the film compression modulus. The Stokes drift acquires a strong dependence on the fluid viscosity inside the viscous sublayer, however, the change is compensated by an opposite change in the Eulerian vertical vorticity. As a result, the vertical dependence of the intensity of eddy currents is given by a sum of two decaying exponents with both decrements being of the order of the wave number. The decrements are numerically different, so the Eulerian contribution becomes dominant at some depth for the surface film with any compression modulus. *

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