Nonlinear water waves

Constantin, Adrian

doi:10.1098/rsta.2011.0594

Cited by 6 publications

(7 citation statements)

References 34 publications

(37 reference statements)

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“…Related research on this theme goes back many years, such as, for example, the studies by Longuett-Higgins (1979) and Simmen & Saffman (1985), among others. A variety of theoretical and experimental (more recent) articles can be found in the special issue edited by Constantin (2012) as well as in the articles by Constantin & Strauss (2004, Constantin (2006), Ehrnström & Villari (2008), Constantin & Varvaruca (2011) and Ehrnström, Escher & Villari (2012) and their respective references.…”

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confidence: 99%

Flow structure beneath rotational water waves with stagnation points

Ribeiro

Milewski²,

Nachbin

2017

J. Fluid Mech.

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The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressure and particle paths can be found and mapped back to the physical domain. We find that the flow beneath the waves contains zero, one, two or three stagnation points in a frame moving with the wave speed, and describe the bifurcations between these flows. When the vorticity is sufficiently strong, the pressure in the flow and on the bottom boundary also has very different features from the usual irrotational wave case.

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confidence: 99%

Flow structure beneath rotational water waves with stagnation points

Ribeiro

Milewski²,

Nachbin

2017

J. Fluid Mech.

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“…In this paper, we have investigated the Lagrangian period, T L , in periodic, nonlinear waves at finite water depth. The Lagrangian period may be of relevance to general studies of nonlinear water waves (e.g., [4]) and to averaging techniques used for wave-current interaction modeling (e.g., [1,7]). The T L is obtained by particle path integration in the experiments and the strongly nonlinear theory where the Fenton [6]-method is used.…”

Section: Resultsmentioning

confidence: 99%

“…A quadratic correction to φ in (1), due to the bound second-order elevation, reads: 3ωk A 2 cosh 2k(y + h) cos 2(kx − ωt)/(4 sinh 4 kh) [8]. This quadratic addition contributes to the wave drift velocity and Lagrangian period by an amount proportional to (k A) 4 and is not evaluated. The fluid velocity v = (u, v) obtained from (1) reads:…”

Section: Mean Drift Velocity Second-order Theorymentioning

confidence: 99%

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On the Lagrangian Period in Steep Periodic Waves

Grue

Kolaas

2019

Water Waves

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We show that, for periodic steep waves at finite water depth, the excess Lagrangian period, T L , made nondimensional by the Eulerian period, T 0 , is equal to the mean Lagrangian drift velocity, u L , made nondimensional by the wave speed, c. This result is exact within second-order theory. Measurements in wave tank obtain that the two quantities are approximately equal. The vertical mean of T L and u L are zero in the experiments. The vertically averaged Lagrangian period thus equals the Eulerian period. The experimental and theoretical vertical derivative of T L are the same in the middle of the water column but strongly differ above the bottom and below the wave surface. These differences are due to the secondary streaming effect in the viscous boundary layers in the experiments, at the bottom and free surface. Fully nonlinear calculations complement the investigation.

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“…The generation of flows using waves opens up the prospects of controlling transport of the surface matter, as well as the dispersion of pollutants, and it is interesting from the point of view of converting wave energy into stationary patterned surface flows. Mathematically, the problem of computing flows produced by surface waves remains very challenging, with just a handful of relatively simple wave configurations solved (see, e.g., [7]). However, in recent years, experimental and numerical studies have demonstrated that waves can generate a broad range of flows by various wave fields.…”

Section: Introductionmentioning

confidence: 99%

Generation of Vortex Lattices at the Liquid–Gas Interface Using Rotating Surface Waves

Xia

Nicolas

Gorce

et al. 2019

Fluids

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In this paper, we demonstrate experimentally that by generating two orthogonal standing waves at the liquid surface, one can control the motion of floating microparticles. The mechanism of the vortex generation is somewhat similar to a classical Stokes drift in linear progression waves. By adjusting the relative phase between the waves, it is possible to generate a vortex lattice, seen as a stationary horizontal flow consisting of counter-rotating vortices. Two orthogonal waves which are phase-shifted by π / 2 create locally rotating waves. Such waves induce nested circular drift orbits of the surface fluid particles. Such a configuration allows for the trapping of particles within a cell of the size about half the wavelength of the standing waves. By changing the relative phase, it is possible to either create or to destroy the vortex crystal. This method creates an opportunity to confine surface particles within cells, or to greatly increase mixing of the surface matter over the wave field surface.

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Nonlinear water waves

Abstract: This introduction to the issue provides a review of some recent developments in the study of water waves. The content and contributions of the papers that make up this Theme Issue are also discussed.

Cited by 6 publications

References 34 publications

Flow structure beneath rotational water waves with stagnation points

Flow structure beneath rotational water waves with stagnation points

On the Lagrangian Period in Steep Periodic Waves

Generation of Vortex Lattices at the Liquid–Gas Interface Using Rotating Surface Waves

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