Large Scale Energy Transfer from an Internal Gravity Wave Reflecting on a Simple Slope

Grisouard, Nicolas; Leclair, Matthieu; Gostiaux, Louis; Staquet, Chantal

doi:10.1016/j.piutam.2013.04.016

Cited by 14 publications

(13 citation statements)

References 21 publications

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“…Laboratory experiments and numerical simulations (Grisouard et al 2013) of the reflection from a slope of a wave beam of finite extent in the transverse direction revealed a wave-induced mean flow with amplitude comparable to that of the incident wave; such a strong mean flow, though, was not observed in two-dimensional simulations, where transverse variations were absent. Moreover, according to linear stability analysis, a uniform wave beam can be unstable to long-wavelength disturbances only if such modulations vary in the along-beam and the transverse directions (Kataoka & Akylas 2013).…”

Section: Introductionmentioning

confidence: 97%

On three-dimensional internal gravity wave beams and induced large-scale mean flows

Kataoka

Akylas

2015

J. Fluid Mech.

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The three-dimensional propagation of internal gravity wave beams in a uniformly stratified Boussinesq fluid is discussed, assuming that variations in the along-beam and transverse directions are of long length scale relative to the beam width. This situation applies, for instance, to the far-field behaviour of a wave beam generated by a horizontal line source with weak transverse dependence. In contrast to the two-dimensional case of purely along-beam variations, where nonlinear effects are minor even for beams of finite amplitude, three-dimensional nonlinear interactions trigger the transfer of energy to a circulating horizontal time-mean flow. This resonant beam-mean-flow coupling is analysed, and a system of two evolution equations is derived for the propagation of a small-amplitude beam along with the induced mean flow. This model explains the salient features of the experimental observations of

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Section: Introductionmentioning

confidence: 97%

On three-dimensional internal gravity wave beams and induced large-scale mean flows

Kataoka

Akylas

2015

J. Fluid Mech.

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“…Extension of the results from a free-slip reflecting surface to a no-slip one may require some extra caution. Laboratory measurements of mean flows within reflecting beams off a no-slip solid slope 45,46 suggest qualitatively different results of the mean-flow structure than those reported in the work of Z&D, which is expected to be a result of the three-dimensional configuration of the experiments. 52 Rodenborn et al 47 also reported discrepancy with the TAL theory 24 in terms of harmonic generation at a solid bottom slope.…”

Section: B Open Questionsmentioning

confidence: 73%

Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

Zhou

Diamessis

2015

Physics of Fluids

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In this paper sequel to Zhou and Diamessis ["Reflection of an internal gravity wave beam off a horizontal free-slip surface," Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes drift cancels each other out completely at the second order in wave steepness A, i.e., O(A 2), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A 2) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A 2) and thus particle dispersion on O(A 4). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.

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“…The three-dimensional laboratory experiments conducted in parallel to the present two-dimensional numerical simulations are also not appropriate to test the theoretical predictions. Indeed a Lagrangian mean flow is induced in the interaction area as a result of nonlinear and dissipative effects, whose amplitude can be as large as that of the incident wave due to cumulative dissipative effect (Grisouard et al 2013). As a result, the incident wave frequency is shifted through Doppler effect by the mean flow and refracted (with the phase lines bending toward the horizontal), which deeply modifies the incident wave geometry.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear reflection of a two-dimensional finite-width internal gravity wave on a slope

2020

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Large Scale Energy Transfer from an Internal Gravity Wave Reflecting on a Simple Slope

Cited by 14 publications

References 21 publications

On three-dimensional internal gravity wave beams and induced large-scale mean flows

On three-dimensional internal gravity wave beams and induced large-scale mean flows

Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

Nonlinear reflection of a two-dimensional finite-width internal gravity wave on a slope

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