Quantitative laboratory observations of internal wave reflection on ascending slopes

Gostiaux, Louis; Dauxois, Thierry; Didelle, Henri; Sommeria, Joël; Viboud, Samuel

doi:10.1063/1.2197528

Cited by 43 publications

(31 citation statements)

References 24 publications

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“…Gostiaux et al 22 confirmed this prediction experimentally and our experiments and simulations are also in accord with the predicted relation. It seems plausible that this result, coupled with the ␣ geom condition ͑equal beam widths at peak harmonic generation͒, would lead to a triad relationship between the wave vectors of the incident, reflected fundamental, and reflected harmonic, as expected from the resonant triad theory of Thorpe;19 however, the results for the wave vectors in our experiments and simulations do not support the triad theory.…”

Section: E Wave Number Of the Second Harmonicsupporting

confidence: 93%

“…10,17,18 Weakly nonlinear analyses for inviscid fluids by Thorpe 19 and by Tabaei et al 20 have predicted the value of the topographic slope angle at which the second harmonic intensity is a maximum. Pioneering experiments and simulations 21,22 studied harmonic generation by reflecting internal waves but did not examine the applicability of the analyses of Thorpe and Tabaei et al to strongly nonlinear reflection processes. The present study examines how the generation of second harmonic waves upon reflection from a sloping boundary depends on boundary angle, wave beam intensity, and fluid viscosity.…”

Section: Introductionmentioning

confidence: 98%

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Harmonic generation by reflecting internal waves

et al. 2011

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The generation of internal gravity waves by tidal flow over topography is an important oceanic process that redistributes tidal energy in the ocean. Internal waves reflect from boundaries, creating harmonics and mixing. We use laboratory experiments and two-dimensional numerical simulations of the Navier-Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from our experiments and simulations agree well but differ markedly from theoretical predictions by S. A. Thorpe ͓"On the reflection of a train of finite amplitude waves from a uniform slope," J. Fluid Mech. 178, 279 ͑1987͔͒ and A. Tabaei et al. ͓"Nonlinear effects in reflecting and colliding internal wave beams," J. Fluid Mech. 526, 217 ͑2005͔͒, except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow ͑where the Dauxois-Young amplitude parameter value is only 0.01͒, we find that the ratio of the reflected wave number to the incoming wave number is very different from the prediction of weakly nonlinear theory. Further, we observe that for incident beams with a wide range of angles, frequencies, and intensities, the second harmonic beam produced in reflection has a maximum intensity when its width is the same as the width of the incident beam. This observation yields a prediction for the angle corresponding to the maximum in second harmonic intensity that is in excellent accord with our results from experiments and numerical simulations.

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Section: E Wave Number Of the Second Harmonicsupporting

confidence: 93%

Section: Introductionmentioning

confidence: 98%

Harmonic generation by reflecting internal waves

et al. 2011

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“…[1][2][3][4][5] The dispersion relation describing these waves, = N cos , relates the frequency to the angle of energy propagation relative to the vertical z. The buoyancy frequency N = ͱ −g ‫ء‬ −1 d 0 / dz is a measure for the background density stratification ‫ء‬ + 0 ͑z͒, where ‫ء‬ is the average density of the fluid, 0 ͑z͒ the vertically varying density, and g gravity.…”

Section: Introductionmentioning

confidence: 99%

Observations on the robustness of internal wave attractors to perturbations

et al. 2010

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Previously, internal wave attractors have been studied in the laboratory in idealized situations. Here, we present a series of experiments in which these conditions are modified. Modifications are made by varying the forcing frequency, by using a nonuniform stratification, by introducing finite amplitude perturbations to the trapezoidal domain, and by using a parabolic domain. All these new experiments reveal the persistence of internal wave attractors that remain reasonably well predictable by means of ray tracing. We conclude that the occurrence of wave attractors is likely to be more general than has previously been thought. The fundamental response of the confined, continuously stratified fluids studied in this paper to a sustained forcing has to be described in terms of internal wave attractors.

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“…So far, only a few experimental studies on the generation of internal waves on the continental margins [ Chapman , 1984; Sutherland et al , 1999; Zhang et al , 2008] have been reported, but they are not able to measure the spatial structure of both the velocity field and the density field of internal waves simultaneously. Nowadays, the Particle Image Velocimetry (PIV) [ Dalziel et al , 2007] and the Synthetic Schlieren [ Dalziel et al , 2000; Sveen and Dalziel , 2005; Gostiaux et al , 2006] techniques have made this possible.…”

Section: Introductionmentioning

confidence: 99%

Laboratory experiments on the generation of internal waves on two kinds of continental margin

Wang

Chen

Jiang

2012

Geophysical Research Letters

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[1] We quantitatively study the relationship and differences between the internal waves generated on two kinds of continental margin in laboratory. Experimental results show that the steepness of the shelf break exerts a strong influence on the spatial structure of the internal waves generated on the continental margin. When the oscillatory barotropic tide flows over the continental margin with an abrupt shelf break and is not resonant with its slope, internal waves with three energy rays are generated, while on the continental margin with a gentle shelf break, only two rays can be found in the internal waves. Moreover, we compare the flux, width and kinetic energy flux of these rays and find that the phases of the internal waves generated by the interaction between the oscillatory barotropic tide and the shelf break lag behind the oscillatory barotropic tide. Citation: Wang, T., X. Chen, and W. Jiang (2012), Laboratory experiments on the generation of internal waves on two kinds of continental margin, Geophys. Res. Lett., 39, L04602,

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Quantitative laboratory observations of internal wave reflection on ascending slopes

Cited by 43 publications

References 24 publications

Harmonic generation by reflecting internal waves

Harmonic generation by reflecting internal waves

Observations on the robustness of internal wave attractors to perturbations

Laboratory experiments on the generation of internal waves on two kinds of continental margin

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