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

Leclair, Matthieu; Raja, Keshav Jayakrishnan; Staquet, Chantal

doi:10.1017/jfm.2019.1077

Cited by 5 publications

(4 citation statements)

References 19 publications

(17 reference statements)

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“…This type of interaction was first studied theoretically assuming weakly nonlinear sinusoidal plane waves in an inviscid fluid, by Thorpe [11], who pointed attention to certain special configurations where resonances of the induced second-and third-harmonic waves are possible. These resonances were revisited in very recent theoretical and numerical work [12], which indicates that, unlike monochromatic sinusoidal waves, in the case of finite-width wave beams the resonant response is bounded. Furthermore, when the boundary slope is increased towards critical, viscous dissipation dominates over the energy transfer to the second harmonic due to nonlinear interactions.…”

Section: Introductionmentioning

confidence: 99%

Viscous reflection of internal waves from a slope

Kataoka

Akylas

2020

Phys. Rev. Fluids

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Motivated by the laboratory experiments of Rodenborn et al. [Phys. Fluids 23, 026601 (2011)], a weakly nonlinear model is developed that accounts for viscous dissipation in the reflection of a finite-width internal wave beam from a uniform slope. Asymptotically, at high Reynolds number, viscous effects come into play predominantly in the immediate vicinity of the critical slope angle equal to the propagation angle to the horizontal of the incident wave beam. However, in the experiments of Rodenborn et al. where the Reynolds number is moderately large, it turns out that viscosity is important throughout the slope range considered, which explains the overall poor agreement of their observations with earlier inviscid models. The predictions of the proposed model, by contrast, are in good qualitative, and in some respects quantitative, agreement with these experiments, and they also compare favorably against numerical Navier-Stokes simulations.

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Section: Introductionmentioning

confidence: 99%

Viscous reflection of internal waves from a slope

Kataoka

Akylas

2020

Phys. Rev. Fluids

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“…Wave interactions within the area A are examined by Leclair et al. (2020) for an incident beam of two-dimensional plane waves of finite width, but only with θ I = 0° and α < β . They calculate the transfer of energy to a second harmonic wave of frequency 2 σ within the area A and take account of its radiation, showing that the effects of viscosity will eventually dominate over those of nonlinear transfer as the slope angle, α , increases.…”

Section: The Layer Of Interacting Incident and Reflected Wave Groups mentioning

confidence: 99%

“…2011; Karimi & Akylas 2014; Chalamalla & Sarkar 2016; Dauxois et al. 2018; Fan & Akylas 2019, 2020; Leclair, Raja & Staquet 2020). The structure of the wave groups is important, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, in conditions to be considered in §§ 1.3.7 and 3, resonant interactions between the incident and reflected waves travelling in groups may lead to wave instability and hence breaking (Thorpe 1987 b , 2000; Leclair et al. 2020). Fronts may also be produced within the surf zone and may strongly modulate mixing (Legg & Adcroft 2003; van Haren & Gostiaux 2012).…”

Section: Introductionmentioning

confidence: 99%

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