Generation of harmonics and sub-harmonics from an internal tide in a uniformly stratified fluid: numerical and laboratory experiments

Pairaud, Ivane; Staquet, Chantal; Sommeria, Joël; Mahdizadeh, Mahdi Mohammad

doi:10.1007/978-94-007-0360-5_5

Cited by 11 publications

(10 citation statements)

References 23 publications

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“…According to this model, the leading-order (quadratic) nonlinear interactions in the overlap region of the incident and the primary reflected beam drive a mean-flow and a second-harmonic disturbance; the former stays in the vicinity of the slope, while the latter, assuming 2ω is less than the background buoyancy frequency, radiates away along a direction specified by the dispersion relation. These predictions are consistent with laboratory experiments [15,16] as well as numerical simulations [17,18].…”

Section: Introductionsupporting

confidence: 89%

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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: Introductionsupporting

confidence: 89%

“…Here ρ has been rescaled to account for the resonant behavior of ρ = O(ε/δ) = O(ε 1/3 ) in the near-critical range δ = O(ε 2/3 ) defined in Eq. (17). Substituting these expansions in Eqs.…”

Section: Near-critical Beam Reflectionmentioning

confidence: 99%

Viscous reflection of internal waves from a slope

Kataoka

Akylas

2020

Phys. Rev. Fluids

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“…It is, however, worth noting that we systematically observe low values of b/a over the Reykjanes Ridge. This bias toward higher frequency possibly suggests that high-frequency waves are generated by interactions between the tide and the topography of the Reykjanes Ridge (Gerkema et al 2006;Gerkema 2006;Pairaud et al 2010). Low values of b/a are also found in the Iberian basin at and below the depth of the Mediterranean outflow water, between 1000 and 1800 m. For an environment located below the Mediterranean outflow water, at a depth of 1400-1500 m in the Canary basin, van Haren and Gostiaux (2009) …”

Section: A Mean Dissipation Rate and Observed Variability Rangementioning

confidence: 98%

Variability of the Turbulent Kinetic Energy Dissipation along the A25 Greenland–Portugal Transect Repeated from 2002 to 2012

Ferron

Kokoszka

Mercier

et al. 2016

Journal of Physical Oceanography

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The variability of the turbulent kinetic energy dissipation due to internal waves is quantified using a finescale parameterization applied to the A25 Greenland-Portugal transect repeated every two years from 2002 to 2012. The internal wave velocity shear and strain are estimated for each cruise at 91 stations from full depth vertical profiles of density and velocity. . The interannual variability in the dissipation rates is remarkably small over the whole transect. A few strong dissipation rate events exceeding the uncertainty of the finescale parameterization occur at depth between the Azores-Biscay Rise and Eriador Seamount. This region is also marked by mesoscale eddying flows resulting in enhanced surface energy level and enhanced bottom velocities. Estimates of the vertical energy fluxes into the internal tide and into topographic internal waves suggest that the latter are responsible for the strong dissipation events. At Eriador Seamount, both topographic internal waves and the internal tide contribute with the same order of magnitude to the dissipation rate while around the Reykjanes Ridge the internal tide provides the bulk of the dissipation rate.

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“…Clark & Sutherland (2010) indirectly linked this breakdown to PSI, a hypothesis also supported by numerical simulations. Furthermore, PSI was noted in an experimental-numerical study of a model internal tide (Pairaud et al 2010), as well as in numerical simulations of the reflection of a localized nearly monochromatic wave beam from a horizontal surface (Zhou & Diamessis 2013). Finally, recent experiments (Bourget et al 2013) have revealed that resonant triad interactions can bring about instability in a localized wave beam that comprises just three wavelengths of a sinusoidal wavetrain.…”

Section: Introductionmentioning

confidence: 94%

Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains

Karimi

Akylas

2014

J. Fluid Mech.

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Internal gravity wavetrains in continuously stratified fluids are generally unstable as a result of resonant triad interactions which, in the inviscid limit, amplify short-scale perturbations with frequency equal to one half of that of the underlying wave. This so-called parametric subharmonic instability (PSI) has been studied extensively for spatially and temporally monochromatic waves. Here, an asymptotic analysis of PSI for time-harmonic plane waves with locally confined spatial profile is made, in an effort to understand how such wave beams differ, in regard to PSI, from monochromatic plane waves. The discussion centres upon a system of coupled evolution equations that govern the interaction of a small-amplitude wave beam with short-scale subharmonic wavepackets in a nearly inviscid uniformly stratified Boussinesq fluid. For beams with general localized profile, it is found that triad interactions are not strong enough to bring about instability in the limited time that subharmonic perturbations overlap with the beam. On the other hand, for quasi-monochromatic wave beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope, PSI is possible if the beam is wide enough. In this instance, a stability criterion is proposed which, under given flow conditions, provides the minimum number of carrier wavelengths a beam of small amplitude must comprise for instability to arise.

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Generation of harmonics and sub-harmonics from an internal tide in a uniformly stratified fluid: numerical and laboratory experiments

Cited by 11 publications

References 23 publications

Viscous reflection of internal waves from a slope

Viscous reflection of internal waves from a slope

Variability of the Turbulent Kinetic Energy Dissipation along the A25 Greenland–Portugal Transect Repeated from 2002 to 2012

Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains

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