Two- and three-dimensional parametric instabilities in finite-amplitude internal gravity waves

Klostermeyer, J.

doi:10.1080/03091929108229035

Cited by 85 publications

(102 citation statements)

References 29 publications

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“…For example, monochromatic waves are unstable to parametric subharmonic instability (Klostermeyer 1991;Lombard & Riley 1996;Benielli & Sommeria 1996;Koudella & Staquet 2006). Such waves interact with themselves, transferring energy to longer time-scale, shorter spatial-scale waves.…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear internal gravity wavepackets

Sutherland

2006

J. Fluid Mech.

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Horizontally periodic, vertically localized internal wavepackets evolve nonlinearly due only to interactions between the waves and their wave-induced mean flow. The corresponding weakly nonlinear equation that describes the evolution of the amplitude envelope before the onset of parametric subharmonic instability is examined. The results are compared with fully nonlinear numerical simulations and are shown to lie in excellent agreement for over 15 buoyancy periods. Analysis of the equation shows that the evolution is modulationally unstable if the wave frequency exceeds that of waves with the fastest vertical group speed and if the amplitude is sufficiently large. Waves that move close to the fastest vertical group speed are unstable even if their relative amplitude is a tiny fraction of the inverse relative vertical extent of the wavepacket. At late times in the evolution of an unstable wavepacket third-order dispersion terms become non-negligible and act in conjunction with weakly nonlinear effects to retard the vertical advance of the wavepacket as a whole.

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Section: Introductionmentioning

confidence: 99%

Weakly nonlinear internal gravity wavepackets

Sutherland

2006

J. Fluid Mech.

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“…Indeed we know by now that these waves show instabilities at all amplitudes, unless damped by viscosity (Mied, 1976;Klostermeyer, 1982Klostermeyer, , 1983Klostermeyer, , 1991Lombard and Riley, 1996a;Sonmor and Klaassen, 1997). As shown by Lombard and Riley (1996a) it is neither the wave-related shear nor the corresponding stratification which are solely responsible for the growth of linear NMs, but a mixture of the two.…”

Section: High-frequency Gravity Wavesmentioning

confidence: 91%

“…They show that the breaking of a HGW typically results in wave decay to amplitudes well below the conventional instability thresholds. The breaking of a statically and dynamically stable HGW can lead to the original wave being replaced by another secondary wave in the course of a resonant wave-wave interaction related to a parametric subharmonic instability (McComas and Bretherton, 1977;Klostermeyer, 1991;Thorpe, 1994;Vanneste, 1995). What had not been settled yet was the question whether this behavior can be tied to the HGW being perturbed by a distinct NM or SV.…”

Section: High-frequency Gravity Wavesmentioning

confidence: 94%

Gravity-wave breaking: Linear and primary nonlinear dynamics

Achatz

2007

Advances in Space Research

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“…A linear stability analysis of this basic state against two-and three-dimensional perturbations was conducted by Klostermeyer (1991); only one orientation of the primary wave vector and of the plane of the three-dimensional perturbation were considered (this plane was perpendicular to the primary wave propagation plane ðk;gÞ). Klostermeyer (1991) found that the most amplified perturbation is three-dimensional and grows at small scale through a parametric instability mechanism. This pioneering work was complemented by Lombard and Riley (1996a) and Sonmor and Klaassen (1997).…”

Section: Basic Processes Leading To Internal Wave Breakingmentioning

confidence: 99%

Gravity and Inertia-Gravity Internal Waves: Breaking Processes and Induced Mixing

Staquet¹

2004

Surv Geophys

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Internal gravity waves, whether influenced or not by the Earth's rotation, are ubiquitous dynamical features in the stratosphere and in the interior of the ocean. We review the mechanisms by which such waves may break when propagating in an infinite (possibly moving) fluid with uniform stratification. The methods and models used to quantify mixing in a stably-stratified fluid are next recalled. The mixing properties induced by the breaking waves as obtained from several field, experimental and numerical experiments reported in the literature are presented.

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Two- and three-dimensional parametric instabilities in finite-amplitude internal gravity waves

Cited by 85 publications

References 29 publications

Weakly nonlinear internal gravity wavepackets

Weakly nonlinear internal gravity wavepackets

Gravity-wave breaking: Linear and primary nonlinear dynamics

Gravity and Inertia-Gravity Internal Waves: Breaking Processes and Induced Mixing

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