Resonant Internal Wave Interactions

Martin, S.; Simmons, William; Wunsch, Carl

doi:10.1038/2241014a0

Cited by 17 publications

(9 citation statements)

References 6 publications

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“…Weakly nonlinear interactions of internal waves arise from the quadratic nonlinearity in the transport terms of the Navier-Stokes equations (Phillips 1960;Martin et al 1969;Tabaei et al 2005). They are best understood in Fourier space, where the velocity term can be expressed in the following form:…”

Section: Interacting Beamsmentioning

confidence: 99%

The magic carpet: an arbitrary spectrum wave maker for internal waves

2019

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We present a novel apparatus for generating internal waves of arbitrary size and shape, including both phase-locked and propagating waves. It is an actively driven, flexible "magic carpet" in the base of a tank. Our wave maker is computercontrolled to enable easy configuration. The actuation of a smooth, flexible surface produces clean waveforms with a predictable spectrum, for which we derive a theoretical model. We demonstrate the versatility of our wave maker through an experimental study of linear and nonlinear, isolated, and combined internal waves, including some that are sufficiently nonlinear to break remote from their source.

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Section: Interacting Beamsmentioning

confidence: 99%

The magic carpet: an arbitrary spectrum wave maker for internal waves

2019

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“…Wave energy can be transferred towards frequencies lower than the forcing frequency (Martin et al, 1969(Martin et al, , 1972McEwan, 1971;McEwan and Robinson, 1975). Any resonant triad consisting of a finite amplitude wave and two infinitesimal components is unstable for the sum interaction and neutrally stable for the difference interaction (Hasselmann, 1967;McEwan, 1971).…”

Section: Introductionmentioning

confidence: 99%

Two Intersecting Internal Wave Rays: a Comparison Between Numerical and Laboratory Results

Javam¹,

Teoh²,

Imberger³

et al. 2013

Physical Processes in Lakes and Oceans

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The interaction between two downward propagating internal wave rays in a linearly stratified fluid was examined numerically and experimentally. The numerical simulations employed a SIMPLE scheme with a third order QUICK discretization for the advective terms and second order Crank-Nicholson scheme on a non-staggered grid to solve the full unsteady equations of motion in an open domain with boundary conditions based on the Sommerfield radiation condition. The laboratory experiments were performed in a glasswalled tank filled with a linearly stratified salt solution with two identical wave paddles used to generate two internal wave rays. The interaction between the two wave rays was visualized by bull eye's rainbow schlieren and shadowgraph techniques, in conjunction with velocity measurements made by particle image velocimetry. Good agreement was found between the observed and simulated interaction mechanisms. The nonlinear nonresonant interaction of two wave rays with identical properties, but opposite horizontal phase velocities, led initially to the formation of small spatial scales followed by the development of evanescent modes. The evanescent modes, with frequencies greater than the local buoyancy frequency, were trapped within the intersection region. The energy transferred to the trapped evanescent modes ultimately causing overturning of the density field in the intersection region.

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“…Hasselmann (1966) presented a general theory for geophysical nonlinear interactions drawing an analogy with quantum field scattering theory. Experiments have recently been reported by McGoldrick (1970) and Kim and Hanratty (1971) for progressive capillary-gravity waves, and by Martin, Simmons and Wunsch (1969) for progressive internal waves. Thorpe (1966A) suggested an experiment in which two progressive surface gravity waves could be made to resonantly generate an internal wave.…”

Section: --77mentioning

confidence: 99%

Nonlinear interactions among standing surface and internal gravity waves

Joyce¹

1972

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A laboratory study has been undertaken to measure the momentum transfer from surface to internal gravity waves in a nonlinear, resonant interaction. The interacting waves form triads for which-1s -Q2sand K. being the frequency and wave-I 1s2s-I=O;QJ number of the jth wave. In particular, the experiment is designed to model a generating mechanism for high frequency, oceanic internal waves.Unlike previously published results involving single triplets of interacting waves, all waves here considered are standing waves. The growth to steady state of a resonant internal wave is observed while two deep water surface eigen modes are simultaneously forced by a paddle. Results are compared to theoretical predictions which assume, ab initio, all waves to be standing. Inclusion of viscous side wall dissipation and slight detuning permit predictions of steady state amplitudes and phases as well as initial growth rates. Good agreement is found between predicted and measured amplitudes and phases. The experiments also suggest that the internal wave in a resonant triad can act as a catalyst, permitting appreciable energy transfer among surface waves.

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Resonant Internal Wave Interactions

Cited by 17 publications

References 6 publications

The magic carpet: an arbitrary spectrum wave maker for internal waves

The magic carpet: an arbitrary spectrum wave maker for internal waves

Two Intersecting Internal Wave Rays: a Comparison Between Numerical and Laboratory Results

Nonlinear interactions among standing surface and internal gravity waves

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