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Effect of gravity waves on turbulence decay in stratified fluids

Published online by Cambridge University Press:  20 April 2006

J. Weinstock
J. Weinstock
Affiliation:
National Oceanic and Atmospheric Administration. Aeronomy Laboratory, Boulder, Colorado 80303
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Abstract

A theoretical calculation is made of the decay of turbulence energy in the presence of coherent internal gravity waves of various intensities. The wave-turbulence interaction considered is energy production by wave shear. The production term (stress) is calculated by a second-order closure, with temperature fluctuations accounted for by buoyancy subrange theory. This formalism applies to large or small turbulence Froude number, both extremes of which are often encountered in experimental turbulence decay. The theoretical turbulence decay is shown to be a universal function of the wave shear (strain rate) and wave frequency provided that the energy is expressed in terms of the buoyancy wavenumber kB, and time is expressed in terms of N, the Brunt-Väisälä frequency. With the amplitude of wave shear characterized by a gradient Richardson number Ri0, the turbulence decay is found to undergo a sudden transition from rapid decay to a much slower oscillating decay when Ri0 is less than about 0.4. The transition time occurs at about t ≈ 2πN−1. If Ri0 exceeds 0.8 the rate of decay exceeds that of a neutral fluid. A transition in turbulence decay was observed in experiments by Dickey & Mellor (1980). It might explain the continued presence of turbulence in dynamically stable regions of oceans or atmosphere. The theory is compared in much detail with the Dickey & Mellor experiment. A briefer comparison is also made with other experiments, and with previous calculations of turbulence maintenance by steady mean shear. A simple explanation is proposed of why a transition is observed in a vertical grid experiment but not in horizontal grid experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 140 , March 1984 , pp. 11 - 26
Copyright
© 1984 Cambridge University Press

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