Breaking internal waves and turbulent dissipation
Abstract:We explore what might be discovered about the breaking of progressive internal waves and the consequent mixing by following some of the methodologies and techniques used to study surface wave breaking. It is suggested that breaking is most likely to occur in wave groups, where the wave field is locally amplified. In a stratified fluid of uniform buoyancy frequency, N, the breaking regions of internal wave groups extend in approximately horizontal directions. Two classes of breaking, “convective overturn” and “shear instability,” are possible in progressive internal waves propagating in uniform stratification with no mean shear. Convective overturning and associated static instability occur at all wave frequencies, but only if the wave slope, s = am, exceeds unity, where a is the wave amplitude and m is the vertical wavenumber. Self-induced shear instability may take place in waves with slopes s < 1, and therefore less than the slopes required for convective overturn, but only when a wave-related Richardson number is sufficiently small; to achieve this, the wave frequency must be close to the inertial frequency. Equations are derived to express the energy dissipated in breaking or the strength of breaking in terms of the characteristics of a breaking wave. A particular measure of breaking analogous to that used to quantify surface wave breaking is ΛI(cb )dcb , the mean area of the fronts of breaking regions, projected onto the vertical and per unit volume, that are produced by internal breakers traveling at speeds between cb and cb + dcb . Estimates are made of the values of ΛI required to sustain a vertical eddy diffusion coefficient of K ρ = 10–5 m2 s–1 through the breaking of internal waves of typical amplitude by convective overturn (with s > 1) and by the self-induced shear instability of near-inertial waves when s < 1. Values of ΛI are of order 1.0 × 10–2 m–1 (i.e., a vertical surface area of about 10 cm × 10 cm in each cubic meter). The predictions are tested by using them to find the fraction of the water column in which turbulence occurs and by comparing the predicted values with existing observations. Additional theoretical studies and laboratory experiments are required to test the proposed analytical relations. Existing sea-going measurement techniques are reviewed and further observations are suggested to advance the understanding of breaking internal waves.
Document Type: Research Article
Publication date: 2010-11-01
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