The relation between unstable shear layer thicknesses and turbulence lengthscales
This note explores the connection between the (i) lengthscales of unstable finescale shear layers which are responsible for turbulence production, (ii) turbulence patch thicknesses and (iii) the outer scales of turbulence, that is, the density overturn (Thorpe) and Ozmidov lengthscales, in the stratified ocean interior. Explanations are offered both for why (i) turbulence patches are often observed to be much thicker than outer turbulence scales and (ii) there is a spectral gap between finescale internal waves and the outer scales of turbulence. A finescale parameterization based on unstable shear predicts Ozmidov lengthscales smaller than unstable-shear-layer thicknesses for moderately unstable gradient Froude numbers |Vz|/N < 5.5 [or equivalently, gradient Richardson numbers Ri = N 2/V 2 z > 0.03 where |Vz|is the instantaneous finescale vertical shear magnitude and N the instantaneous buoyancy frequency] for a critical gradient Froude number δ c = 2; this is little changed for critical gradient Froude numbers as low as 1. Thus, assuming that patch thicknesses correspond to unstable shear-layer thicknesses, outer turbulence lengthscales will be smaller than patch thicknesses for moderately unstable shear but not strongly unstable shear. A spectral gap between internal wave and turbulent shear arises for similar reasons.
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Document Type: Research Article
Publication date: March 1, 2014
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