Relevance of the Thorpe length scale in stably stratified turbulence

Abstract

Direct numerical simulations of stably stratified turbulence are used to compare the Thorpe overturn length scale, L T , with other length scales of the flow that can be constructed from large-scale quantities fundamental to shear-free, stratified turbulence. Quantities considered are the turbulent kinetic energy, k, its dissipation rate, , and the buoyancy frequency, N. Fundamental length scales are then the Ozmidov length scale, L O , the isotropic large scale, L k , and a kinetic energy length scale, L kN . Behavior of all three fundamental scales, relative to L T , is shown to be a function of the buoyancy strength parameter NT L , where T L = k/ is the turbulence time scale. When buoyancy effects are dominant (i.e., for NT L > 1), L T is shown to be linearly correlated with L kN and not with L O as is commonly assumed for oceanic flows. Agreement between L O and L T is only observed when the buoyancy and turbulence time scales are approximately equal (i.e., for the critical case when NT L ≈ 1). The relative lack of agreement between L T and L O in strongly stratified flows is likely due to anisotropy at the outer scales of the flow where the energy transfer rate differs from . The key finding of this work is that observable overturns in strongly stratified flows are more reflective of k than . In the context of oceanic observations, this implies that inference of k, rather than , from measurements of L T is fundamentally correct when NT L ≈ 1 and most appropriate when NT L > 1. Furthermore, we show that for NT L < 1, L T is linearly correlated with L k when mean shear is absent. C 2013 AIP Publishing LLC. [http://dx.

The characteristics of billows generated by internal solitary waves

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