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, LT, 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, ε, and the buoyancy frequency, N. Fundamental length scales are then the Ozmidov length scale, LO, the isotropic large scale, Lkε, and a kinetic energy length scale, LkN. Behavior of all three fundamental scales, relative to LT, is shown to be a function of the buoyancy strength parameter NTL, where TL = k/ε is the turbulence time scale. When buoyancy effects are dominant (i.e., for NTL > 1), LT is shown to be linearly correlated with LkN and not with LO as is commonly assumed for oceanic flows. Agreement between LO and LT is only observed when the buoyancy and turbulence time scales are approximately equal (i.e., for the critical case when NTL ≈ 1). The relative lack of agreement between LT and LO in strongly stratified flows is likely due to anisotropy at the outer scales of the flow where the energy transfer rate differs from ε. The key finding of this work is that observable overturns in strongly stratified flows are more reflective of k than ε. In the context of oceanic observations, this implies that inference of k, rather than ε, from measurements of LT is fundamentally correct when NTL ≈ 1 and most appropriate when NTL > 1. Furthermore, we show that for NTL < 1, LT is linearly correlated with Lkε when mean shear is absent.