Diapycnal diffusivities in homogeneous stratified turbulence

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Abstract
Quantifying diapycnal mixing in stably stratified turbulence is fundamental to the understanding and modeling of geophysical flows. Data of diapycnal mixing from direct numerical simulations of homogeneous stratified turbulence and from grid turbulence experiments, are analyzed to investigate the scaling of the diapycnal diffusivity. In these homogeneous flows the instantaneous diapycnal diffusivity is given exactly by Kd = ερ/(∂/∂z)2 where ρ is the dissipation rate of density fluctuations, and ∂ is the mean density gradient. The diffusivity Kd may be expressed in terms of the large scale properties of the turbulence as Kd = γLE2/TL, where LE is the Ellison overturning length‐scale, TL is the turbulence decay time‐scale, and γ is half the mechanical to scalar time‐scale ratio. Our results show that LE and TL can explain most of the variations in Kd over a wide range of shear and stratification strengths while γ remains approximately constant.

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