Publication Date:
2019-03-21
Description:
Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient Γ = ∈PE/∈ in stratified flows as a function of the turbulent Froude number Fr = ∈/Nk. Here, N is the buoyancy frequency, k is the turbulent kinetic energy, ∈ is the rate of dissipation of turbulent kinetic energy and ∈PE is the rate of dissipation of turbulent potential energy. We show that for Fr≫1, Γ ∝ Fr-2, for Fr∼ O(1), Γ ∝ Fr-1 and for Fr ≪ 1, Γ ∝ Fr0. These scaling results are tested using highresolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of Fr that encompasses weakly stratified to strongly stratified flow conditions. Given that the Fr cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the Fr from readily measurable quantities in the field. Scaling analyses show that Fr ∝ (LT/LO)-2 for LT/LO 〉 O(1), Fr ∝ (LT/LO)-1 for LT/LO ∼ O(1), and Fr∝(LT/LO)-2/3 for LT/LO 〈O(1), where LT is the Thorpe length scale and LO is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows. © 2019 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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