Abstract

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 high-resolution 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 T 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.

Department(s)

Civil, Architectural and Environmental Engineering

Comments

Office of Naval Research, Grant N00014-16-1-3015

Keywords and Phrases

stratified flows; stratified turbulence; turbulent mixing

International Standard Serial Number (ISSN)

1469-7645; 0022-1120

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Cambridge University Press, All rights reserved.

Publication Date

25 May 2019

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