Abstract

In this analysis the quantification of diapycnal diffusivity Kρ in stratified flows such as those found in the ocean and atmosphere is explored. There are two simplifications that are routinely made when estimating mixing rates in stably stratified flows. First, a constant value is commonly assumed for the (irreversible) mixing coefficient Γ . Second, dissipation rates of turbulent kinetic energy ϵ are inferred using either the Thorpe (or Ellison) length scales or from microstructure measurements using the isotropy assumption. Data from three independent direct numerical simulations of homogeneous stratified turbulence are used as a testbed to highlight impacts of these assumptions on estimates of Kρ . A systematic analysis compares the inferred diffusivities to exact DNS diffusivities as a function of the turbulent Froude number Frt . Use of a constant Γ results in an under-prediction of Kρ by up to a factor of 5 for strongly stratified conditions (low Frt) and an over-prediction of Kρ by up to two orders of magnitude in weakly stratified conditions (high Frt). The use of inferred dissipation rates ϵ based on the assumption of isotropy results in an over-prediction of Kρ by a factor of 2 for low Frt (which is within the instrumentation error) and converges on the exact Kρ for Frt≥ 1. However, the use of kinematic length scales, such as the Thorpe or Ellison scales, to infer ϵ result in significant errors. The implications of these findings are applied in a simple demonstration to show how these tools can be used for improved estimates of mixing rates in stably stratified flows.

Department(s)

Civil, Architectural and Environmental Engineering

Comments

National Science Foundation, Grant OCE-2149047

Keywords and Phrases

Diapycnal mixing; Mixing efficiency; Osborn model; Stratified turbulence

International Standard Serial Number (ISSN)

1573-1510; 1567-7419

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Springer, All rights reserved.

Publication Date

01 Oct 2023

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