Mixing in stratified gravity currents: Prandtl mixing length

TL;DR

This study experimentally investigates shear-induced vertical mixing in stratified gravity currents, demonstrating that a Prandtl mixing length model effectively describes the mixing processes better than traditional eddy viscosity models.

Contribution

The paper introduces the application of a Prandtl mixing length model to stratified gravity currents, providing a better understanding of mixing physics in such flows.

Findings

Prandtl mixing length model accurately describes momentum and density fluxes.

Constant mixing lengths are observed at specific Richardson and Reynolds numbers.

Eddy viscosity models are inadequate for capturing the physics of stratified shear mixing.

Abstract

Shear-induced vertical mixing in a stratified flow is a key ingredient of thermohaline circulation. We experimentally determine the vertical flux of momentum and density of a forced gravity current using high-resolution velocity and density measurements. A constant eddy viscosity model provides a poor description of the physics of mixing, but a Prandtl mixing length model relating momentum and density fluxes to mean velocity and density gradients works well. For $<Ri_g > \approx 0.08$ and $Re_\lambda \approx 100$, the mixing lengths are fairly constant, about the same magnitude, comparable to the turbulent shear length.