Understanding and modeling turbulent fluxes and entrainment in a gravity current

TL;DR

This study experimentally investigates turbulent mixing and entrainment in a gravity current on an inclined plane, demonstrating a Prandtl mixing length model and analyzing flux fluctuations and entrainment mechanisms.

Contribution

It introduces a Prandtl mixing length model for turbulent fluxes in gravity currents and relates the mixing length to flow shear length, providing new insights into mixing and entrainment processes.

Findings

Turbulent fluxes scale quadratically with mean gradients.

The mixing length is approximately constant in the stratified shear layer.

A quantitative measure of local entrainment and detrainment is proposed.

Abstract

We present an experimental study of the mixing processes in a gravity current flowing on an inclined plane. The turbulent transport of momentum and density can be described in a very direct and compact form by a Prandtl mixing length model: the turbulent vertical fluxes of momentum and density are found to scale quadratically with the vertical mean gradients of velocity and density. The scaling coefficient, the square of the mixing length, is approximately constant over the mixing zone of the stratified shear layer. We show how, in different flow configurations, this length can be related to the shear length of the flow ($\epsilon$/$\partial$ z u^3)^1/2. We also study the fluctuations of the momentum and density turbulent fluxes, showing how they relate to mixing and to the entrainment/detrainment balance. We suggest a quantitative measure of local entrainment and detrainment derived from observed conditional correlations of density flux and density or vertical velocity fluctuations.