Mixing and entrainment are suppressed in inclined gravity currents

TL;DR

This study uses direct numerical simulations to analyze inclined gravity currents, revealing how slope angle influences mixing parameters and demonstrating that entrainment diminishes as the flow approaches a critical Richardson number, with turbulence intensity vanishing at small slopes.

Contribution

The paper introduces a model predicting mixing behavior and entrainment laws in inclined gravity currents, showing turbulence diminishes with slope angle, challenging previous assumptions about turbulent buoyancy flux.

Findings

Entrainment coefficient approaches zero as slope angle decreases.

Flow reaches a maximum Richardson number of approximately 0.15.

Turbulent Prandtl number remains constant across slope angles.

Abstract

We explore the dynamics of inclined temporal gravity currents using direct numerical simulation, and find that the current creates an environment in which the flux Richardson number $Ri_f$, gradient Richardson number $Ri_g$, and turbulent flux coefficient $\Gamma$ are constant across a large portion of the depth. Changing the slope angle $\alpha$ modifies these mixing parameters, and the flow approaches a maximum Richardson number $Ri_\textrm{max}\approx 0.15$ as $\alpha \rightarrow 0$ at which the entrainment coefficient $E \rightarrow 0$. The turbulent Prandtl number remains $O(1)$ for all slope angles, demonstrating that $E\rightarrow 0$ is not caused by a switch-off of the turbulent buoyancy flux as conjectured by Ellison (1957). Instead, $E \rightarrow 0$ occurs as the result of the turbulence intensity going to zero as $\alpha\rightarrow 0$, due to the flow requiring larger and larger shear to maintain the same level of turbulence. We develop an approximate model valid for small $\alpha$ which is able to predict accurately $Ri_f$, $Ri_g$ and $\Gamma$ as a function of $\alpha$ and their maximum attainable values. The model predicts an entrainment law of the form $E=0.31(Ri_\textrm{max}-Ri)$, which is in good agreement with the simulation data. The simulations and model presented here contribute to a growing body of evidence that an approach to a marginally or critically stable, relatively weakly stratified equilibrium for stratified shear flows may well be a generic property of turbulent stratified flows.