Entrainment and mixing in gravity currents using simultaneous velocity-density measurements

TL;DR

This study investigates how gravity currents entrain ambient fluid and transition between flow regimes using simultaneous velocity-density measurements, revealing a critical Reynolds number for mixing transition.

Contribution

It introduces a flux-based method to measure entrainment and identifies a mixing transition at Re≈2700 in gravity currents.

Findings

Entrainment coefficient varies with Reynolds number.

Flow transitions from Holmboe waves to Kelvin-Helmholtz instabilities.

Mixing transition occurs at Re≈2700.

Abstract

Gravity currents modify their flow characteristics by entraining ambient fluid, which depends on a variety of governing parameters such as the initial density, $\Delta \rho$, the total initial height of the fluid, $H$, and the slope of the terrain, $\alpha$, from where it is released. Depending on these parameters, the gravity current may be designated as sub-critical, critical, or super-critical. It is imperative to study the entrainment dynamics of a gravity current in order to have a clear understanding of mixing transitions that govern the flow physics, the shear layer thickness, $\delta_{u}$, and the mixing layer thickness, $\delta_{\rho}$. Experiments were conducted in a lock-exchange facility in which the dense fluid was separated from the ambient lighter fluid using a gate. As the gate is released instantaneously, an energy conserving gravity current is formed, for which the only governing parameter is the Reynolds number defined as $Re=\frac{Uh}{\nu}$, where $U$ is the front velocity of the gravity current, and $h$ is the height of the current. In our study, the bulk Richardson number, $Ri_{b}$=$\frac{g^{'}H}{U_{b}^{2}}$=1, takes a constant value for all the experiments, with $U_{b}$ being the bulk velocity of the layer defined as $U_{b}$=$\sqrt{g^{'}H}$. Simultaneous Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) measurement techniques are employed to get the velocity and density statistics. A flux-based method is used to calculate the entrainment coefficient, E$_{F}$, for a Reynolds number range of $Re\approx$400-13000 used in our experiments. The result shows a mixing transition at $Re\approx$2700 that is attributed to the flow transitioning from weak Holmboe waves to Kelvin-Helmholtz type instabilities.