Dynamics of a buoyant gravity current propagating in a linearly stratified medium

Abstract

In this study, we investigate partial- and full-depth buoyant gravity currents propagating along the top surface in a linearly stratified medium. Two- and three-dimensional numerical simulations are performed to study the effect of stratification and initial current depth, on the front speed, internal wave field, and turbulence characteristics. The stratification is varied through a non-dimensional parameter R=ρ0−ρCρb−ρ0, ranging between 0.04 and 85, where ρC is the constant bulk density of the current fluid and ρ0,ρb represent the densities of the ambient fluid at the top and bottom surfaces, respectively. For large values of R (ρ0−ρC≫ρb−ρ0), we observe that the resulting Froude number (Fr=UNH) is greater than 1/π, and the flow is characterized as supercritical, where the front speed exceeds the long wave speed. In the supercritical regime, Kelvin–Helmholtz billows are prominently seen along with an internal solitary wave, which propagates with the density front. As the R value decreases, the relative strength of the ambient stratification increases when compared to the horizontal density difference at the top surface, leading to a subcritical flow regime where the front speed is smaller when compared to the long-wave speed. The Kelvin–Helmholtz billows and the solitary wave gradually disappear, and vertically propagating high-mode internal waves are prominently seen for R< 1. Quantification of the Froude number for various values of R and h/H shows that it follows a power law, Fr∝(h/H×R)1/2, with the proportionality constant 0.72. This scaling works well for all the partial-depth cases considered in this study, i.e., h/H= 1/8, 1/6, 1/4, and 1/3, while a slight deviation is observed for the full-depth gravity currents that correspond to h/H= 1.