Mixing of a cylindrical gravity current in a stratified ambient

Abstract

Simulation results from direct numerical simulations (DNSs) of cylindrical gravity currents propagating into a linearly stratified ambient with stratification strengths ranging from 0 to 0.8, at a moderate Reynolds number of Re=3450 are presented. The simulations are based on the incompressible Navier–Stokes equations, assuming small density differences such that the Boussinesq approximation is valid. The density of the ambient fluid increases linearly from the top (ρ0) to the bottom (ρb) of the domain. A comparative analysis is conducted between the stratified cases and the unstratified case to investigate the impact of ambient stratification strength on the mixing behaviour of cylindrical gravity currents. The energy conversion processes are analysed using the mechanical framework proposed by Winters et al. (1995). The energy budget is formulated by considering gravitational available potential energy, and the evolution of potential energy due to reversible stirring and irreversible diapycnal mixing in the system. The findings reveal a decrease in available potential energy and kinetic energy with increasing stratification strength, indicating lower energy exchange for gravity currents propagating in the stratified environment. Instantaneous and cumulative mixing efficiency calculations during the slumping phase indicate that Kelvin–Helmholtz billow play an important role in stirring the heavy fluid and causing irreversible mixing with the ambient fluid.