The influence of stable stratification on the transition to turbulence in a temporal mixing layer

Abstract

The transition to turbulence in a stably stratified flow is a problem of considerable interest in fluid dynamics with applications in both geophysical sciences and engineering. This transition is controlled by competition between the vertical shear of the base flow and the buoyancy forces due to the density stratification. The present work investigates numerically the effect of stable stratification on the development of a Kelvin-Helmholtz (KH) instability and the formation of streamwise vortices, which are developed after the saturation of the primary billows of KH. The Direct Numerical Simulation (DNS) technique was used to solve the complete Navier-Stokes equations, in the Boussinesq approximation. Numerical tests were done with different Richardson numbers and forced initial conditions for velocity fluctuations. The results showed that high stratification inhibits the pairing process, reduces the buoyancy flux, weakens the vertical motions, decreases the thickness of the mixing layer and affects the formation of streamwise vortices. The three-dimensional results demonstrated that the streamwise vortices are clearly formed in non-stratified cases. In the stratified cases, on the other hand, the streamwise vortices are weakened, due to the streamwise density gradient, which decrease the levels of vorticity in the billows of KH, while increase in the braid zone.