Turbulence in forced stratified shear flows

Continuously forced, stratified shear flows occur in many geophysical systems, including flow over sills, through fjords and at the mouths of rivers and estuaries. These continuously forced shear flows can be unstable and drive turbulence, which can enhance the rate of mixing. In this study, we analyse three-dimensional direct numerical simulations of an idealized stratified shear flow that is continuously forced by weakly relaxing both the buoyancy and streamwise velocity towards prescribed mean profiles. We explore a range of large and small Richardson numbers, for constant Reynolds and Prandtl numbers ( and ). After a turbulent steady state develops, three regimes are observed: (i) a weakly stratified, overturning regime, (ii) a strongly stratified, scouring regime and (iii) an intermediately stratified, intermittent regime. The overturning regime exhibits partially formed overturning billows that break down into turbulence and broaden the velocity and buoyancy interfaces. Conversely, the scouring regime exhibits internal gravity waves propagating along the strongly stratified buoyancy interface, while turbulence on either side of the buoyancy interface reinforces the stratification. The intermediate regime quasi-periodically alternates between behaviours associated with the overturning and scouring regimes. For each case, we quantify an appropriate measure of the efficiency of mixing and examine its dependence on relevant parameters including appropriate definitions of the buoyancy Reynolds number, gradient Richardson number and horizontal Froude numbers. Using a framework involving sorted buoyancy coordinates as introduced by Nakamura (J. Atmos. Sci., vol. 53, 1996, pp. 1524-1537) and Winters & D'Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179-193), we examine the underlying physical mechanisms leading to broadening and thinning of the buoyancy interface.