Evolution of a stratified rotating shear layer with horizontal shear. Part 2. Nonlinear evolution

Abstract

AbstractDirect numerical simulation is used to investigate the nonlinear evolution of a horizontally oriented mixing layer with uniform stable stratification and coordinate system rotation about the vertical axis. The important dimensional parameters governing inviscid dynamics are maximum shear $S(t)$, buoyancy frequency $N$, angular velocity of rotation $\Omega $ and characteristic shear thickness $L(t)$. The effect of rotation rate, $\Omega $, on the development of fluctuations in the shear layer is systematically studied in a regime of strong stratification. An instability mechanism, qualitatively distinct from the inertial instability, is found to deform columnar vortex cores in vertical planes for a strongly stratified rotating mixing layer. This mechanism emerges when centreline absolute vertical vorticity, $\langle {\omega }_{3} \rangle (t)+ 2\Omega $, is nearly zero as predicted by the linear stability analysis in Part 1 (J. Fluid. Mech., vol. 703, 2012, pp. 29–48). When the initial rotation rate is moderately anticyclonic, strong destabilization and a cascade to small scales is observed, consistent with prior studies involving horizontally sheared flow in the presence of rotation. Examination of enstrophy budgets in cases which are initially inertially unstable reveal the importance of baroclinic torque in maintaining lateral enstrophy fluctuations substantially beyond the time when the flow becomes inertially stable. The cyclonic stratified cases show weak nonlinearity in vortex dynamics. At high Reynolds number, despite the strong stratification, the flow exhibits three-dimensional, nonlinear dynamics and significant vertical mixing except for cases where the rotation is stabilizing.