The eddy, wave, and interface structure of horizontal turbulent shear layers below/above stably stratified regions

High resolution 3-dimensional numerical simulations are presented of the interactions between horizontal turbulent shear flows moving with mean relative velocity $\Delta U$ below a stably stratified region with buoyancy frequency ($N_+$). An artificial forcing function in the simulation, with a similar effect as a small level of negative eddy viscosity, leads to a steady state flow which models thin interfaces in high Reynolds number turbulence. Characteristic eddies of the turbulence have an rms velocity $w_+$ and length scale $L$. If the bulk Richardson number $Ri_b=(LN_+ / \Delta U)^2$ lies between lower and upper critical values denoted as $ Ri^*(<~1/5) $ and $\tilde Ri(~\sim 1)$), a 'detached' layer is formed in the stable region with thickness $L_+$ greater than $L$, in which rotational fluctuations and inhomogeneous turbulence are induced above an interface with large gradients of density/temperature. When $Ri_b > \tilde Ri$, vertical propagating waves are generated, with shear stresses carrying significant momentum flux with maximum magnitude of about 10 to 20 percent of the velocity variance, and progressively less as $Ri_b$ increases. Similar results are obtained for a jet and a turbulent mixing layer. A perturbation analysis, based on inhomogeneous Rapid Distortion Theory, models the transition zone between shear eddies moving at relative speed $\Delta U$ below the interface and the fluctuations in the stratified region, consistent with the simulations. It demonstrates how the wave momentum flux has a maximum when $Ri_b \sim 2$, and then decreases as $Ri_b$ increases. It also shows the transition to rotational motion when $ Ri_b < \tilde Ri$, which defines the detached layer thickness $L_+ \sim L/ \sqrt{1-Ri_b}$. This coupling mechanism between eddies and waves which is neglected in eddy viscosity models for geophysical shear layers, can drive flows in the stratosphere and the deeper ocean, with significant consequences for short and long term flow phenomena. The 'detached layer' is a likely mechanism for the formation of stratus clouds and polluted layers above the atmospheric boundary layer.