A laboratory study of localized boundary mixing in a rotating stratified fluid

Abstract

Oceanic observations indicate that abyssal mixing tends to be localized to regions of rough topography. How localized mixing interacts with the ambient fluid in a stratified, rotating system is an open question. To gain insight into this complicated process laboratory experiments are used to explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a single vertically oscillating horizontal bar of finite horizontal extent, located at mid-depth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady-state height and collapses into the interior. The mixed-layer thickness, $h_m\,{\sim}\,\gamma ({\omega}/{N})^{1/2}$, is spatially uniform and independent of the Coriolis frequency $f$. $N$ is the initial buoyancy frequency, $\omega$ is the bar oscillation frequency, and $\gamma\,{\approx}\,1$ cm is an empirical constant determined by the bar geometry. Surprisingly, the export of mixed fluid does not occur as a boundary current along the tank perimeter. Rather, mixed fluid intrudes directly into the interior as a radial front of uniform height, advancing with a speed comparable to a gravity current. The volume of mixed fluid grows linearly with time, $V\,{\propto}\,({N}/{f})^{3/2}h_m^3 \textit{ft}$, and is independent of the lateral extent of the mixing bar. Entrainment into the turbulent zone occurs principally through horizontal flows at the level of the mixing that appear to eliminate export by a geostrophic boundary flow. The circulation patterns suggest a model of unmixed fluid laterally entrained at velocity $u_e \,{\sim}\,Nh_m $ into the open sides of a turbulent zone with height $h_{m}$ and a length, perpendicular to the boundary, proportional to $L_f \,{\equiv}\,\gamma ({\omega}/{f})^{1/2}$. Here $L_{f}$ is an equilibrium length scale associated with rotational control of bar-generated turbulence. The model flux of exported mixed fluid $Q\,{\sim}\,h_m L_f u_e$ is constant and in agreement with the experiments.