Mixed Layer Deepening due to Wind-Induced Shear-Driven Turbulence and Scaling of the Deepening Rate in the Stratified Ocean

Wind-induced shear-driven turbulence mixes the stratified oceans to form the surface mixed layer (ML). The depth of the ML (MLD), a key quantity for several upper ocean processes, is often scaled as $U_{\ast }/\sqrt{Nf}$ after one-half inertial period ($0.5T_f$), where $U_{\ast }$ is the friction velocity, $N$ is the Brunt-V\"ais\"al\"a frequency, and $f$ is the Coriolis parameter. Here, large-eddy simulations (LESs) were performed to evaluate this scaling. It was found that the MLD increases rapidly until $0.5T_f$. Thereafter, the deepening of the ML slows down but it continues. LESs performed with several $U_{\ast }$, $N$, and $f$ showed that the deepening rate of the ML depends on the Rossby and Froude numbers. Therefore, time-dependent scalings of the ML deepening rate and the MLD as a function of the Rossby and Froude numbers, which cover the classical scaling but can be extended even after $0.5T_f$, are proposed in this study.