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

Yusuke Ushijima, Kyoto University, Kyoto, Japan and Yutaka Yoshikawa, Kyoto University Rigakubu, Kyoto, Japan
##### Abstract:
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 after one-half inertial period (), where is the friction velocity, is the Brunt-V\"ais\"al\"a frequency, and is the Coriolis parameter. Here, large-eddy simulations (LESs) were performed to evaluate this scaling. It was found that the MLD increases rapidly until . Thereafter, the deepening of the ML slows down but it continues. LESs performed with several , , and 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 , are proposed in this study.