Wind-mixed layer deepening in a rotating frame

Under wind forcing, the oceanic mixed layer deepens over time. Scaling laws exist to predict the deepening rate, but either neglect Earth's rotation or do not take into account the vertical structure of the mixed layer. This study aims to address these limitations by investigating the long-term dynamics of a wind-driven mixed layer in a rotating, linearly stratified fluid. We derive an analytical scaling law for the mixed layer depth h as a function of time t, (Formula presented.) with (Formula presented.) the initial stratification, f the rotation parameter and (Formula presented.) the friction velocity. This law extends classical theories by considering rotational effects and is consistent with recent Large Eddy Simulations. We show that mixing, mostly concentrated within the entrainment layer, is primarily controlled by the stationary component of the velocity and that inertial oscillations have little effect on entrainment.