THE SUBINERTIAL MIXED-LAYER APPROXIMATION

The density of the mixed layer is approximately uniform in the vertica l but has dynamically important horizontal gradients. These nonuniform ities in density result in a vertically sheared horizontal pressure gr adient. Subinertial motions balance this pressure gradient with a vert ically sheared velocity. Systematic incorporation of shear into a thre e-dimensional mixed layer model is both the goal of the present study and its major novelty. The sheared flow is partitioned between a geost rophic response and a frictional, ageostrophic response. The relative weighting of these two components is determined by a nondimensional pa rameter mu = 1/ftau(U), where tau(U) is the timescale for vertical mix ing of momentum and f-1 is the inertial timescale. If mu is of order u nity, then the velocity has vertical shear at leading order. Different ial advection by this shear flow will tilt over vertical isosurfaces o f heat and salt so as to ''unmix'' or ''restratify'' the mixed layer. The unmixing process is balanced by intermittent mixing events, which drive the mixed layer back to a state of vertical homogeneity. All of these processes are captured by a new set of reduced or filtered dynam ics called the subinertial mixed layer (SML) approximation. The SML ap proximation is obtained by expanding the equations of motion in both R ossby number and a second small parameter that is the ratio of the ver tical mixing timescale to the dynamic time scale. The subinertial dyna mics of slab mixed layer models is captured as a special case of the S ML approximation by taking the limit mu --> infinity.