The Subinertial Mixed Layer Approximation

Abstract

Abstract The density of the mixed layer is approximately uniform in the vertical but has dynamically important horizontal gradients. These nonuniformities in density result in a vertically sheared horizontal pressure gradient. Subinertial motions balance this pressure gradient with a vertically sheared velocity. Systematic incorporation of shear into a three-dimensional mixed layer model is both the goal of the present study and its majority novelty. The sheared flow is partitioned between a geostrophic response and a frictional, ageostrophic response. The relative weighting of them two components is determined by a nondimensional parameters μ≡1/fτU, where τU is the timescale for vertical mixing of momentum and f−1 is the inertial timescale. If μ is of order unity, then the velocity has vertical shear at leading order. Differential advection by this shear flow will tilt over vertical isosurfaces of heat and salt so as to “unmix” or “restratify” the mixed layer. The unmixing process is balanced by intermit...