A Numerical Investigation of Mixed-Layer Dynamics

Abstract

Abstract The structure of the stratified turbulent upper mixed layer of the ocean has been numerically investigated by using the turbulence closure model of Gibson and Launder, under the action of an impulsive wind stress τ0 and zero surface heat flux. The values of buoyancy and Coriolis frequencies assumed are N = 0.94 × 10−2 s−1 and f = 10−4 s−1, respectively. The solutions indicate that the turbulent diffusion terms, small in general, transfer kinetic energy downward, although its effect on the deepening is negligible. Let ti be the time in inertial periods and u* be the friction velocity. Then for 0.05 < ti < 0.3, the rate of increase of potential energy in the water column varies as ∂(PE)/∂t ∝ t½, rising to a maximum of ∼1.1u*3 and implying a mixed layer depth h∝t½ as in the Pollard-Rhines-Thompson (PRT) model. For 1 < ti < 6, ∂(PE)/∂t decreases only slightly from a quasi-steady value of ∂(PE)/∂t ≈ 0.25u*3, implying a deepening rate slightly smaller than the Kraus-Turner h ∝ t⅓. The reason for this d...