# Gravitational, symmetric, and baroclinic instability of the ocean mixed layer.

(Haine, TWN and Marshall, J), *JOURNAL OF PHYSICAL OCEANOGRAPHY*, vol. 28, no. 4, pp. pages, 1998.

## Abstract

A hierarchy of hydrodynamical instabilities controlling the transfer of buoyancy through the oceanic mixed laver is reviewed. If a resting ocean of horizontally uniform stratification is subject to spatially uniform buoyancy loss at the sea surface, then gravitational instability ensues in which buoyancy is drawn from depth by upright convection. But if spatial inhomogeneities in the ambient stratification or the forcing are present (as always exist in nature), then horizontal density gradients will be induced and, within a rotation period, horizontal currents in thermal-wind balance with those gradients will be set up within the mixed layer. There are two important consequences on the convective process: 1) Upright convection will become modified by the presence of the thermal wind shear; fluid parcels are exchanged not along vertical paths but, rather, along slanting paths in symmetric instability. Theoretical considerations suggest that this slantwise convection sets the potential vorticity of the mixed layer fluid to zero but, in general, will leave it stably stratified in the vertical. 2) The convective process ultimately gives way to a baroclinic instability of the horizontal mixed layer density gradients. The resulting baroclinic waves are important agents of buoyancy transport through the mixed layer and can be so efficient that the convective process all but ceases. The authors illustrate and quantify these ideas by numerical experiment with a highly resolved nonhydrostatic Navier-Stokes model. Uniform spatial cooling at the surface of a resting, stratified fluid in a 2 1/2-dimensional model on an f plane, in which zonal strips of fluid conserve their absolute momentum. causes energetic vertical overturning. A well-mixed boundary layer develops over a depth that is accurately predicted by a simple 1D law. In contrast, differential surface cooling induces a mixed layer front. Fluid parcels, made dense at the surface. sink along slanting trajectories in intense nonhydrostatic plumes. After cooling ceases the Ertel potential vorticity within the convective layer is indeed found to br vanishingly small, corresponding to convective neutrality measured in the absolute momentum surfaces that are tilted from the vertical by the horizontal vorticity of the thermal wind. In analogous fully three-dimensional calculations, the absolute momentum constraint is broken, and the convection at first coexists with, but is ultimately dominated by, baroclinic instability of the mixed layer. For typical mixed layer depths of 500 m stability analysis predicts, and our explicit calculations confirm, that baroclinic waves with length scales O(5 km) develop with timescales of a day or so. By diagnosis of fully developed mixed layer turbulence, the authors assess the importance of the baroclinic eddy field as an agency of lateral and vertical buoyancy flux through the layer. A novel scaling for the lateral buoyancy flux due to the baroclinic eddies is suggested. These ideas are based on analysis of several experiments in which the initial stratification, rotation rate, and buoyancy forcing are varied, and the results are compared to previous attempts to parameterize the effects of baroclinic instability. There is a marked difference between the scaling that accounts for the resolved experiments and the Fickian schemes used traditionally in large-scale ocean models. Finally, consideration of the results in light of high-resolution mixed layer hydrographic surveys in the northeast Atlantic suggests mixed layer baroclinic instability may be very important at fronts. The authors speculate that the process exerts a large influence on the character of newly subducted thermocline water throughout the extratropical ocean.