Parameterization of mixing in upper ocean

Because boundary layers with small thermal and mechanical inertias approximate steady-state conditions, the associated density and momentum fluxes tend to be constant with depth. As a result, these fluxes may be chosen as external parameters, and it then becomes possible to apply Monin-Obukhov similarity theory. For fluids with large thermal inertias such as the ocean, the density flux is a function of depth; thus, the external thermal forcing is no longer a governing parameter. In addition, if the mechanical inertia is also large, the structure of the boundary layer is not universal because it depends on the previous evolution of the thermal and mechanical forcing. However, if the mechanical inertia is small, the dynamical structure of the boundary layer adjusts almost instantaneously to the density structure and the mechanical forcing. This property allows us to generalize the Monin-Obukhov theory for stratifiedboundary layers through specification of a stratification parameter which characterizes the internal density structure instead of the external density flux. The thermal time scale for the upper ocean is relatively large whereas the dynamical time scale is 1-2 orders of magnitude shorter. Consequently, the upper ocean may be considered steady-state in a dynamical sense and any dynamical property depends primarily on the depth, surface momentum flux, and the vertical density structure.