Turbulent mixing of properties such as salt or temperature and the frictional effect it has on momentum is of great importance to all ocean processes. However, turbulence closure, the solution of an exact representation of the effects of unresolved turbulent motions on the integral or large-scale motions, remains an unsolved problem. All hydrodynamic models use approximations of these unresolved turbulent motions, that is, turbulence parame-trizations. Handling the parametrization of the interface between the atmosphere and ocean which is dependent on turbulent stresses remains one of the greatest challenges for ocean modeling, and this issue is particularly acute for biogeochemical models. The exchange of chemical constituents with the atmosphere, and their injection into the ocean is mediated through the surface ocean turbulent boundary layer or mixed layer. This surface mixed layer also directly drives the pelagic food web because it determines the average light available for photosynthesis at the surface. Ocean mixed layer modeling remains an active research topic. The most widely used mixed layer models can be separated into bulk formulations such as the Krauss-Turner model that does not resolve vertical structure in the boundary layer, and those models such as the K-profile parametrization or Mellor-Yamada turbulence closure model that determine vertical diffusivity and viscosity coefficients as a function of the model state variables and applied surface forcing. The latter two approaches yield values for turbulent mixing that are resolved throughout the water column, not just the surface mixed layer thickness, and may also be used to represent bottom boundary layer and even overflow processes.
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