Vertical mixing schemes in the coastal ocean: Comparison of the level 2.5 Mellor-Yamada scheme with an enhanced version of the K profile parameterization

The performance of two vertical mixing parameterizations in idealized continental shelf settings is analyzed to assess in what aspects and under what conditions they differ. The level 2.5 Mellor-Yamada turbulence closure (M-Y) is compared with an enhanced version of the K profile parameterization (KPP), which has been appended to include a representation of the bottom boundary layer. The two schemes are compared in wind-driven one- and two-dimensional shallow ocean settings to examine differences in (1) the surface boundary layer response, (2) the response when surface and bottom boundary layers are in close proximity, and (3) the response when the horizontal advective effects of a coastal upwelling circulation compete with the vertical mixing processes. The surface boundary layer experiments reveal that M-Y mixes deeper and entrains more than KPP when the pycnocline beneath the wind-mixed layer is highly stratified and mixes less when it is weaker. This is related to the role of vertical diffusion of turbulent kinetic energy in M-Y and the nature of the interior shear mixing parameterization of KPP. In shallow water when surface and bottom boundary layers impinge on each other, the stronger mixing at the interface produced by KPP can lead to much more rapid disintegration of the pycnocline. The two-dimensional upwelling circulation experiments show that the two schemes can produce quite similar or significantly different solutions in the nearshore region dependent on the initial stratification. The differences relate to the stronger suppression of turbulence by M-Y under the restratifying influence of horizontal advection of denser water in the bottom boundary layer.