Vertical Mixing and Cabbeling in Layered Models

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Abstract
A consistent scheme for vertical mixing in layered numerical models is derived in this paper. The fact that the vertical coordinate (density) depends on the properties being transported (namely salinity and potential temperature) renders the inclusion of vertical mixing in layered models a subtle problem. The approach the authors have taken is based upon the entrainment into a layer being proportional to the turbulent activity in that layer. Across each interface there are then two entrainment velocities, one upward velocity that is the entrainment of fluid into the layer above the interface, and one downward velocity, being the entrainment velocity into the layer below the interface. This double entrainment accounts for both the diffusive and the advective consequences of turbulent mixing. The proposed scheme works without approximation for a nonlinear equation of state and can readily handle the production of density caused by cabbeling. Several examples are given. Abstract A consistent scheme for vertical mixing in layered numerical models is derived in this paper. The fact that the vertical coordinate (density) depends on the properties being transported (namely salinity and potential temperature) renders the inclusion of vertical mixing in layered models a subtle problem. The approach the authors have taken is based upon the entrainment into a layer being proportional to the turbulent activity in that layer. Across each interface there are then two entrainment velocities, one upward velocity that is the entrainment of fluid into the layer above the interface, and one downward velocity, being the entrainment velocity into the layer below the interface. This double entrainment accounts for both the diffusive and the advective consequences of turbulent mixing. The proposed scheme works without approximation for a nonlinear equation of state and can readily handle the production of density caused by cabbeling. Several examples are given.

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