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 pot
ential temperature) renders the inclusion of vertical mixing in layere
d models a subtle problem. The approach the authors have taken is base
d upon the entrainment into a layer being proportional to the turbulen
t activity in that layer. Across each interface there are then two ent
rainment velocities, one upward velocity that is the entrainment of fl
uid into the layer above the interface, and one downward velocity, bei
ng the entrainment velocity into the layer below the interface. This d
ouble entrainment accounts for both the diffusive and the advective co
nsequences of turbulent mixing. The proposed scheme works without appr
oximation for a nonlinear equation of state and can readily handle the
production of density caused by cabbeling. Several examples are given
.