It is not unusual to use zeroth order
closure models for these diffusivities and regard them as
constants throughout. This is rather counter-intuitive, since
these values are functions of the prevailing turbulence field in
the fluid and strictly speaking should be derived from properties
of turbulent mixing occurring in the fluid. However, away from the
fully turbulent mixed layers near the surface and the bottom of
the ocean, very little is known about intermittent mixing
processes that occur in the interior of the ocean. Traditionally,
, , and are prescribed
* a priori* as constant values and
these values are ``tuned'' to obtain the desired results. However
because of the sensitivity of the model output to these values,
this * ad-hoc* procedure has become increasingly untenable and better
prescriptions often using higher order closures have become the
norm. For example, this model uses first-order closure for and
, thus relating them to mean deformation rates in the fluid,
while and are obtained from second order
closure (also
called second moment closure) for small-scale turbulent mixing
that principally determines the vertical diffusivities in the
upper and benthic mixed layers. In the interior of the ocean,
and are still often assumed to be constant, even though there
is ample evidence
[20]
to suggest that both and
should be
functions of vertical stratification of the water column and that
for heat should be different from that for salt. The model
includes an option to prescribe and in the interior
as

where **N** is the Brunt--Vaisala frequency indicative of the stability
of the fluid column and is a constant. **N** is given by

where
**c** is the sound speed defined as