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5.2 Governing Equations     continued...

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