On the Effect of Dissipation on Seasonal Thermocline Models

Abstract

This paper considers several parameterizations of dissipation in a Kraus-Turner (1967) seasonal mixed-layer model with no net annual surface buoyancy flux. By studying the behavior of the turbulent kinetic energy equation near the end of the cooling season it is determined for a given parameterization of dissipation whether or not the mixed layer deepens to infinite depth at the end of the cooling season. It is concluded that the following two conditions together form a sufficient condition for the maximum mixed-layer depth to be finite. First, the dissipation must be able to balance the wind generation of turbulent kinetic energy in the absence of a surface buoyancy flux. Second, the dissipation must exactly balance the turbulent kinetic energy generated by the wind and released by convection near the end of the cooling season. For two parameterizations of dissipation, cyclic solutions of the Kraus-Turner model are obtained. With the constant background dissipation used by Niiler (1977) the mixed-layer depth stays finite; whereas, with the parameterization of dissipation used by Kamenkovich and Khar'kov (1975) the mixed layer deepens to infinite depth at the end of the cooling season. It is also mentioned that with the parameterizations of dissipation used by Gill and Turner (1976) and Elsberry et al. (1976) the mixed layer deepens to infinite depth at the end of the cooling season. Finally, the potential usefulness of these findings for numerical ocean modeling is discussed.