A 3-DIMENSIONAL, BAROCLINIC SHELF SEA CIRCULATION MODEL .1. THE TURBULENCE CLOSURE SCHEME AND THE ONE-DIMENSIONAL TEST MODEL

The primitive shallow water equations of momentum, heat, mass and passive tracer are considered. Parameterizations are examined for the vertical Reynolds stresses, as well as for the horizontal, in order to increase the accuracy of three-dimensional prognostic calculations of hydrographic stratification. Starting out from the differential equations of the Reynolds stresses, the shallow water flow approximation results in a time independent local turbulence energy equilibrium. A new quantity, the "turbulence frequency", q, is introduced. The resulting algebraic expressions for all Reynolds stresses on the basis of q are presented, followed by a detailed discussion of the solution domain. The behaviour of the closure scheme in numerical calculations and the resulting effects upon the temporal evolution of hydrographic stratification are investigated with a one-dimensional test model.