where p is the density, v is the horizontal velocity vector, h is the layer thickness, ( is the potential temperature, S is the salinity, p is the pressure, Am and As are the eddy momentum and scalar (temperature/salinity) diffusion coefficients, cp is the specific heat of sea water, Q is the heat flux, Rk P-E is the fresh water flux due to precipitation minus evaporation (zero except for k = 1), and τ is the stress between the layers. The terms which include w represent exchange processes between layers through entrainment /detrainment, cross- isopycnal mixing, and convection. The terminology ()kl indicates a transfer from the 1-the layer to the k-the layer. The stress between neibouring layers is parameterized as
with
For the internal stresses, the drag coefficient Cd = 10 -4 and for the bottom stress, Cd = 10 -3. The wind stress, heat flux, and fresh water flux are discussed in section 2.3. The density is related to temperature, salinity, and pressure by the equation of state for sea water [UNESCO, 1981]. The diffusion coefficients are parameterized [Smagorinsky, 1963] by relating it to the deformation of the flow field:
Here, c = 5 x 10 9m2 a minimum diffusion coefficient of A 0 s = 10 3m2s-1
2.2. Surface Mixed-layer Model
The surface boundary conditions for the interior flow are determined via the bulk mixed-layer model which is forced by the atmosphere. The mixed layer has the same dynamics as the isopycnal layers except that the temperature and salinity are arbitrary. The equations for the entrainment rate w in the mixed layer is
