Turbulent Vertical Mixing and Viscosity

The latter process also has to be parameterized because the model equations are based on the hydrostatic approximation. Convection is of special importance in the surface layer during the autumn and winter, and it is responsible for the formation of winter water layers in the deep basins of the Baltic Sea. Surface salinity well below 24 implies a maximum density at temperatures above the freezing point and a stable re-stratification before the freezing point is reached. Hence, a good approximation for the equation of state is required to simulate such processes, even if the existence of large density gradients could suggest that a simple and numerically cheap approximation could be sufficient. 

The advantage of the k-profile scheme is its treatment of the convective limit. Since convection implies strong vertical mixing that destroys vertical gradients, the calculation of vertical fluxes from gradient formulas becomes inaccurate. This problem is circumvented in the k-profile approach by a special term in the expression for the turbulent vertical tracer fluxes, ww(J), which is active in the convective case and redistributes the surface flux, ivx(O), of a tracer X over the surface boundary layer in depth d. 

if a negative heat flux drives convection, it acts also directly on the thermocline, and provides a more efficient vertical mixing than schemes based on gradient approximations only. Details on the calculation of the turbulent mixing coefficient and the parameter 7 are given in Large et al, (1994) and the hterature cited therein. 

FIGURE 19.4 Time series of vertical temperature profiles simulated (a) and measured at station 271 in the eastern Gotland Basin (b). Note, that the station data have been interpolated in time to fill gaps. 

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