ON THE PERFORMANCE OF A MIXED-LAYER MODEL-BASED ON THE KAPPA-EPSILON TURBULENCE CLOSURE

This paper investigates the interaction between stratification and tur bulence by means of turbulence models. The standard and the advanced t urbulent kinetic energy - dissipation (k-epsilon) model are derived th eoretically, including algebraic stress relations. It is shown that a certain empirical constant in the standard model turns out to be a com plicated implicit function in the advanced model, namely, a function o f the turbulent shear number, the turbulent buoyancy number, and a wal l correction. For a better understanding and physical interpretation o f the k-epsilon models, an analysis is carried out for a simplified ca se where diffusive fluxes are neglected. For this idealization it is s hown that (1) the flux Richardson number R(f) has a certain lower boun d R(f)(-) due to the establishment of convection, (2) a steady state f lux Richardson number R(f)(st) (which is defined here for this purpose ) labels the borderline between the tendency of turbulence to decrease or collapse (R(f) > R(f)(st)) or to increase (R(f) < R(f)(st)), and ( 3) the well-known upper limit for turbulent shear flow, R(f)(+) approx imate to 0.25, fits our theory. Using the standard model, the advanced model, a modified version of the level-2 model of Mellor and Yamada a nd a modified version of Kochergin's model, the evolution of thermal s tratification in the northern North Sea during the Fladen Ground Exper iment (FLEX'76) is simulated numerically and compared with the measure ments. In this specific application, the two k-epsilon models performe d best.