Velocity shear and vertical mixing in the Ekman layer in the presence of a horizontal density gradient

The wind-driven turbulent Ekman layer is studied in the presence of a horizontal density gradient. The stabilizing case, i.e. when the wind brings light water out on top of heavier water, is treated using a 1-1/2 order turbulence model (a k-epsilon model). It is found that the velocity shear within the mixed layer (ML) interacts with the horizontal density gradient and that an equilibrium ML depth is reached in a shorter time than the inertial period. The situation modelled bears some similarities to the competing effects of wind-mixing and surface heating. However, the stabilizing effect arises from the velocity shear, which, in combination with the horizontal density gradient, tends to create a stable stratification within the ML. The non-dimensional equilibrium ML depth and the velocity shear are shown to depend on L(E)/L(A) (=\inverted iota b/partial derivative x\f(-2)). [L(E) = u* f(-1) is the Ekman length and L(A) = u*f\partial derivative b/partial derivative x\(-1) is a length introduced by J. Rodhe (1991) in the Journal of physical Oceanography, 21, 1080-1083. u* is the friction velocity defined from the wind stress, fis the Coriolis parameter, b = g(rho(o) - rho)/rho(0) is buoyancy (g is gravity, rho is density and rho(0) is a reference density) and x is a coordinate in the direction of the horizontal buoyancy gradient.] (C) 1996 Elsevier Science Ltd.