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-s 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 LE/LA (=vb∂b/∂χ| ∥−2). [LE = u∗ ∥−1 is the Ekman length and LA = u∗, f |∂b/∂χ|−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, f is the Coriolis parameter, b = g(ϱ0 - ϱ)/ϱ0 is buoyancy (g is gravity, ϱ is density and ϱ0 is a reference density) and x is a coordinate in the direction of the horizontal buoyancy gradient.]