Wind Mixing In a Turbulent Surface Layer in the Presence of a Horizontal Density Gradient

Abstract

The effect of a horizontal density gradient of buoyancy on the turbulent kinetic energy budget of the surface mixed layer in the ocean is discussed. The combination of a horizontal buoyancy gradient and a vertical shear of the horizontal velocity within the mixed layer will give rise to a “shear flow dispersion” effect within the layer. A vertical flux of buoyancy will be induced. This will act as a source or a sink of energy, depending on the relative direction between the horizontal buoyancy gradient and the surface velocity. An expression for the vertical flux of buoyancy due to this process is derived and discussed in relation to the shape of the velocity profile in the mixed layer. The contribution to the energy budget is calculated and specialized to the case when the transport in the layer is given by the Ekman solution. A length scale LA of the same significance as the Monin–Obukhov length is derived from the friction velocity u*. and the “shear flow buoyancy flux.” With the horizontal transport given by the Ekman solution it is shown that LA = u*f|∂b/∂x|−1, where f is the Coriolis parameter and b = gg(ρ0 − ρ)/ρ0 is the buoyancy. The shear flow buoyancy flux should be included in the turbulent kinetic energy budget for the mixed layer when the mixed layer depth is of magnitude LA. If the effect of the shear flow buoyancy flux dominates, the mixed layer depth is determined by LA.