Sensitivity of boundary layer features to depth-dependent baroclinic pressure gradient and turbulent mixing in an ocean of finite depth

Abstract

The present numerical study builds on Ekman (1905)’s work in surface boundary layer and extends the boundary value problem to overcome some of its limitations. Previous studies addressed model’s limitations by assuming that deviations from observations are usually ascribed to different eddy viscosity shapes, but seldom to the presence of baroclinic pressure gradients and shallow seas, which are the mainstays of this work. Improved solutions in the ocean boundary layer are obtained considering both depth-dependent wind-induced eddy viscosity and horizontal density gradients, ranging from well-mixed to highly-stratified conditions in a finite-depth ocean. High-order numerical solutions extend those in previous analytical and numerical works in the literature and widens the parameter space analyzed. Remarkably, the current profiles are obtained without ambiguity as a truly superposition of a geostrophic and a ageostrophic terms. Results indicate that, for a vertically-uniform eddy viscosity without density gradients and in shallow waters, currents are practically aligned with wind. As depth increases, misalignment between currents and wind increases and the complexity of the vertical structure increases. At large depths, Ekman’s values are attained, i.e., deflection angles relative to wind direction, θW, are θS−θW=−45∘ at the surface, where the current is maximum, and θT−θW=−90° for the depth-integrated transport (negative for deflections to the right in the Northern Hemisphere). These features remain regardless of the magnitude of the eddy-viscosity. For non-uniform eddy viscosity, θS−θW decreases from −45∘ up to −90∘ from low to high stratification level, respectively, whereas θT−θW is rather insensitive (θT−θW≈−90∘). Contrary to wind effects, the presence of the only vertically-uniform density gradient forcing, with constant eddy viscosity, deflects the surface angle θS−θD=+45∘ relative to the density-gradient direction, θD, in deep waters. Maximum currents no longer occur at the surface in this case. For non-uniform density-gradient profiles, current magnitude decreases overall while θS−θD≈+45∘ as long as the gradient affects the entire surface boundary layer. The deflection angle θT−θD∼+95∘ remains less sensitive to changes in density-gradient profile.