Flow near the sea surface: Steady currents and Langmuir circulations.

Abstract

The current system in the upper ocean is studied by developing and solving a system of equations governing the temporally averaged current system. In the theory, a perturbation expansion procedure is applied to derive this set of equations. In contrast to previous theoretical investigations, we include Coriolis effects, and we employ a second order turbulence closure scheme instead of a constant eddy viscosity model to treat the turbulent stresses. Using this model, the study of wind driven steady currents, the linear instability of the steady current, and the nonlinear evolution of Langmuir circulations are incorporated into an integrated investigation. In studying the wind driven currents, a nonlinear two point boundary value problem is solved numerically. The mass transport velocity is obtained as the sum of a turbulent version of the Ekman spiral and a Stokes drift. The computed surface mass transport velocity is roughly equal to the three percent of the wind speed generally quoted in the observational literature, and is approximately 10$\sp\circ$ to the right of the wind direction in the Northern Hemisphere, again in qualitative agreement with observations. We find that the deviation of the mass transport velocity from the wind direction is caused by the Coriolis effect. A linear instability analysis is performed by solving a generalized eigenvalue problem. The results show that the Coriolis effect causes the most unstable Langmuir circulation modes to be three-dimensional and unsteady. The computed Langmuir vortices are aligned a few degrees to the right of the wind direction and travel slightly to the right of the cross wind direction. This motion agrees with observations. The finite amplitude development of Langmuir cells is studied by integrating a system of nonlinear equations using a pseudospectral method. The following results are obtained: a surface downwind jet is formed over regions of subsurface downwelling, with the downwind current anomaly up to 10 cm $s\sp{-1}$, the order of magnitude of the horizontal surface sweeping speed is a few centimeters per second; and the downwelling jet below the surface convergence zones, is well resolved, with a downwelling speed of order 3 cm $s\sp{-1}$. These results are also supported by observations. The upper ocean current system is influenced by the wind, surface waves, the Coriolis force, and turbulence effects. Our study shows that all of these influences must be incorporated in a theoretical model to achieve satisfactory agreement with in situ measurements.