Large-eddy simulations of the wind-induced turbulent Ekman layer

Abstract

At urbulent Ekman layer created by a steady wind near the water surface is investigated using the numerical method of large-eddy simulations. The classical case of a flow unaffected by density stratification and surface waves is revisited to understand the internal structure of the flow and implications of the traditional assumptions of constant effective viscosity and the ‘f -plane’ approximation. A series of numerical experiments reveals that the Ekman solution needs correcting even in this case. The examination of the effective viscosity hypothesis confirms its validity but shows that the viscosity varies strongly with depth. It increases in the subsurface layer of thickness about 1/4 the turbulent length scale and decreases below this level. A Bessel function solution is proposed that corresponds to the approximate effective viscosity profile and matches with the LES results. Strong flow dependence on the latitude and wind direction is detected and explained by the effects of redistribution of turbulent kinetic energy between the velocity components and modification of the vertical transfer of turbulent momentum. In this paper, we consider the classical problem of a turbulent flow generated near the ocean surface by a steady wind stress in the presence of Earth’s rotation. Interest in this flow goes back to Ekman’s landmark work published in 1905. (An interesting historical review of Fridtjof Nansen’s polar expedition and other events preceding Ekman’s paper is given by Walker (1991).) Ekman assumed a balance between the Coriolis force, viscous friction and the pressure gradient, adopted the approximation of constant vertical eddy viscosity Az ,a ndderived a solution now known as the ‘Ekman spiral’. In the case of a steady wind in the x-direction, the steady-state Ekman velocity profile in the open ocean is (for the northern hemisphere) u = V0 cos π + π D z