On the “Resistance Law” of a Turbulent Ekman Layer

Abstract

The turbulent Ekman layer differs from the two-dimensional turbulent boundary layer in that it may exist with its thickness remaining constant in the direction of the flow. Dimensional arguments show that the layer equilibrium thickness and the magnitude and the direction of the shear stress at the boundary surface are functions of the surface Rossby number U/Fz0. In analogy with two dimensional turbulent boundary layers, similar “wall layer” velocity profiles near the boundary and a “velocity defect law” in the outer region of the Ekman layer may be postulated. The overlapping of the two laws produces a logarithmic velocity profile and yields a resistance law for an Ekman layer, for both the magnitude and the direction of the shear stress, connecting these to the surface Rossby number. What experimental evidence there is on the geostrophic drag coefficient appears to agree with the resistance law so derived. Abstract The turbulent Ekman layer differs from the two-dimensional turbulent boundary layer in that it may exist with its thickness remaining constant in the direction of the flow. Dimensional arguments show that the layer equilibrium thickness and the magnitude and the direction of the shear stress at the boundary surface are functions of the surface Rossby number U/Fz0. In analogy with two dimensional turbulent boundary layers, similar “wall layer” velocity profiles near the boundary and a “velocity defect law” in the outer region of the Ekman layer may be postulated. The overlapping of the two laws produces a logarithmic velocity profile and yields a resistance law for an Ekman layer, for both the magnitude and the direction of the shear stress, connecting these to the surface Rossby number. What experimental evidence there is on the geostrophic drag coefficient appears to agree with the resistance law so derived.