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A numerical study of the turbulent Ekman layer

Published online by Cambridge University Press:  26 April 2006

G. N. Coleman ,
J. H. Ferziger  and
P. R. Spalart
G. N. Coleman
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford CA 94305, USA
J. H. Ferziger
Affiliation:
NASA Ames Research Center, Moffett Field CA 94035, USA
P. R. Spalart
Affiliation:
NASA Ames Research Center, Moffett Field CA 94035, USA
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Abstract

The three-dimensional time-dependent turbulent flow in a neutrally stratified Ekman layer over a smooth surface is computed numerically by directly solving the Navier–Stokes equations. All the relevant scales of motion are included in the simulation so that no turbulence model is needed. Results of the simulations indicate that the horizontal component of the rotation vector has a significant influence on the turbulence; thus the ‘f-plane’ approximation fails. Differences as large as 20% in the geostrophic drag coefficient, u*/G, and 70% in the angle between the freestream velocity and the surface shear stress are found, depending on the latitude and the direction of the geostrophic wind. At 45° latitude, differences of 6 and 30% are noted in the drag coefficient and the shear angle, respectively, owing to the variation of the wind direction alone. Asymptotic similarity theory and a higher-order correction are first tested for the range of low Reynolds numbers simulated, and then used to predict the friction velocity and stress direction at the surface for flows at arbitrary Reynolds number. A model for the variation of these quantities with latitude and wind angle is also proposed which gives an acceptable fit to the simulation results. No large-scale longitudinal vortices are found in the velocity fields, reinforcing the conjecture that unstable thermal stratification, in addition to inflectional instability, is required to produce and maintain the large-scale rolls observed in the Earth's boundary layer. Comparisons of the Ekman layer with a related three-dimensional boundary layer reveal similarities of the mean profiles, as well as qualitative differences.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 313 - 348
Copyright
© 1990 Cambridge University Press

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