Analytical solutions for the Ekman layer |
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| Authors: | John Miles |
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| Institution: | (1) Institute of Geophysics and Planetary Physics, University of California, 92093-0225 San Diego, La Jolla, CA, USA |
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| Abstract: | The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value  U
*z ( 0.4,U
*=friction velocity,z=elevation) to the geostrophic asymptoteK
G U
*d forz d is solved through an expansion in  fd/U
* 1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationK U
*d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U
*d exp(– z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U
* (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U
* and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U
*d1–exp(–z/d)] are developed in appendices. |
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| Keywords: | |
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