Mathematics – Logic
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994bolme..67....1m&link_type=abstract
Boundary-Layer Meteorology, Volume 67, Issue 1-2, pp. 1-10
Mathematics
Logic
1
Scientific paper
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 viscosity K(z) is assumed to vary smoothly from the surface-layer value κ U *z (κ≅0.4, U *=friction velocity, z=elevation) to the geostrophic asymptote K G≡κ U *d for z≫d is solved through an expansion in δ≡ fd/κ 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 for z≪d and is O(δ) relative to the Ekman component for z≫d. The approximation K˜κ U *d is supported by the solution of Nee and Kovasznay's phenomenological transport equation for K(z), which yields K-κ U *d exp(-βz/d), where β is an empirical constant for which observation implies, β≪1. The parameters A and B in Kazanskii and Monin's similarity relation for G/ U * ( G=geostrophic velocity) are determined as functions of δ. The predicted values of G/U * and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value of B based on the assumption of asymptotically constant K 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 arbitrary K(z) and δ≫1, and an exact (unrestricted δ) solution for K(z)=κ U *d[1-exp(- z/d)] are developed in appendices.
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