Abstract
The Ekman boundary-layer model is extended analytically for a gradually varying eddy diffusivity K(z) ≥ 0, z ≥ 0. A solution for the Ekman layer is provided having similar structure to the constant-K case; that is, exponentially decaying sine functions for the two horizontal wind components. The analytical asymptotic solution compares well with its numerical counterpart for various K(z). The result can be useful in theoretical studies such as Ekman pumping, for efficient estimation of the Ekman layer profiles in various analyses with near-neutral stratifications, or for a rapid initialization of mesoscale models.
Similar content being viewed by others
References
C.M Bender S.A. Orszag (1999) Advanced Mathematical Methods for Scientists and Engineers Springer New York. 593
B.W Berger B. Grisogono (1998) ArticleTitleThe Baroclinic, Variable Eddy Viscosity Ekman Layer. An Approximate Analytical Solution Boundary-Layer Meteorol 87 363–380
T.K. Chereskin (1995) ArticleTitleEvidence for an Ekman Balance in the California Current J. Geophys. Res. 100 IssueIDC9 12727–12748
Corless, R. M., Jeffrey, D. J., and Knuth, D. E. (1997). A Sequence of Series for the Lambert W Function’, Proceedings ISSAC ‘97, Maui, Ed. Wolfgang W. Kuechlin, pp. 197–204. http://www.apmaths.uwo.ca/∼rcorless/frames/PAPERS/LambertW / [2003-07-23]
Ekman V.W. (1905). On the Influence of the earth’s Rotation on Ocean-Currents. Arkiv. Matem., Astr. Fysik, Stockholm. 2(11)
B. Grisogono (1995) ArticleTitleA Generalized Ekman Layer Profile with Gradually-Varying Eddy Diffusivities’) Quart. J. Roy. Meteorol. Soc. 121 445–453
B Grisogono J. Oerlemans (2001) ArticleTitleKatabatic Flow: Analytic Solution for Gradually Varying Eddy Diffusivities J. Atmos. Sci. 58 3349–3354
B Grisogono J. Oerlemans (2001) ArticleTitleA Theory for the Estimation of Surface Fluxes in Simple Katabatic Flows Quart. J. Roy. Meteorol. Soc. 127 2125–2739
B Grisogono J. Oerlemans (2002) ArticleTitleJustifying the WKB Approximation in Pure Katabatic Flows Tellus. 54 453–462
J.R. Holton (1992) An Introduction to Dynamic Meteorology EditionNumber3 Academic Press San Diego, Calif, London. 511
P.K Kundu I.M. Cohen (2002) Fluid Mechanics EditionNumber2 Academic Press San Diego, Calif, London. 730
J.J. O’Brien (1970) ArticleTitleA Note on the Vertical Structure of the Eddy Exchange Coefficient in the Planetary Boundary Layer J. Atmos. Sci. 27 1213–1215
O. Parmhed J. Oerlemans B. Grisogono (2004) ArticleTitleDescribing Surface-Fluxes in Katabatic Flow on Breidamerkurjökull, Iceland Quart J. Roy. Meteorol. Soc. 130 1137–1151
R.A. Pielke (1984) Mesoscale Meteorological Modeling Academic Press Orlando, Florida, London. 611
R.B. Stull (1988) An Introduction to Boundary Layer Meteorology Kluwer Academic Publishers Dordrecht. 666
Z.-M. Tan (2001) ArticleTitleAn Approximate Analytical Solution for the Baroclinic and Variable Eddy Diffusivity Semi-Geostrophic Ekman Boundary Layer Boundary-Layer Meteorol. 98 361–385
Y Zhang Z.-M. Tan (2002) ArticleTitleThe Diurnal Wind Variation in a Variable Eddy Viscosity Semi-Geostrophic Ekman Boundary-Layer model: Analytical Study. Meterol Atmos. Phys. 81 207–217
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Parmhed, O., Kos, I. & Grisogono, B. An Improved Ekman Layer Approximation for Smooth Eddy Diffusivity Profiles. Boundary-Layer Meteorol 115, 399–407 (2005). https://doi.org/10.1007/s10546-004-5940-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10546-004-5940-0