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On the solution of the stationary, baroclinic Ekman-layer equations with a finite boundary-layer height

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Abstract

The stationary, Ekman-layer equations have been solved in closed form for two expressions of the eddy viscosity as a function of height, z: v τ=cu*z(1−z/h)and v τ=cu*z(1−z/h) 2, where u* is the friction velocity, h the boundary-layer height and c a constant. The main difference between both solutions is that the quadratic K-profile leads to a velocity discontinuity at the top of the boundary layer, while the solution for the cubic profile approaches the geostrophic wind at z=h smoothly. We discuss the characteristics of the solutions in terms of a dimensionless parameter C=fh/cu*, where f is the Coriolis parameter. The dependence on C can be interpreted in terms of a varying boundary-layer height or in terms of stability. The results for C ~ 1 are related to a neutral boundary layer. They agree well with results of a second-order model. The limit C → 0 is investigated in detail. We find that the stress profile becomes linear. The velocity profile shows different characteristics depending on whether we consider a shallow or a very unstable boundary layer. The results agree with observations. Finally we consider the influence of baroclinicity on the wind and stress profiles.

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  1. Royal Netherlands Meteorological Institute, De Bilt, The Netherlands

    F. T. M. Nieuwstadt

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  1. F. T. M. Nieuwstadt
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Nieuwstadt, F.T.M. On the solution of the stationary, baroclinic Ekman-layer equations with a finite boundary-layer height. Boundary-Layer Meteorol 26, 377–390 (1983). https://doi.org/10.1007/BF00119534

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  • DOI: https://doi.org/10.1007/BF00119534

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