Free Convection in the Turbulent Ekman Layer of the Atmosphere

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  • 1 Dept. of Aerospace Enginerring, The Pennsylvania State University, University Park
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Abstract

This paper deals with the problem of fully developed free convection in the atmospheric boundary layer. In free convection, the height of the Ekman layer is much larger than the absolute value of the Monin-Oboukhov length. The kinetic energy budget of the turbulence above the surface layer shows that the standard deviations of vertical velocity and of temperature are related to h/L by σw/u*∝(−h/L) and σθ*∝(−h/L). Because convection has no natural length scale, the height of the neutral Ekman layer (hu*/f) is used to explore the consequences of the proposed expressions for σw and σθ. The dissimilarity between the heat flux and the momentum flux is studied in terms of time- and length-scale ratios and in terms of a flux Richardson number. A definitive solution of the problem, however, cannot be formulated until an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer, can he found.

Abstract

This paper deals with the problem of fully developed free convection in the atmospheric boundary layer. In free convection, the height of the Ekman layer is much larger than the absolute value of the Monin-Oboukhov length. The kinetic energy budget of the turbulence above the surface layer shows that the standard deviations of vertical velocity and of temperature are related to h/L by σw/u*∝(−h/L) and σθ*∝(−h/L). Because convection has no natural length scale, the height of the neutral Ekman layer (hu*/f) is used to explore the consequences of the proposed expressions for σw and σθ. The dissimilarity between the heat flux and the momentum flux is studied in terms of time- and length-scale ratios and in terms of a flux Richardson number. A definitive solution of the problem, however, cannot be formulated until an expression for the height of unstable Ekman layers, as a function of the time of day and the stability conditions at the top of the boundary layer, can he found.

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