Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

Abstract

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wallwake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10 5 . The data show low Rossby number effects for Ro < 10 5 and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10 3 .Keywords Clauser's outer layer · Intermediate layer · Izakson-Millikan-Kolmogorov hypothesis · Mesolayer effect · Neutral barotropic planetary boundary layer · Rossby number effects IntroductionAtmospheric (planetary) turbulent boundary-layer descriptions have been presented by Hess and Garratt (2002) showing the influence of geostrophic wind. Further, Garratt and Hess (2002, p. 256, Fig. 2) compared the geostrophic velocity profile observations (including