The structure of the Ekman layer for geostrophic flows with lateral shear

Abstract

A generalized Ekman flow is obtained for the boundary layer of a semi‐infinite, rotating homogeneous fluid with lateral variation in the horizontal velocity components far from the boundary surface. The fields of motion considered include uni‐directional motion with lateral shear, symmetric and elongated eddies, and cols. A solution for the first of these cases is obtained to fifth order; for the others, to second order. In all cases the magnitude of the vertical velocities induced by convergence in the boundary layer is greater for systems with negative relative vorticity than for systems with positive relative vorticity. The result differs substantially from first‐order theory, for which the magnitude of the vertical velocity is proportional to the relative vorticity. A number of meteorological applications are considered.

A Comprehensive Analysis of Nonlinear Corrections to the Classical Ekman Pumping

“…The validity of our solutions in (62)- (69) are confirmed by comparing them to the OðRo 1 Þ solutions obtained by Benton et al (1964). The full particular solution g 1 to (57) is obtained by superposing (62)-(65).…”

“…Following Benton et al (1964) and Bannon (1998), we consider the model atmosphere to be a semi-infinite Boussinesq fluid moving over a flat surface (z à ¼ 0) on an f plane with a Cartesian coordinate system, where the asterisk means a dimensional quantity from now on. The horizontal pressure gradient is assumed to be parallel to the x à -axis.…”

“…In Section 2, we give the mathematical formulation of the steady nonlinear Ekman pumping. The setup of the problem examined in the study are unidirectional flows with a general horizontal shear, which were originally examined by Benton et al (1964). In Section 3, the steady nonlinear Ekman pumping for uni-directional flows with a constant horizontal shear is discussed.…”

“…Benton et al (1964) considered the Ekman pumping for the primitive equations in the steady nonlinear case by using a perturbation method of a small Rossby number e. They presented formulae for the Ekman pumping for unidirectional flows with a constant horizontal shear up to Oðe 2 Þ analytically, and Oðe 4 Þ numerically. Recently, Hart (2000) also studied the steady nonlinear Ekman pumping for the primitive equations.…”

Nonlinear stratified spindown over a slope

“…A. Benthuysen and L. N. Thomas number, = U/f L, Ekman advection of momentum weakens Ekman pumping in cyclonic regions, ζ > 0, and strengthens Ekman suction in anticyclonic regions, ζ < 0 (Benton, Lipps & Tuann 1964;Hart 1995Hart , 2000Pedlosky 2008), where U is the characteristic flow speed, f is the planetary vorticity (assumed positive in this work), and L is the characteristic lateral length scale.…”