A note on nonlinear corrections to the Ekman layer pumping velocity

High order corrections to the Ekman pumping formula are derived analyticall y by a regular perturbation expansion in the external flow Rossby number. G eneral shear lines V(x) and general circular vortices V(r) are considered. The results extend previous calculations based on the assumption of constan t vorticity in the exterior fields. At each order in the expansion, higher derivatives of the basic external flow are introduced, thus rendering the p umping more and more nonlocal as additional orders in Rossby number are inc luded. For general profiles of exterior velocity, the constant vorticity si milarity and perturbation solutions may be corrected using the formulas pre sented here. (C) 2000 American Institute of Physics. [S1070-6631(99)02612-4 ].