Steady nonlinear Ekman--Hartmann boundary layers

The steady, axially symmetric Ekman-Hartmann boundary layer on a flat insulating surface is analyzed in its fully nonlinear form. Emphasis is placed on evaluation of Ekman pumping and induced Hartmann current as functions of Rossby number, magnetic interaction parameter, and magnetic Prandtl number. Significant quantitative departures from the estimates of linear theory are found. Yet, for some purposes (such as for predicting its influence on spin-up) the strength of this hydromagnetic pump is shown to be adequately described by an analytic series solution truncated after the terms quadratic in Rossby number.