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The spin-up of a homogeneous fluid bounded below by a permeable medium

The spin-up of a homogeneous rotating fluid bounded at the top and/or bottom by a permeable medium has been proposed by Bretherton & Spiegel (1968) as a model for the spin-up in natural flows where turbulent processes transmit the direct effect of the boundaries deeper into the fluid than does the laminar Ekman layer. The theoretical analysis for the spin-up of a laterally unbounded fluid bounded by a permeable medium below is presented here. In addition, an experimental study of the process is presented. Theory and experiment agree reasonably well with a maximum difference of about 8% in the predicted and measured spin-up times. The effects of the side-wall boundary have been studied theoretically by Howard (1969). Experimental observations in the side-wall boundary layer confirm qualitatively the results of Howard's theory.