On Taylor-Proudman columns and geostrophic flow in rotating porous media

Taylor-Proudman columns are a well-known phenomenon in rotating flows in pure fluids (non-porous domains). A theoretical formulation of the problem of incompressible fluid flow in rotating porous media is presented. The criteria for the relative significance of different terms in the equations are identified leading to a formulation which is based on the traditional Darcy's law but extended to include the Coriolis and centrifugal terms resulting from rotation. Finally a proof is provided showing that Taylor-Proudman columns exist in porous media as well. This occurs in the limit of small values of the porous media Ekman number. The corresponding consequences are that a stream function exists in this otherwise three-dimensional flow and this stream function and the pressure are the same in the limit of high rotation rates. This type of geostrophic flow means that isobars represent stream-lines of the leading order for small values of Ekman number. (Author)