INTEGRAL TRANSFORM TECHNIQUE APPLIED TO FREE SHEAR LAYERS IN A ROTATING RIGID SATURATED POROUS MEDIUM

The hydrodynamic free shear layers that arise in a steady, linear, axisymmetric flow of a homogeneous fluid in a rotating porous medium confined between differentially rotating parallel plates are investigated using a combination of integral transform and boundary layer method. The flow dynamics are seen to depend upon two non-dimensional parameters, viz, the Ekman number E and the rotational Darcy number Λ. As the rotational Darcy number Λ increases beyond O(E<sup>1/2</sup>) the flow structure is significantly altered from the pure hydrodynamic case. The interior region is characterized by an azimuthal velocity which is less than O(1). As a result, it assumes a z-dependent structure. The outer Stewartson (E/Λ )<sup>1/2</sup> layer becomes weak and the inner Stewartson E<sup>1/3</sup> layer alone supports the mass flux. For Darcy friction regime corresponding to low permeability, characterized by E<sup>1/3</sup> less than Λ , the E<sup>1/3</sup> viscous layer becomes an inviscid Λ layer to carry the mass flux. The viscous boundary layer is suppressed for all practical purposes. All these results are reminiscent of the hydromagnetic flow in a rotating system with magnetic field perpendicular to the vertical shear layers and rotation vector. In addition, the possible analogy between this porous medium problem, rotating hydromagnetic and stratified flow problem is discussed.