Fluid Seepage into a Rotating Channel Filled with a Porous Medium

Abstract

Liquid or gas seeps into one side of a porous layer. Coriolis forces affect the flow due to system rotation. The problem models seepage flow into a porous rock fault under planetary rotation. Using similarity, the three-dimensional Darcy–Brinkman equations reduce to a sixth-order ordinary differential equation governed by two nondimensional parameters: the Darcy number D and the rotation number β. The complex exact solution is supplemented by asymptotic analyses for extreme values of D and β. Although the Reynolds number is small, it is found that boundary layers may exist. For small D, matched asymptotic expansions show the interior is Darcy flow with boundary layer thickness O(D) on the boundary. For large β, the interior has almost constant velocity parallel to the rotation vector with boundary layer thickness O(1/β). Streamlines, velocity profiles, shear stress, and pressure distributions show different characteristics for different D and β. The asymptotic solutions compare well with the exact solution in their respective regions of validity.