Changes in the hydrodynamic stability of plane porous-Couette flow due to vertical throughflow
B. M. Shankar, I. S. Shivakumara
Abstract
A detailed study on the linear stability of plane porous-Couette flow in the presence of a uniform vertical throughflow using the Brinkman–extended Darcy equation has been presented. The equivalent of the Orr–Sommerfeld eigenvalue problem is formulated and solved numerically using the Chebyshev collocation method. The throughflow introduces an asymmetry in the basic flow amounting to the existence of a different set of onset modes. The contributions of the throughflow dependent modified Reynolds number and the modified porous parameter on the critical values defining the threshold for the onset of instability are presented. It is found that the stability characteristics of plane Couette flow in a porous medium in the presence of throughflow are remarkably different from no throughflow and non-porous cases.