Hydrodynamic instability of a flow through a rotating channel filled with anisotropic porous material

Due to its relevance in numerous industrial and geophysical applications, there is an increasing need to understand the dynamics and stability of flow through porous media. In recent times, sufficient effort has been put into gaining pure hydrodynamic instability covering a wide range of permeabilities, effective viscosity, fluid viscosity, and flow speeds for different types of porous-fluid systems. The current work investigates the linear stability of a revolving flow in a spanwise rotating channel loaded with an anisotropic porous substance. The extended Darcy-Brinkman model is considered to depict such physical systems in which the Coriolis force terms are incorporated into the momentum equations. The ratio of vertical permeability to horizontal permeability is taken into analysis to describe the anisotropic flow phenomena. Applying normal mode analysis, we get a fourth-order coupled Orr-Sommerfeld-Squire eigenvalue problem that encapsulates the linear instability of the perturbed flow, which is solved numerically by the Chebyshev collocation method. The main goal of this study is to investigate the effect of Coriolis force and anisotropy of the porous layer in the marginal stability boundaries and estimate the critical parameters that destabilize the flow.