Hydrodynamic instability of flow through a rotating channel filled with isotropic porous media

Abstract

Various geophysical and engineering applications have underlying physics, comprising system rotation's effects on the dynamics and transport phenomena in porous media flows. Comprehensive knowledge of the instability in a rotating fluid-saturated porous layer is beneficial for controlling the transport phenomena and the mixing process. The present study focuses on the temporal evolution of small disturbances in a pressure-induced fluid flow through a spanwise rotating channel filled with an isotropic porous material. A Darcy–Brinkman model, including the Coriolis force term in the momentum equation, is employed to describe the developed flow. A normal mode analysis is performed, and the coupled Orr–Sommerfeld–Squire eigenvalue problem is formulated to capture the linear instability of the perturbed flow. The Chebyshev collocation technique is used to solve the fourth-order eigenvalue problem to capture the transient behavior of the finite-amplitude disturbances. The temporal growth rate and marginal stability curves related to the Coriolis force-based instabilities are investigated. The rotating porous media flow is unstable at a much lower Reynolds number than the non-rotating configuration. The analysis confirms co-existing unstable modes and mode coalescence for a specific range of parameters, which can enhance the mixing and transport inside the porous layer. The neutral stability curves show the appearance of two different unstable zones corresponding to the long and moderate waves. Moreover, the higher permeability and porosity of the porous medium have a destabilizing influence.