Long-time instability and transient behavior of pressure-driven flow of a power-law fluid in a plane channel overlying a porous layer

The present study is undertaken to analyze the hydrodynamic stability of pressure-driven flow of non-Newtonian fluid-porous systems, where the fluid exhibits the power-law rheology. Such combined fluid-porous flow systems are widely prevalent in diverse geophysical and industrial applications. In the beginning, modal analysis has been performed for comprehending the long-time flow transition characteristics. The plots of the eigenfunctions corresponding to the critical eigenmodes demonstrate the intricate interplay between the non-Newtonian viscosity (quantified by the flow behavior index n) and the porous layer (quantified by depth ratio). It is observed that for a shear-thinning fluid, the flow transition is less sensitive to a variation in depth ratio than that for a shear-thickening fluid. In addition, by exploring the transient energy growth and pseudospectrum in the framework of non-modal stability analysis, the responses to initial conditions and external excitations have been investigated in detail.