Effect of the transition layer on the stability of a fluid-porous configuration: Impact on power-law rheology

One of the crucial aspects in the case of describing flow through a fluid-porous double layer configuration is the quantification of the flow behavior near the fluid-porous interface. Both theoretical as well as experimental studies indicate that in the case of real-life fluid-porous geometries, the shift from the fluid layer to the porous layer is not sharp and immediate. Instead, there exists a transition layer in between the fluid and the porous layers. In order to get a realistic picture of flow transition characteristics for such systems, it is imperative that this transition layer be taken into consideration in the hydrodynamic stability analysis. The same has been carried out in the present study, and the effect of the transition layer on the stability characteristics has been assessed. The current study has investigated the effect of the transition layer on the flow of a power-law fluid overlying a porous layer in a channel flow configuration, as the earlier studies were restricted to Newtonian fluids only. A rigorous three-dimensional perturbation framework has been adopted, as Squire's theorem is not applicable for the power-law rheology unlike Newtonian rheology. Both modal and nonmodal analyses are attempted in order to reveal the long-time response as well as short-time amplifications of the system to external disturbances. The intricate interaction between the non-Newtonian rheology of the fluid and the thin transition layer is found to affect the transient amplifications of the flow system significantly.