Modal and non-modal linear stability analysis of plane channel flow through a Darcy-Brinkman porous medium with symmetric and asymmetric slippery walls

Abstract

This study investigates the linear stability and transient growth behavior of fluid flow in a channel influenced by varying slip boundary conditions, porous parameters, and viscosity ratios. The Chebyshev Collocation Method (CCM) was used to solve the modified eigenvalue problem, leveraging basic routines of MATLAB 2024b and the QZ algorithm for high precision in capturing stability characteristics. Using modal and non-modal stability analyses, the results reveal that boundary conditions—no-slip, symmetric slip, and asymmetric slip—strongly influence flow stability, eigenvalue spectra, and velocity profiles. With increasing slip length, symmetric slip enhances stability by raising the critical Reynolds number, while asymmetric slip introduces complex stability dynamics, particularly at higher viscosity ratios. Non-modal analysis highlights transient energy growth, pseudospectrum, and contour plots, especially under asymmetric slip, suggesting that disturbances could cause significant short-term deviations even in stable regimes. The results from the modal analysis appear to align well with those from the non-modal analysis.