This study focuses on temporal stability of plane Couette and Poiseuille flows of Walters' liquid B viscoelastic fluid between two plates embedded in homogeneous porous medium in which Darcy law is modified to incorporate the flow of viscoelastic fluid in porous medium using modal and non-modal stability investigations. The spectral collocation and shooting methods are utilized to assess stability of viscoelastic fluid in porous medium. The modal analysis reveals that the Walters' liquid B has destabilizing impact on flow, while the presence of a porous medium stabilizes the same flow. The unstable mode for the Poiseuille flow belongs to the wall mode which is shown to be a continuation to the Newtonian fluid. The neutral stability curves reveal that higher elasticity numbers lead to a reduction in the critical Reynolds number, promoting flow destabilization. The non-modal analysis shows that the flow instability is inferred from ϵ-pseudospectral contours protruding into the unstable region highlighting non-modal sensitivity. The transient growth of the perturbed quantities reveals disturbances in both flows initially amplify exponentially, then decay, followed by either sustained monotonic growth or continuous decay, dictated by porous parameters or elasticity numbers. The energy budget analysis of the perturbed quantities confirms these interesting features. It reveals regions with negative production due to Reynolds stress and positive production from viscous dissipation and porous medium contributions.
Amrutha et al. (Wed,) studied this question.