Modal, Non-Modal, and Energy Budget Analyses of the Stability of Viscoelastic Plane Poiseuille Flow under a Transverse Magnetic Field

Abstract The linear-stability of plane Poiseuille, channel flow of a viscoelastic, Navier-Stokes-Voigt, (Kelvin-Voigt) fluid is analysed under a transverse magnetic field, with direct relevance to the stability and control of magneto-viscoelastic flows in engineered channel systems. High accuracy Chebyshev collocation and Galerkin methods are employed to solve the resulting modified Orr-Sommerfeld stability equations. Unlike earlier studies, this work links energy budget analysis with non-modal growth suppression to reveal distinct viscoelastic and magnetic dissipation mechanisms across the channel. The modal stability analysis, including eigenspectrum and temporal growth rate evaluations, reveals that both viscoelastic effects (parameterized by Λ) and magnetic damping (via the Hartmann number M) exert strong stabilizing influences by suppressing instabilities and shifting the critical Reynolds number to higher values. Neutral stability curves and growth rate profiles confirm that increasing Λ and M enlarges the stable parameter space, delaying the onset of linear instability. Beyond modal analysis, transient growth calculations capture the potential for non modal amplification in linearly stable regimes. Results show that both Λ and M significantly reduce the peak transient energy growth and expedite its decay, thereby limiting the risk of subcritical transition. e-pseudospectrum analysis supports these findings, illustrating that the extent of spectral bulging into the unstable region diminishes with increasing damping. An in depth energy budget analysis highlights spatially localized stabilization: viscoelasticity acts near the walls by attenuating shear production and enhancing Voigt dissipation, while magnetic damping dominates in the channel core via enhanced Lorentz force-induced dissipation.