Dual analysis of stability in plane Poiseuille channel flow with uniform vertical crossflow

Abstract

In this paper, we investigate the effect of uniform vertical crossflow on the plane Poiseuille channel flow. The derivation and linearization of the Navier–Stokes equations are performed to enable numerical solution through the fourth-order Orr–Sommerfeld equation. The Chebyshev collocation method is employed for this purpose. A dual approach is employed to examine the basic velocity profile, involving both reference velocity analysis (z = 0) and maximum streamwise velocity analysis (z = zmax). The two approaches provide distinct perspectives on the flow and may yield different stability predictions, depending on the values of the parameters used. Modal analysis is conducted to comprehend the asymptotic behavior of the system, achieved through the plotting of eigenspectrum, neutral stability curves, and growth rate curves for disturbances. Accurate values of critical triplets are obtained, aligning with the existing literature. The non-modal analysis is performed to understand the short-term behavior of the system, aided by pseudospectra, evolutionary patterns of energy amplification of the disturbances G(t) over time, and delineation of regions, indicating stability, potential instability, and instability. The collective results from both analyses reveal that the crossflow serves as a dual agent, contributing to both the stabilization and destabilization of the system.