Revisiting Crossflow-Based Stabilization in Channel Flows

Abstract

Stabilization schemes in wall-bounded flows often invoke fluid transpiration through porous boundaries. While these have been extensively validated for external flows, their efficacy in channels, particularly from the standpoint of non-modal perturbations, is yet to be demonstrated. Here, we show that crossflow strengths previously considered ``ideal'' for optimizing stability in channels in fact admit strong non-modal energy amplification. We begin by supplementing existing modal calculations and then show via the resolvent that extremely strong and potentially unfeasible crossflows are required to suppress non-modal growth in linearly stable regimes. Investigation of unforced algebraic growth paints a similar picture. Here, a component-wise budget analysis reveals that energy redistribution through pressure-velocity correlations plays an important role in driving energy growth/decay. The superposition of a moving wall is also considered, and it is shown that while energy amplification generally worsens, it can potentially be suppressed beyond a regime shift in parameter space. However, these flows are marred by rapidly declining mass transport, rendering their ultimate utility questionable. Our results suggest that crossflow-based stabilization might not be useful in internal flows.