Revisiting Crossflow-Based Stabilization in Channel Flows

TL;DR

This paper critically examines the effectiveness of crossflow-based stabilization in channel flows, revealing that strong crossflows needed for suppression cause significant non-modal energy amplification and are impractical due to mass transport issues.

Contribution

It demonstrates that existing stabilization strategies are ineffective in channels and highlights the limitations of crossflow control in internal flows through modal, resolvent, and algebraic growth analyses.

Findings

Strong crossflows cause significant non-modal energy amplification.

Suppression of non-modal growth requires unfeasibly high crossflows.

Flow control via crossflow is limited by mass transport decline.

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.