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Revisiting crossflow-based stabilization in channel flows
Phys. Rev. Fluids 9, 113901 – Published 18 November, 2024
DOI: https://doi.org/10.1103/PhysRevFluids.9.113901
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 nonmodal perturbations, is yet to be demonstrated. Here, we show that crossflow strengths previously considered “ideal” for optimizing stability in channels in fact admit strong nonmodal 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 nonmodal growth in linearly stable regimes. Investigation of unforced algebraic growth paints a similar picture. Here, a componentwise 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 in certain regions of 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.
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