A deep dive into Tollmien-Schlichting wave control via passive wall deformations: The battle between local and downstream stabilization, lessons learned, and implications for phononic subsurfaces
Abstract
A decade ago, a landmark study on flow control via subsurface phonons transformed our understanding of fluid-structural interactions, compelling us to reimagine ways by which to suppress boundary layer instabilities. While subsequent investigations have steadily enriched this landscape, several questions remain largely unanswered. The notion of Tollmien-Schlicting (TS) wave stabilization relies on phase-engineered surface interactions, which destructively engage with the wave and impede its growth. Although the fundamental drivers of the phenomenon are established, its granular physics remain insufficiently resolved, particularly as it pertains to directional effects, competing energy production mechanisms, and the precise streamwise locations governing the process. Revisiting this initial vision, we confront these open questions, revealing fresh insights, and establishing broad foundational strokes to guide the next era of investigations. We begin by defining the amplitude and phase criteria of an elastic wall admittance driving perturbation energy changes relative to a rigid wall. The established framework isolates the roles of the work-rate, viscous energy, production, and dissipation in shaping the fluid's response and clarifies how each contributes to the collective outcome. Crucially, we demonstrate how streamwise translation of the interaction surface significantly alters these parameters, revealing critical thresholds at which the control result is fully reversed. Our model identifies specific pathways to sustained TS wave attenuation, and defines the limits of what can be accomplished passively. Finally, we conceptualize a two-dimensional phononic subsurface, whose tailored and disproportional response to the flow in the wall-normal and streamwise directions, brings about the elusive combination of local and downstream stabilization.
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BibTeX
@misc{yousef2026deep,
title = {{A deep dive into Tollmien-Schlichting wave control via passive wall deformations: The battle between local and downstream stabilization, lessons learned, and implications for phononic subsurfaces}},
author = {H. Yousef and H. Hassan and I. Roy and T. Toki and C. Scalo and M. Nouh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16144},
eprint = {2609.16144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A deep dive into Tollmien-Schlichting wave control via passive wall deformations: The battle between local and downstream stabilization, lessons learned, and implications for phononic subsurfaces
AU - H. Yousef
AU - H. Hassan
AU - I. Roy
AU - T. Toki
AU - C. Scalo
AU - M. Nouh
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16144
UR - https://arxiv.org/abs/2609.16144
AB - A decade ago, a landmark study on flow control via subsurface phonons transformed our understanding of fluid-structural interactions, compelling us to reimagine ways by which to suppress boundary layer instabilities. While subsequent investigations have steadily enriched this landscape, several questions remain largely unanswered. The notion of Tollmien-Schlicting (TS) wave stabilization relies on phase-engineered surface interactions, which destructively engage with the wave and impede its growth. Although the fundamental drivers of the phenomenon are established, its granular physics remain insufficiently resolved, particularly as it pertains to directional effects, competing energy production mechanisms, and the precise streamwise locations governing the process. Revisiting this initial vision, we confront these open questions, revealing fresh insights, and establishing broad foundational strokes to guide the next era of investigations. We begin by defining the amplitude and phase criteria of an elastic wall admittance driving perturbation energy changes relative to a rigid wall. The established framework isolates the roles of the work-rate, viscous energy, production, and dissipation in shaping the fluid's response and clarifies how each contributes to the collective outcome. Crucially, we demonstrate how streamwise translation of the interaction surface significantly alters these parameters, revealing critical thresholds at which the control result is fully reversed. Our model identifies specific pathways to sustained TS wave attenuation, and defines the limits of what can be accomplished passively. Finally, we conceptualize a two-dimensional phononic subsurface, whose tailored and disproportional response to the flow in the wall-normal and streamwise directions, brings about the elusive combination of local and downstream stabilization.
ER -