Effects of Distributed Roughness on Crossflow Instability through Generalized Resonance Mechanisms

TL;DR

This paper investigates how distributed surface roughness influences crossflow instability in boundary layers by exploring resonant interactions with eigenmodes, revealing mechanisms that significantly alter growth rates and promote transition.

Contribution

It introduces generalized resonance mechanisms, including triadic resonance and Bragg scattering, to explain the effects of roughness on crossflow instability, extending analysis to multiple interacting vortices.

Findings

Small roughness can significantly change growth rates of instabilities.

Resonant interactions involve modes with comparable growth rates.

Mechanisms include triadic resonance and Bragg scattering.

Abstract

Experiments have shown that micron-sized distributed surface roughness can significantly promote transition in a three-dimensional boundary layer dominated by crossflow insta- bility. This sensitive effect has not yet been fully explained physically and mathematically. Unlike past researches focusing on the receptivity of the boundary layer to surface roughness, or on the local stability of the modified mean flow, this paper seeks possible inherent mechanisms by investigating the effects of distributed surface roughness on crossflow instability through resonant interactions with eigenmodes. A key observation is that the perturbation induced by roughness with specific wavenumbers can interact with two eigenmodes (travelling and stationary vortices) through triadic resonance, or interact with one eigenmode (stationary vortices) through Bragg scattering. Unlike the usual triadic resonance of neutral, or nearly neutral, eigenmodes, the present triadic resonance can take place among modes with O(1) growth rates, provided that these are equal; unlike the usual Bragg scattering involving neutral waves, crossflow stationary vortices can also be unstable. For these amplifying waves, the generalized triadic resonance and Bragg scattering are put forward, and the resulting corrections to the growth rates are derived by a multiple-scale method. The analysis is extended to the case where up to four crossflow vortices interact with each other in the presence of suitable roughness components. The numerical results for Falkner-Skan-Cooke boundary layers show that roughness with a small height (a few percent of the local boundary-layer thickness) can change growth rates substantially (by a more-or-less O(1) amount)....