Sinuous and Varicose Modes in Turbulent Flow Through a Compliant Channel

Abstract

We study the stability of two-dimensional fully-developed turbulent flow through a channel having spring-backed compliant walls. We decompose the FSI system into sinuous (symmetric disturbances relative to channel centre-line) and varicose (anti-symmetric) modes to assess the effect of wall compliance and structural damping on the stability of the flow-induced wall-based instabilities, Travelling Wave Flutter (TWF) and Divergence. The results show that varicose TWF and Divergence instabilities are more unstable than their sinuous counterparts. Varicose TWF, with long wavelength and high wavespeed, is the critical instability for a system with low levels of structural damping. Sinuous and varicose Divergence instabilities have similar wave characteristics and originate from a downstream propagating, downstream-stable hydrodynamic mode branch found in turbulent rigid-wall channel flow. The onset of Divergence is largely insensitive to the effect of structural damping. Finally, larger amplitudes of fluctuating wall shear stress occur for instabilities that feature larger amplitudes of vertical-disturbance wall velocity.