Parametric instability of steady fluid flow in a corrugated pipe

Abstract: In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow, and shows that parametric instability occurs even if the velocity of the base flow is zero. Stability diagrams of the system as a function of the amplitude and period of the corrugation, for different velocities of the base flow, are obtained using parallel numerical computation. The analysis shows that the higher-order bands of instability are strongly dependent on the base flow velocity.