The stability of a flexibly mounted rotating cylinder in turbulent annular fluid flow

In this paper, we determine the inviscid linear stability with respect to two-dimensional disturbances of a fluid flow between two concentric cylinders. The inner rigid cylinder rotates with the angular velocity Ω0 and is fixed on elastic hinges at each end in the transverse direction. The outer cylinder does not rotate and is rigidly fixed. We assume that the fluid flow has an inner core that rotates as a solid body with angular velocity Ω0/2 and outside the core there are turbulent boundary layers. The velocity profile of the turbulent boundary layers satisfies the viscous Camassa−Holm equations. The perturbed fluid flow is derived from Rayleigh's equation. The analysis yields an equation of motion of the cylinder equivalent to previous work without boundary layers and a basic flow of constant angular vorticity. The analysis is not restricted to a small gap between the cylinders. The results are compared with the results by Antunes et al. (1996), who consider a similar problem with uniform velocity profile and the limit of small gap. For ρc/ρf<1 the results disagree in that the present analysis shows stability whereas Antunes et al. find instability. For ρc/ρf>1 both theories predict stability and for larger values of ρc/ρf the agreement is good especially for small gap.