Radiative instability of the flow around a rotating cylinder in a stratified fluid

Abstract

The stability of the flow around a rotating cylinder in a fluid linearly stratified along the cylinder axis is studied numerically and experimentally for moderate Reynolds numbers. The flow is assumed potential and axisymmetric with an angular velocity profile Ω = 1/r2, where r is the radial coordinate. Neglecting density diffusion and non-Boussinesq effects, the properties of the linear normal modes are first provided. A comprehensive stability diagram is then obtained for Froude numbers between 0 and 3 and Reynolds numbers below 1000. The main result is that the potential flow, which is stable for a homogeneous fluid, becomes unstable for Froude number close to one and for Reynolds numbers larger than 360. The numerical results are then compared with experimental results obtained using shadowgraph and synthetic Schlieren techniques. Two symmetrical helical modes are found to be simultaneously unstable. We show that these modes exhibit an internal gravity wave structure extending far from the cylinder in agreement with the theory. Their wavelength and frequency are shown to be in good agreement with the numerical predictions for a large range of Froude and Reynolds numbers. These experimental results are the first indisputable evidence of the radiative instability.