Three-dimensional instability of axisymmetric flow in a rotating lid-cylinder enclosure

The axisymmetry-breaking three-dimensional instability of the axisymmetric flow between a rotating lid and a stationary cylinder is analysed. The flow is governed by two parameters-the Reynolds number Re and the aspect ratio gamma (=height/radius). Published experimental results indicate that in dif ferent ranges of gamma axisymmetric or non-axisymmetric instabilities can b e observed. Previous analyses considered only axisymmetric instability. The present analysis is devoted to the linear stability of the basic axisymmet ric flow with respect to the non-axisymmetric perturbations. After the line arization the stability problem separates into a family of quasi-axisymmetr ic subproblems for discrete values of the azimuthal wavenumber k. The compu tations are done using the global Galerkin method. The stability analysis i s carried out at various densely distributed values of gamma in the range 1 < gamma < 3.5. It is shown that the axisymmetric perturbations are dominan t in the range 1.63 < gamma < 2.76. Outside this range, for gamma < 1.63 an d for gamma > 2.76, the instability is three-dimensional and sets in with k = 2 and k = 3 or 4, respectively. The azimuthal periodicity, patterns, cha racteristic frequencies and phase velocities of the dominant perturbations are discussed.