Wave speeds in wavy Taylor-vortex flow

The speed of travelling azimuthal waves on Taylor vortices in a circular Couette system (with the inner cylinder rotating and the outer cylinder at rest) has been determined in laboratory experiments conducted as a function of Reynolds number R, radius ratio of the cylinders 7, average axial wavelength h , number of waves m, and the aspect ratio r (the ratio of the fluid height to the gap between the cylinders). Wave speeds have also been determined numerically for axially periodic flows in infinite-length cylinders by solving the Navier-Stokes equation with a pseudospectral technique where each Taylor-vortex pair is represented with 32 axial modes, 32 azimuthal modes (in an azimuthal angle of 27c/m,) and 33 radial modes. Above the onset of wavy-vortex flow thc wave speed for a given 71 decreases with increasing R until i t reaches a plateau that persists for some range in R . In the radius-ratio range examined in our experiments wc find that the wave speed in the plateau region increases monotonically from 0.1452 at 7 = 0.630 to 0.4552 a t 11 = 0.950 (where the wave speed is expressed in terms of the rotation frequency 52 of the inner cylinder). There is a much weaker dependence of the wavc speed on h, m, and r. For three sets of parameter values (R, h, 7 and m,) the wavc speeds have been measured, extrapolated to infinite aspect ratio, and compared with the numerically computed values. For each of these three cases the agreement is within 0.1 yo.