Wave speeds in wavy Taylor-vortex flow

Author :Gregory P. King, Y . Li, W. Lee, Harry L. Swinney, and Philip S. Marcus
Publication :Journal of Fluid Mechanics
Volume :141
Pages :36C5390
Year :1984

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.