W.F. Langford, R. Tagg, E. Kostelich, H.L. Swinney and M. Golubitsky
Primary instabilities and bicriticality in flow between counter-rotating cylinders
Phys. Fluids. 31(4) (1988) 776-785.
The primary instabilities and bicritical curves for flow between
counter-rotating cylinders have been computed numerically from the
Navier-Stokes equations assuming axial periodicity. The computations
provide values of the Reynolds numbers, wavenumbers, and wave speeds at the
primary transition from Couette flow for radius ratios from 0.40-0.98.
Particular attention has been focused on the bicritical curves that separate
(as the magnitude of counter-rotation is increased) the transitions from
Couette flow to flows with different azimuthal wavenumbers m and m + 1.
This lays the foundation for further analysis of nonlinear mode interactions
and pattern formation occuring along the bicritical curves and serves
as a benchmark for experimental studies. Preliminary experimental measurements
of transition Reynolds numbers and wave speeds presented here agree well with
the computations from the mathematical model.