Results of numerical simulations of a forced shear flow in an annular geome
try are presented. The particular geometry used in this work reduces the ef
fects of centrifugal and Coriolis forces. However, there are still a large
number of system parameters (shear width, shear profile, radius of curvatur
e, initial conditions, etc.) to characterize. This set of variables is limi
ted after the code has been validated with experimental results (Rabaud & C
ouder 1983; Chomaz et al. 1988) and with the associated linear stability an
alysis. As part of the linear stability characterization, the pseudo-spectr
um for the associated Orr-Sommerfeld operator for plane, circular Couette f
low is calculated, and it is found to be insensitive to perturbations.
The numerical simulation code is a highly accurate de-aliased spectral meth
od which utilizes banded operators to increase the computational efficiency
. Viscous dissipation terms enter the code directly from the equations of m
otion. The results from the simulation code at low Reynolds numbers are com
pared with the results from linear stability analysis and are used to give
predictions for the coefficients of the Landau equation describing the satu
ration behaviour near the critical Reynolds number. Numerical results at hi
gher Reynolds numbers demonstrate the effects of spin-up and spin-down, inc
luding the experimentally observed hysteresis. The properties of two-dimens
ional shears at high Reynolds numbers, at which temporal states are formed,
are also addressed.