Abstract.
We have performed a numerical bifurcation study of the classical
Taylor-Couette flow, in the case where the angular momentum increases
outwards. Since the basic flow is linearly stable for all Reynolds
numbers, it is difficult to obtain nonlinear solutions without a
starting instability. Our approach is to impose a temperature
difference across the cylinders to induce a convective instability.
Once finite-amplitude flows are initiated, they are numerically
continued down to zero Rayleigh number to remove the convective
instability. Two-dimensional solutions were thus obtained in the
form of nonlinear traveling wave.
The existence of these solutions is related to
the experimentally observed transition to turbulence.
