Symmetry Breading Bifurcations and the Growth of Chaos in a Rotating Fluid

摘要

Bifurcations in flow between independently rotating circular cylinders are being investigated experimentally, numerically, and theoretically. A nonlinear stability analysis of the primary instability exploits symmetry properties to make predictions about the form of the secondary flows; the predictions for the critical Reynolds numbers, wavespeeds, and wavenumbers of the secondary flows (spirals, ribbons, and Taylor vortices) are in good accord with experiment. In another area of study, measurements of mass transport at high Reynolds numbers show that transport in the axial direction is well-described by an effective diffusion coefficient D that has an exponential dependence on the Reynolds number R, D proportional to R to the 3/4 power, while theory suggests that the exponent should be 1 instead of 3/4. Keywords: Instability; Chaos; Turbulence; Bifurcation; Nonlinear dynamics; Computational fluid mechanics.