Fully nonlinear mode competitions of nearly bicritical spiral or Taylor vortices in Taylor-Couette flow
K. Deguchi and S. Altmeyer
Accepted
Interactions between nearly bicritical modes in Taylor-Couette ow, which have been concerned in the framework of weakly nonlinear theory, are extended to fully nonlinear Navier-Stokes compu- tation. For this purpose, standard Newton solver for axially periodic ows is generalized to compute any mixed solutions having up to two phases, which typically arise from interactions of two spiral or Taylor vortex modes. Also, a simple theory is developed in order to classify the mixed solu- tions. With these methods, we elucidate pattern formation phenomena which has been observed in Taylor-Couette ow experiment. Focusing on counter-rotating parameter range, all possible classes of interaction of various solutions with different azimuthal and axial wavenumbers are considered within our computational restriction and we observe numerous connection branches, e.g. footbridge solutions. Some of the mixed solutions result in rst identi ed type of nite-amplitude solutions such as three-dimensional wavy spiral solution with axial relative periodicity or axially doubly periodic toroidally closed vortex solution. The possible connection of the former solution family to spiral turbulence which has been observed in highly counter-rotating Taylor-Couette ow is discussed.