Bifurcation Corresponding to the Onset of Asymmetric Periodic Structures and a Self-Induced Pressure Gradient in a Modified Taylor Flow

Abstract

With reference to the example of a modified Taylor flow, the bifurcation of the loss of flow symmetry with the onset of a self-induced pressure gradient is studied theoretically and numerically. A linear analysis shows that the bifurcation is supercritical. It is necessarily accompanied by the appearance of a longitudinal pressure gradient and takes place at values of the parameters for which the solution of the linear system for the perturbations satisfies the condition of zero mass flow. It is established that, as a result of the bifurcation, two asymmetric solutions with oppositely directed pressure gradients are simultaneously generated. In the supercritical region, the symmetric branch of the solutions is also retained but becomes unstable. Bifurcation of the loss of symmetry and a self-induced pressure gradient can occur only in nonlinear systems.