Taylor—Couette instability of travelling waves with a continuous spectrum

Abstract

The nonlinear evolution of a continuous spectrum of travelling waves resulting from the growth of unstable disturbances in circular Couette flow has been investigated. Numerical solution of the governing integro-differential equations for different initial conditions shows that the equilibrium states of Taylor-vortex, wavy-vortex or spiralvortex flows are not unique, but depend on the initial disturbance. The presence of multiple solutions at a fixed Reynolds number for a given Taylor–Couette geometry has been known since Coles’ seminal contribution in 1965. The current study indicates that the equilibrium state of flows on a stable bifurcation branch is a natural consequence of nonlinear wave resonance and is dependent on the initial conditions. The resulting wavenumber can take any value within an accessible finite band. Since such multiple solutions have also been found numerically for mixed-convection flows and experimentally for several other flows, there is evidence to support the conclusion that a non-uniqueness in the sense of Coles is a generic property for all fluid flows.