Nonlinear dynamics at a Hopf bifurcation with axisymmetry breaking in a jet

A complex dynamics with several bifurcations within a 4% variation of the Reynolds number has been found to accompany the transition from a steady to a chaotic flow in a homogeneous round fluid jet. The results of direct numerical simulations are explained using a fifth order weakly nonlinear theory describing the interaction of two counter-rotating helical modes, arising as a consequence of degeneracy of the linearized Navier-Stokes operator spectrum. Two secondary bifurcations and three different asymptotic states are shown to be correctly accounted for by the theory. The validity of the fifth order theory ceases shortly before the onset of chaos.