Double Hopf bifurcation in corotating spiral Poiseuille flow

Nonlinear dynamics of the spiral Poiseuille problem for moderate axial through flow is investigated numerically within the corotating regime for medium gap geometry. The neighborhood of a double Hopf bifurcation point of the linear stability boundary, where spiral waves of opposite axial phase propagation compete, is explored by accurately solving time-dependent Navier-Stokes equations with a solenoidal spectral method. The mode interaction generates a quasiperiodic stable regime of interpenetrating spirals, which coexists with stable limit cycles associated with the aforementioned spiral waves of opposite helicoidal orientation. The spatiotemporal properties of the computed solutions are explained and discussed in terms of equivariant bifurcation and normal form theories. Similar flows have also been observed experimentally in the past within the corotating region.