Phase dynamics for the wavy vortex state of the Taylor instability

We present dynamic equations for the slow macroscopic variables of the wavy vortex state. The static solutions explain in a qualitative way recent experimental results of Ahlers et al. on the variation of the vortex diameter throughout the cell. In addition, we predict the existence of a pair of propagating or overdamped normal modes (depending on the wave vector of the disturbance) formed by the slow variables.