Phase diffusion in the vicinity of an oscillatory secondary bifurcation

The phase dynamics of a one-dimensional cellular pattern is studied on a regular array of liquid columns formed below an overflowing horizontal cylinder. When a uniform wavelength dilation is imposed by static boundaries, an oscillatory secondary bifurcation is observed ~‘‘optical mode’’!. The case of a moving boundary ~sinusoidal motion! allows us to observe three dynamical states: phase diffusion, phase diffusion coupled with the oscillatory state, and propagation of dilation waves. The dependence of the phase diffusion coefficient D upon the pattern wavelength is investigated for different flow rates: D is nearly constant until the appearance of the oscillations and jumps to a larger value when the optical mode is excited. This unusual behavior is recovered by an analytical treatment of Coullet-Ioss equations. @S1063-651X~98!12002-0#