Phase dynamics near a parity-breaking instability

In a directional viscous fingering experiment, a phase diffusion behavior of the regular array of cells is demonstrated. At constant wave number, the evolution of the phase diffusion coefficient D with the parameter of the instability ε is reported. This coefficient D is found to decrease at low ε values in agreement with the presence of an Eckhaus instability, but to increase strongly at large ε values. This unusual increase of D is also present in the analytical and numerical study of two coupled amplitude equations for the modes k and 2k. The phase diffusion coefficient is found to diverge at the threshold of the parity-breaking bifurcation.