L. Bellon, L. Fourtune, V. Ter Minassian and M. Rabaud, Physical Review E 58 565-574 (1998)
We present a mechanism of limitation for the possible wave numbers above an instability threshold. This mechanism is experimentally investigated in the interfacial instability of directional viscous fingering in a finite system. It is shown experimentally to be controlled by the divergence of a phase-diffusion constant. Theoretically, this limitation on the low value of the accessible wave numbers is a consequence of the interaction between the fundamental and the first harmonic modes. The analysis of coupled amplitude equations demonstrates theoretically the existence of a divergence of a phase-diffusion constant when approaching the threshold of a parity-breaking instability.