WAVE-NUMBER SELECTION AND PARITY-BREAKING BIFURCATION IN DIRECTIONAL VISCOUS FINGERING

We present a mechanism of limitation for the possible wave numbers abo ve an instability threshold. This mechanism is experimentally investig ated in the interfacial instability of directional viscous fingering i n a finite system. It is shown experimentally to be controlled by the divergence of a phase-diffusion constant. Theoretically, this limitati on 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 theoreticall y the existence of a divergence of a phase-diffusion constant when app roaching the threshold of a parity-breaking instability.