Elastic properties of cellular dissipative structure
Résumé
Transition towards spatio-temporal chaos in one-dimensionalinterfacial patterns often involves two degrees of freedom:drift and out-of-phase oscillations of cells, respectively associatedto parity breaking and vacillating-breathing secondary bifurcations. In this paper, the interaction between these two modes is investigatedin the case of a single domain propagating along a circular array ofliquid jets. As observed by Michalland and Rabaud for the printer'sinstability \cite{Rabaud92}, the velocity $V_g$ of a constant widthdomain is linked to the angular frequency $\omega$ of oscillations andto the spacing between columns $\lambda_0$ by the relationship $ V_g =\alpha \lambda_0 \omega$. We show by a simple geometrical argumentthat $\alpha$ should be close to $1/ \pi$ instead of the initial value$\alpha = 1/2$ deduced from their analogy with phonons. This fact isin quantitative agreement with our data, with a slight deviationincreasing with flow rate.