Elastic properties of cellular dissipative structure

Transition towards spatio-temporal chaos in one-dimensional interfacial patterns often involves two degrees of freedom: drift and out-of-phase oscillations of cells, respectively associated to parity breaking and vacillating-breathing secondary bifurcations. In this paper, the interaction between these two modes is investigated in the case of a single domain propagating along a circular array of liquid jets. As observed by Michalland and Rabaud for the printer’s instability [1], the velocity Vg of a constant width domain is linked to the angular frequency ω of oscillations and to the spacing between columns λ0 by the relationship Vg = αλ0ω. We show by a simple geometrical argument that α should be close to 1/π instead of the initial value α = 1/2 deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate. PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 47.20.Lz Secondary instability – 47.20.Ma Interfacial instability