Eur. Phys. J. B 35, 525-530 (2003)
https://doi.org/10.1140/epjb/e2003-00306-1

Elastic properties of a cellular dissipative structure

Drift and oscillations in a 1-D pattern

Laboratoire PMMH-ESPCI, 10 rue Vauquelin, 75005 Paris, France

Corresponding author: ^a brunet@pmmh.espci.fr

Received: 13 June 2002
Revised: 10 June 2003
Published online: 24 October 2003

Abstract

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 V_g of a constant width domain is linked to the angular frequency ω of oscillations and to the spacing between columns by the relationship . We show by a simple geometrical argument that α should be close to instead of the initial value deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate.