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
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 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.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 47.20.Lz – Secondary instability / 47.20.Ma – Interfacial instability
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003