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 \(\omega\) of oscillations and to the spacing between columns \(\lambda_0\) by the relationship \(V_g = \alpha \lambda_0 \omega\). We show by a simple geometrical argument that \(\alpha\) should be close to \(1/ \pi\) instead of the initial value \(\alpha = 1/2\) deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate.
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Received: 10 June 2003, Published online: 24 October 2003
PACS:
05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 47.20.Lz Secondary instability - 47.20.Ma Interfacial instability
J.-M. Flesselles: Present Address: Saint-Gobain Recherche, 39 quai Lucien Lefranc, 93303 Aubervilliers Cedex, France
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Brunet, P., Flesselles, JM. & Limat, L. Elastic properties of a cellular dissipative structure. Eur. Phys. J. B 35, 525–530 (2003). https://doi.org/10.1140/epjb/e2003-00306-1
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DOI: https://doi.org/10.1140/epjb/e2003-00306-1