Pattern selection and transition to turbulence in propagating waves

Victor Steinberg*, Jay Fineberg, Elisha Moses, Ingo Rehberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


We present a study of oscillatory convection in two experimental systems: ethanol-water mixtures in a rectangular container heated from below and a thin layer of nematic liquid crystals under low frequency ac voltage. In both systems the first bifurcation is the transition to travelling waves (TW) with finite wave vector and frequency. We report experimental observations of a sequence of spatial structures and dynamical behaviour of nonlinear TW in a regime of a weak nonlinearity. Most of the rich variety of spatial and dynamical behaviour which we observe in one-dimensional finite geometries has been reproduced by numerical simulations based on a simple model of coupled Ginzburg-Landau equations which considers only the combination of translation and finite geometry. More complicated spatio-temporal behaviour of TW in cells with two-dimensional geometry which initiated by defect nucleation is attributed to the mechanism of modulational instability of TW.

Original languageAmerican English
Pages (from-to)359-383
Number of pages25
JournalPhysica D: Nonlinear Phenomena
Issue number1-3
StatePublished - Jul 1989
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported in part by the US-Israel Binational Science Foundation and the Minerva Foundation.


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