Numerical analysis of the Eckhaus instability in travelling-wave convection in binary mixtures
Departament de Fısica Aplicada, Universitat Politècnica de Catalunya, Campus Nord, Mòdul B4, 08034, Barcelona, Spain
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Accepted: 21 October 2004
Published online: 22 November 2004
The Eckhaus stability boundaries of travelling periodic roll patterns arising in binary fluid convection is analysed using high-resolution numerical methods. We present results corresponding to three different values of the separation ratio used in experiments. Our results show that the subcritical branches of travelling waves bifurcating at the onset of convection suffer sideband instabilities that are restabilised further away in the branch. If this restabilisation is produced after the turning point of the travelling-wave branch, these waves do not become stable in a saddle node bifurcation as would have been the case in a smaller domain. In the regions of instability of the uniform travelling waves we expect to find either transitions between states of different wave number or modulated travelling waves arising in these bifurcations.
PACS: 47.20.Ky Nonlinearity (including bifurcation theory) – / 47.20.Bp Buoyancy-driven instability – / 47.27.Te Convection and heat transfer – / 47.54.+r Pattern selection; pattern formation –
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2004