J. Phys. II France
Volume 6, Numéro 6, June 1996
Page(s) 945 - 951
DOI: 10.1051/jp2:1996213
J. Phys. II France 6 (1996) 945-951

Critical Self-Tuning: the Example of Zero Prandtl Number Convection

K. Kumar1, S. Fauve1 and O. Thual2

1  Laboratoire de Physique CNRS-GDR 1024, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon, France
2  INPT/ENSEEIHT/IMFT CNRS-GDR 1024, avenue du Pr. C. Soula, 31400 Toulouse, France

(Received 2 September 1994, revised 6 June 1995, accepted 20 February 1996)

We present a new type of bifurcation scenario where nonlinear saturation of a stationary instability takes place only because of the competition with an oscillatory one. This is shown on the example of convection at zero Prandtl number between stress-free boundaries. We show with direct numerical simulations that time-dependent wavy rolls are generated at the onset of convection. Using a Galerkin model, we analyze the nonlinear interactions between rolls and waves and find that they maintain the system in the vicinity of the oscillatory instability onset, thus preventing the blow-up of the growing nonlinear roll solution. An interesting feature of this type of dynamics is that the system is self-tuned in the vicinity of a transition point.

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