Fluctuations of the tip of an interface curved by an instabilityP. Pelce
IRPHE - 49 rue Joliot-Curie, BP 146, 13384 Marseille Cedex 13, France
received 22 September 2005; accepted in final form 26 May 2006
published online 16 June 2006
We determine the amplitude of fluctuations in the tip region of a moving interface of large tip radius curved by an instability. The interface dynamics is derived for viscous fingering, solidification, and flame propagation. It is implemented, as for the Langevin equation, by a stochastic source, of zero mean and infinitely short-distance correlation. A selection diagram for dendrites can be deduced by limiting a large domain of experimental relevance where fluctuations exceed exponentially small terms which, in a purely deterministic theory, are cancelled by the anisotropy of surface tension.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
81.10.-h - Methods of crystal growth; physics of crystal growth.
47.20.-k - Flow instabilities.
© EDP Sciences 2006