Subcritical instabilities in a convective fluid layer under a quasi-1D heating

Abstract

The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of wave number $k_s$ which undergoes a globally subcritical transition to traveling waves by parity-breaking symmetry. The experimental results show how the emerging traveling mode ($2/3k_{s}$) switches on a resonant triad ($k_s$, $k_s/2$, $2k_{s}/3$) within the cellular pattern yielding a ``mixed'' pattern. The nature of this transition is described quantitatively in terms of the evolution of the fundamental modes by complex demodulation techniques. The B\' enard-Marangoni convection accounts for the different dynamics depending on the depth of the fluid layer and on the vertical temperature difference. The existence of a hysteresis cycle has been evaluated quantitatively. When the bifurcation to traveling waves is measured in the vicinity of the codimension-2 bifurcation point, we measure a decrease of the subcritical interval in which the traveling mode becomes unstable. From the traveling wave state the system under goes a {\it new} global secondary bifurcation to an alternating pattern which doubles the wavelength ($k_{s}/2$) of the primary cellular pattern, this result compares well with theoretical predictions [P. Coullet and G. Ioss, {\em Phys. Rev. Lett.} {\bf 64}, 8 66 (1990)]. In this cascade of bifurcations towards a defect dynamics, bistability due to the subcritical behavior of our system is the reason for the coexistence of two different modulated patterns connected by a front. These fronts are stationary for a finite interval of the control parameters.