Subcritical instabilities in a convective fluid layer under a quasi-one-dimensional 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 ks which undergoes a globally subcritical transition to traveling waves by paritybreaking symmetry. The experimental results show how the emerging traveling mode 2ks /3 switches on a resonant triad ks ,ks /2,2ks /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 Bénard-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 undergoes a global secondary bifurcation to an alternating pattern which doubles the wavelength ks /2 of the primary cellular pattern; this result compares well with theoretical predictions P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 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.