Fixed-flux Rayleigh-Benard convection in doubly periodic domains

This work studies two-dimensional fixed-flux Rayleigh-Benard convection with periodic boundary conditions in both horizontal and vertical directions and analyzes its dynamics using numerical continuation, secondary instability analysis and direct numerical simulation. The fixed-flux constraint leads to time-independent elevator modes with a well-defined amplitude. Secondary instability of these modes leads to tilted elevator modes accompanied by horizontal shear flow. For Pr=1, where Pr is the Prandtl number, a subsequent subcritical Hopf bifurcation leads to hysteresis behavior between this state and a time-dependent direction-reversing state, followed by a global bifurcation leading to modulated traveling waves without flow reversal. At high Rayleigh numbers, chaotic behavior dominated by modulated traveling waves appears. In the low Pr regime, relaxation oscillations between the conduction state and the elevator mode appear, followed by quasiperiodic and chaotic behavior as the Rayleigh number increases. At high Pr, the large-scale shear weakens, and the flow shows bursting behavior that can lead to significantly increased heat transport or even intermittent stable stratification.