Transition to fully developed turbulence in liquid-metal convection facilitated by spatial confinement

Abstract

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$ , implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ( $Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$ . Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma <1$ , the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.