Spontaneous onset of three-dimensional motion with subsequent spatial and temporal reduction in convective flow systems

We numerically observe the spontaneous emergence of three-dimensional motion from a quiescent, purely conductive state in convective flows, which ultimately self-organizes into a two-dimensional steady state. Our study examines a stably-stratified fluid in a V-shaped valley heated from below. A dominant three-dimensional instability is identified through modal stability analysis. Direct numerical simulations show that after an initial period of spontaneous growth of three-dimensional motion, the flow self-organizes into a two-dimensional steady state over time on its own. This self-organization manifests consistently for any arbitrary infinitesimal three-dimensional disturbance. We demonstrate that the mechanism driving this self-organization is the increasing dominance of viscous dissipation over buoyant production of disturbance kinetic energy at later stages of flow evolution from the initial quiescent state. Our discovery reveals that the disturbance pathway to the final state can be more complex than the state itself, suggesting that the "fastest" route to the final state may involve transitioning through a higher-dimensional intermediate state.