2025/04/29 by Stofanak, Patrick J., Xiao, Cheng-Nian, Senocak, Inanc
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2504.21173
We investigate the three-dimensional stability of a stably stratified fluid in a valley-shaped cavity heated from below using linear stability analysis and direct numerical simulations. We first describe the pure-conduction flow state and derive a dimensionless criterion that provides a lower bound for the onset of instability, valid for any slope angle. We then examine the sequence of flow regimes for a slope angle of α= 30∘ and Prandtl number Pr = 7, including two-dimensional steady states, the emergence of a Hopf bifurcation, and the formation of steady and oscillatory three-dimensional structures preceding the transition to fully unsteady, chaotic flow. Although the nonlinear governing equations depend on two dimensionless parameters, we find that the flow dynamics across a wide parameter range collapse to depend on a single parameter--the composite stratification parameter Πc. However, as the system becomes more unstable, sensitivity to the second parameter, Πh, increases. We construct a regime map of all observed flow states as a function of Πc and Πh, and confirm the onset of chaos using Lyapunov exponents. Across all regimes, asymmetric circulation remains the dominant flow structure, persisting even in time-averaged fields of chaotic states. Finally, we characterize heat transfer in the cavity using the Nusselt number, which scales as Nu ∼ Πc0.43 or equivalently Nu ∼ Ra0.275. This result further establishes Πc as a key dimensionless parameter governing the flow dynamics preceding the chaotic regime.