Quasi-steady transitions in confined convection

We study the effect of geometrical confinement on thermal convection by laboratory experiments and direct numerical simulations using Hele-Shaw geometries (typically the gap-to-height aspect ratio $0.12$ ) for the Prandtl number $Pr \geq 40$ and the Rayleigh number $Ra \leq 6 \times 10^7$ . Under such strong unidirectional confinement, the convective flows are forced to squeeze within the narrow gap and exhibit unique spatiotemporal signatures, which contrast those in unconfined systems. With the increase of $Ra$ , we identify that the system experiences five convective regimes that can be classified from two aspects, time dependency and flow dimensionality: (I) quasi-two-dimensional (quasi-2-D) steady flow; (II) quasi-2-D flow with oscillatory corner rolls; (III) three-dimensional (3-D) flow with oscillatory corner rolls; (IV) 3-D steady flow; and (V) 3-D time-dependent motion of plumes around sidewalls. Notably, unsteadiness does not emerge globally, but is localised near the sidewalls as oscillatory corner rolls, resulting in the regime transitions happening in a quasi-steady manner. We confirm that these regime transitions show less dependence on both $Pr$ and the other (wider) horizontal scale of the geometry. Moreover, we find that a recently proposed criterion ‘degree of confinement’ (Noto et al. , Proc. Natl Acad. Sci. USA , vol. 121, issue 28, 2024, e2403699121) successfully explains the emergence of 3-D structures, expanding its applicable range to smaller $Ra$ . This study deepens the comprehension of the thermal convection emerging in tight geometries, impacting across disciplines, such as Earth and planetary science, and thermal engineering.