Dynamic confinement controls the porous-to-free convection transition.

Abstract

Convection in porous materials governs heat transport across scales ranging from planetary subsurface systems to engineered cooling devices. While the onset of buoyancy-driven flow is well described by linear stability theory within a porous-continuum representation, the subsequent transition from viscous, matrix-dominated convection toward inertia-influenced and ultimately bulk fluid-like plume convection has lacked a unified description. Here we develop a confinement-based scaling framework that connects these flow states through a common scale-ratio perspective and quantitatively bridges classical porous convection with laterally confined Rayleigh-Bénard systems. Because random porous and fractured media do not admit an obvious static scale-ratio, we recover an effective confinement measure from the onset condition. This links permeability-based systems to the classical confinement framework and defines a characteristic pore length for natural convection. Comparing this pore length with the thermal boundary-layer thickness yields a dynamic criterion for the emergence of unconfined behavior. Embedding experimental and numerical porous-convection datasets into a unified phase diagram of buoyant forcing and static confinement reveals a systematic progression from viscous, drag-dominated heat transport to inertia-corrected flow and ultimately to plume-driven convection whose statistics approach those of unconfined fluids. The resulting framework delineates the limits of porous-continuum validity, clarifies when inertial corrections become relevant, and highlights the dynamical analogy between strongly confined porous flows and thin-gap Hele-Shaw configurations. By linking heat-transport scaling to static and dynamic length scales, the phase diagram provides a practical diagnostic for selecting appropriate governing equations across geophysical and engineered porous systems.