Onset of thermal convection in a rotating porous sphere

This study offers the first comprehensive analysis of convective onset in a uniformly internally heated, rotating porous sphere. By incorporating the Coriolis force into Darcy’s law, we formulate the linear stability problem using a vector potential expansion combined with spherical harmonic decomposition. The resulting equations are solved numerically via a spectral method based on Worland polynomials. In the absence of rotation, the most unstable mode corresponds to a spherical harmonic degree $l = 2$ , with a critical Rayleigh number of 91.95. When rotation is introduced, the Coriolis force further stabilises the flow, causing the critical Rayleigh number to increase monotonically with the Taylor number. Notably, the system consistently favours an azimuthal wavenumber $m = 2$ across nearly the entire parameter range. This behaviour contrasts sharply with rotating fluid convection, where the preferred wavenumber increases indefinitely with the rotation rate. This fundamental difference arises from the disruption of the quasi-geostrophic balance by the strong Darcy resistance, leading to the failure of the Proudman–Taylor theorem. Under strong rotation, the system exhibits power-law scaling and develops an Ekman-like boundary layer localised near the polar axis, which channels global heat and mass transport. These findings provide novel theoretical insights into the thermal structure and evolution of early evolutionary bodies, such as rapidly rotating planetesimals or undifferentiated asteroids with high permeability, and lay the groundwork for future nonlinear studies of rotating porous convection.