Scale-dependent force balance governs transition to the geostrophic regime in liquid metal rotating convection

Abstract

Rotating convection in low-Prandtl-number liquid metal drives dynamo action in the Earth's outer core and is central to planetary interior dynamics. It has been proposed that flow regime transitions in rotating convection are controlled by competition between the thermal and Ekman boundary layers. However, through laboratory experiments and direct numerical simulations of rotating liquid-metal convection, we find that this mechanism breaks down in the low-Prandtl-number regime. Here we show that increasing rotation reorganises the bulk flow: the large-scale circulation is suppressed and replaced by smaller-scale structures, producing a characteristic horizontal length scale $\ell$. Transitions to the geostrophic regime are then governed by a buoyancy--Coriolis balance defined on $\ell$ rather than by the boundary-layer crossing. This scale-dependent mechanism also yields heat-transport scalings that depart from boundary-layer-based predictions in the geostrophic regime. Our results reveal a distinct route to the geostrophic regime in low-Prandtl-number rotating convection with implications for rotating liquid metal flows in planetary interiors.