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Convection is a fundamental physical process in the fluid cores of planets. It is the primary transport mechanism for heat and chemical species and the primary energy source for planetary magnetic fields. Key properties of convection—such as the characteristic flow velocity and length scale—are poorly quantified in planetary cores owing to the strong dependence of these properties on planetary rotation, buoyancy driving and magnetic fields, all of which are difficult to model using realistic conditions. In the absence of strong magnetic fields, the convective flows of the core are expected to be in a regime of rapidly rotating turbulence1, which remains largely unexplored. Here we use a combination of non-magnetic numerical models designed to explore this regime to show that the convective length scale becomes independent of the viscosity when realistic parameter values are approached and is entirely determined by the flow velocity and the planetary rotation. The velocity decreases very rapidly at smaller scales, so this turbulent convective length scale is a lower limit for the energy-carrying length scales in the flow. Using this approach, we can model realistically the dynamics of small non-magnetic cores such as the Moon. Although modelling the conditions of larger planetary cores remains out of reach, the fact that the turbulent convective length scale is independent of the viscosity allows a reliable extrapolation to these objects. For the Earth’s core conditions, we find that the turbulent convective length scale in the absence of magnetic fields would be about 30 kilometres, which is orders of magnitude larger than the ten-metre viscous length scale. The need to resolve the numerically inaccessible viscous scale could therefore be relaxed in future more realistic geodynamo simulations, at least in weakly magnetized regions. Numerical modelling of rotating turbulent convective flows shows that the length scale of convection in planetary cores is set by the flow speed and not by the fluid viscosity.

Stably stratified layers may be present at the top of the electrically conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the segregation of chemical elements. Here we study the double‐diffusive processes taking place in such a stable layer, considering the case of Mercury's core where the temperature gradient is stable but the composition gradient is unstable over a 800 km‐thick layer. The large difference in the molecular diffusivities leads to the development of buoyancy‐driven instabilities that drive radial flows known as fingering convection. We model fingering convection using hydrodynamical simulations in a rotating spherical shell and varying the rotation rate and the stratification strength. For small Rayleigh numbers (i.e., weak background temperature and composition gradients), fingering convection takes the form of columnar flows aligned with the rotation axis and with an azimuthal size comparable with the layer thickness. For larger Rayleigh numbers, the flows retain a columnar structure but the azimuthal size is drastically reduced leading to thin sheet‐like structures that are elongated in the meridional direction. The azimuthal size decreases when the thermal stratification increases, following closely the scaling law expected from the linear planar theory (Stern, 1960, https://doi.org/10.1111/j.2153-3490.1960.tb01295.x). We find that the radial flows always remain laminar with local Reynolds number of order 1–10. Equatorially symmetric zonal flows form due to latitudinal variations of the axisymmetric composition. The zonal velocity exceeds the non‐axisymmetric velocities at the largest Rayleigh numbers. We discuss plausible implications for planetary magnetic fields. Convection occurs in planetary interiors due to local changes of density, which can be produced by changes of temperature or chemical composition. In particular, convection occurs in the electrically conducting fluid layers located deep inside planets and is at the origin of the generation of planetary magnetic fields. However, for many planets, the upper part of this electrically conducting region might not be subject to standard convection because the gradients of either temperature or chemical composition produce a further increase of the density with depth, leading to the formation of a stable layer. In some cases, the gradients of these two components act in opposition. Such might be the case of the upper part of Mercury's core, where the stable layer is maintained by the thermal gradient, but the compositional gradient is unstable. This situation is prone to fingering convection, where fluid instabilities release the potential energy associated with the compositional gradient. Here we show that fingering convection consists of sheet‐like flows with a narrow longitudinal size of approximately 1 m in Mercury‐like conditions. Strong zonal (i.e., east/westward) flows also form. The presence of fingering convection in stable layers might have important consequences for the magnetic fields observed at the planet's surface. Fingering convection in a Mercury‐like stable layer produces thin sheet‐like radial flows that are elongated in the meridional directionThe radial flows are always laminar and their azimuthal length is expected to be about 1 m in planetary coresStrong zonal flows form as a by‐product of the latitudinal variations of the composition transport Fingering convection in a Mercury‐like stable layer produces thin sheet‐like radial flows that are elongated in the meridional direction The radial flows are always laminar and their azimuthal length is expected to be about 1 m in planetary cores Strong zonal flows form as a by‐product of the latitudinal variations of the composition transport