Céline Guervilly

Accurate measurement of fluid velocity remains a significant challenge in experimental fluid dynamics, as it requires capturing detailed spatial and temporal information within flows that are frequently turbulent. Obtaining velocity fields requires tracking identifiable features within the flow, such as particles, tracer elements, or coherent flow structures, over time. This typically requires accurate optical visualization of the flow. The most prevalent and effective method for measuring fluid velocity in the laboratory is particle image velocimetry (PIV), which uses the tracking of suspended reflective or fluorescent particles to determine the fluid's velocity. The mathematical method commonly used to track particles is the cross-correlation between two images. PIV relies on a laser sheet to illuminate the particles in a plane and requires the fluid to be transparent to visible light. To overcome these optical constraints, we propose to use the surface temperature field, which is accurately measurable in the context of thermal convection experiments. This provides structures that can be tracked if the temperature field is mainly advected by the flow. We employ the Farneback dense optical flow algorithm [Farnebäck, Two-frame motion estimation based on polynomial expansion, in , edited by J. Bigun and T. Gustavsson (Springer, Berlin, 2003), pp. 363–370] to track the features of the temperature field. Similar methods have proven effective in tracking planetary flows, as demonstrated by measuring Jupiter's surface or Earth's ocean currents. We present here a benchmark study using a simple, synthetic two-dimensional advection-diffusion simulation, as well as a rapidly rotating quasigeostrophic simulation based on the “Coreaboloid” experimental setup [Lonner, Aggarwal, and Aurnou, Planetary core-style rotating convective flows in paraboloidal laboratory experiments, ]. We investigate the applicability of thermal image velocimetry to measuring the velocity field in rotating convection experiments. The reconstructed velocity field allows for a quantitative physical analysis of the flow dynamics.

Convection is the main heat transport mechanism in the Earth's liquid core and is thought to power the dynamo that generates the geomagnetic field. Core convection is strongly constrained by rotation while being turbulent. Given the difficulty in modeling these conditions, some key properties of core convection are still debated, including the dominant energy‐carrying lengthscale. Different regimes of rapidly rotating, unmagnetized, turbulent convection exist depending on the importance of viscous and inertial forces in the dynamics, and hence different theoretical predictions for the dominant flow lengthscale have been proposed. Here we study the transition from viscously dominated to inertia‐dominated regimes using numerical simulations in spherical and planar geometries. We find that the cross‐over occurs when the inertial lengthscale approximately equals the viscous lengthscale. This suggests that core convection in the absence of magnetic fields is dominated by the inertial scale, which is hundred times larger than the viscous scale.

Convection is the main heat transport mechanism in the Earth's liquid core and is thought to power the dynamo that generates the geomagnetic field. Core convection is strongly constrained by rotation while being turbulent. Given the difficulty in modelling these conditions, some key properties of core convection are still debated, including the dominant energy-carrying lengthscale. Different regimes of rapidly-rotating, unmagnetised, turbulent convection exist depending on the importance of viscous and inertial forces in the dynamics, and hence different theoretical predictions for the dominant flow lengthscale have been proposed. Here we study the transition from viscously-dominated to inertia-dominated regimes using numerical simulations in spherical and planar geometries. We find that the cross-over occurs when the inertial lengthscale approximately equals the viscous lengthscale. This suggests that core convection in the absence of magnetic fields is dominated by the inertial scale, which is hundred times larger than the viscous scale.

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.

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 800km-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 length decreases when the thermal stratification increases, following closely the scaling law expected from the linear non-rotating planar theory (Stern, 1960). 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 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.

The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection, opens up new avenues for studying energy transfer in strongly anisotropic three-dimensional flows such as atmospheric or oceanic circulations.

Convection is a fundamental physical process in the fluid cores of planets because 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 lengthscale, are poorly quantified in planetary cores due to their strong dependence on planetary rotation, buoyancy driving and magnetic fields, which are all difficult to model under realistic conditions. In the absence of strong magnetic fields, the core convective flows are expected to be in a regime of rapidly-rotating turbulence, which remains largely unexplored to date. Here we use a combination of numerical models designed to explore this low-viscosity regime to show that the convective lengthscale becomes independent of the viscosity and is entirely determined by the flow velocity and planetary rotation. For the Earth's core, we find that the characteristic con-vective lengthscale is approximately 30km and below this scale, motions are very weak. The 30-km cutoff scale rules out small-scale dynamo action and supports large-eddy simulations of core dynamics. Furthermore, it implies that our understanding of magnetic reversals from numerical geodynamo models does not relate to the Earth, because they require too intense flows. Our results also indicate that the liquid core of the Moon might still be in an active convective state despite the absence of a present-day dynamo.