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In magnetostrophic rotating magnetoconvection, a fluid layer heated from below and cooled from above is equidominantly influenced by the Lorentz and the Coriolis forces. Strong rotation and magnetism each act separately to suppress thermal convective instability. However, when they act in concert and are near in strength, convective onset occurs at less extreme Rayleigh numbers ( R a , thermal forcing) in the form of a stationary, large-scale, inertia-less, inviscid magnetostrophic mode. Estimates suggest that planetary interiors are in magnetostrophic balance, fostering the idea that magnetostrophic flow optimizes dynamo generation. However, it is unclear if such a mono-modal theory is realistic in turbulent geophysical settings. Donna Elbert first discovered that there is a range of Ekman ( E k , rotation) and Chandrasekhar ( C h , magnetism) numbers, in which stationary large-scale magnetostrophic and small-scale geostrophic modes coexist. We extend her work by differentiating five regimes of linear stationary rotating magnetoconvection and by deriving asymptotic solutions for the critical wavenumbers and Rayleigh numbers. Coexistence is permitted if E k < 16 / ( 27 π ) 2 and C h ≥ 27 π 2 . The most geophysically relevant regime, the Elbert range , is bounded by the Elsasser numbers 4 3 ( 4 4 π 2   E k ) 1 / 3 ≤ Λ ≤ 1 2 ( 3 4 π 2 E k ) − 1 / 3 . Laboratory and Earth’s core predictions both exhibit stationary, oscillatory, and wall-attached multi-modality within the Elbert range. 

We present laboratory measurements of the interaction between thermoelectric currents and turbulent magnetoconvection. In a cylindrical volume of liquid gallium heated from below and cooled from above and subject to a vertical magnetic field, it is found that the large-scale circulation (LSC) can undergo a slow axial precession. Our experiments demonstrate that this LSC precession occurs only when electrically conducting boundary conditions are employed, and that the precession direction reverses when the axial magnetic field direction is flipped. A thermoelectric magnetoconvection (TEMC) model is developed that successfully predicts the zeroth-order magnetoprecession dynamics. Our TEMC magnetoprecession model hinges on thermoelectric current loops at the top and bottom boundaries, which create Lorentz forces that generate horizontal torques on the overturning large-scale circulatory flow. The thermoelectric torques in our model act to drive a precessional motion of the LSC. This model yields precession frequency predictions that are in good agreement with the experimental observations. We postulate that thermoelectric effects in convective flows, long argued to be relevant in liquid metal heat transfer and mixing processes, may also have applications in planetary interior magnetohydrodynamics. 

The interplay between convective, rotational and magnetic forces defines the dynamics within the electrically conducting regions of planets and stars. Yet their triadic effects are separated from one another in most studies, arguably due to the richness of each subset. In a single laboratory experiment, we apply a fixed heat flux, two different magnetic field strengths and one rotation rate, allowing us to chart a continuous path through Rayleigh–Bénard convection (RBC), two regimes of magnetoconvection, rotating convection and two regimes of rotating magnetoconvection, before finishing back at RBC. Dynamically rapid transitions are determined to exist between jump rope vortex states, thermoelectrically driven magnetoprecessional modes, mixed wall- and oscillatory-mode rotating convection and a novel magnetostrophic wall mode. Thus, our laboratory ‘pub crawl’ provides a coherent intercomparison of the broadly varying responses arising as a function of the magnetorotational forces imposed on a liquid-metal convection system. 

Abstract The large-scale circulation (LSC) is the most fundamental turbulent coherent flow structure in Rayleigh-Bénard convection. Further, LSCs provide the foundation upon which superstructures, the largest observable features in convective systems, are formed. In confined cylindrical geometries with diameter-to-height aspect ratios of , LSC dynamics are known to be governed by a quasi-two-dimensional, coupled horizontal sloshing and torsional (ST) oscillatory mode. In contrast, in cylinders, a three-dimensional jump rope vortex (JRV) motion dominates the LSC dynamics. Here, we use dynamic mode decomposition (DMD) on direct numerical simulation data of liquid metal to show that both types of modes co-exist in and cylinders but with opposite dynamical importance. Furthermore, with this analysis, we demonstrate that ST oscillations originate from a tilted elliptical mean flow superposed with a symmetric higher-order mode, which is connected to the four rolls in the plane perpendicular to the LSC in tanks.