We present investigations of rapidly rotating convection in a thick spherical shell geometry relevant to planetary cores, comparing results from quasigeostrophic (QG), 3D and hybrid QG3D models. The 170 reported calculations span Ekman numbers, Ek, between 10−4 and 10−10, Rayleigh numbers, Ra, between 2 and 150 times supercritical and Prandtl numbers, Pr, between 10 and 10−2. The default boundary conditions are noslip at both the ICB and the CMB for the velocity field, with fixed temperatures at the ICB and the CMB. Cases driven by both homogeneous and inhomogeneous CMB heat flux patterns are also explored, the latter including lateral variations, as measured by Q*, the peaktopeak amplitude of the pattern divided by its mean, taking values up to 5. The QG model is based on the opensource pizza code. We extend this in a hybrid approach to include the temperature field on a 3D grid. In general, we find convection is dominated by zonal jets at middepths in the shell, with thermal Rossby waves prominent close to the outer boundary when the driving is weaker. For the thick spherical shell geometry studied here the hybrid method is best suited for studying convection at modest forcing, $Ra \le 10 \, Ra_c$ when Pr = 1, and departs from the 3D model results at higher Ra, displaying systematically lower heat transport characterized by lower Nusselt and Reynolds numbers. We find that the lack of equatoriallyantisymmetric motions and zcorrelations between temperature and velocity in the buoyancy force contributes to the weaker flows in the hybrid formulation. On the other hand, the QG models yield broadly similar results to the 3D models, for the specific aspect ratio and range of Rayleigh numbers explored here. We cannot point to major disagreements between these two data sets at Pr ≥ 0.1, with the QG model effectively more strongly driven than the hybrid case due to its cylindrically averaged thermal boundary conditions. When Pr is decreased, the range of agreement between the hybrid and 3D models expands, for example up to $Ra \le 15 \, Ra_c$ at Pr = 0.1, indicating the hybrid method may be better suited to study convection in the low Pr regime. We thus observe a transition between two regimes: (i) at Pr ≥ 0.1 the QG and 3D models agree in the studied range of Ra/Rac while the hybrid model fails when $Ra\gt 15\, Ra_c$ and (ii) at Pr = 0.01 the QG and 3D models disagree for $Ra\gt 10\, Ra_c$ while the hybrid and 3D models agree fairly well up to $Ra \sim 20\, Ra_c$. Models that include laterally varying heat flux at the outer boundary reproduce regional convection patterns that compare well with those found in similarly forced 3D models. Previously proposed scaling laws for rapidly rotating convection are tested; our simulations are overall well described by a triple balance between Coriolis, inertia and Archimedean forces with the lengthscale of the convection following the diffusionfree Rhinesscaling. The magnitude of Pr affects the number and the size of the jets with larger structures obtained at lower Pr. Higher velocities and lower heat transport are seen on decreasing Pr with the scaling behaviour of the convective velocity displaying a strong dependence on Pr. This study is an intermediate step towards a hybrid model of core convection also including 3D magnetic effects.
Single sidewall cooling modulation on Rayleigh–Bénard convection
We experimentally explored the effect of singlesidewall cooling on Rayleigh–Bénard (RB) convection. Canonical RB was also studied to aid insight. The scenarios shared tank dimensions and bottom and top wall temperatures; the single sidewall cooling had the top wall temperature. Turbulence was explored at two canonical Rayleigh numbers, $Ra=1.6\times 10^{10}$ and $Ra=2\times 10^9$ under Prandtl number $Pr=5.4$ . Particle image velocimetry described vertical planes parallel and perpendicular to the sidewall cooling. The two $Ra$ scenarios reveal pronounced changes in the flow structure and largescale circulation (LSC) due to the sidewall cooling. The density gradient induced by the sidewall cooling led to asymmetric descending and ascending flows and irregular LSC. Flow statistics departed from the canonical case, exhibiting lower buoyancy effects, represented by an effective Rayleigh number with effective height dependent on the distance from the lateral cooling. Velocity spectra show two scalings, $\varPhi \propto f^{5/3}$ Kolmogorov (KO41) and $\varPhi \propto f^{11/5}$ Bolgiano (BO59) in the larger $Ra$ ; the latter was not present in the smaller setup. The BO59 scaling with sidewall cooling appears at higher frequencies than its canonical counterpart, suggesting weaker buoyancy effects. The LSC core motions allowed us to identify a characteristic time scale of the order of vortex turnover time associated with distinct vortex modes. The velocity spectra of the vortex core oscillation along its principal axis showed a scaling of $\varPhi _c \propto f^{5/3}$ for the single sidewall cooling, which was dominant closer there. It did not occur in the canonical case, evidencing the modulation of LSC oscillation on the flow.
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 Award ID(s):
 1912824
 NSFPAR ID:
 10421242
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 957
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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SUMMARY 
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