Souvik Naskar

We use direct numerical simulations to investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh–Bénard convection. The kinetic and magnetic energies are divided into mean and turbulent components to study the production, transport and dissipation in large- and small-scale dynamos. This energy balance-based characterisation reveals distinct mechanisms for large- and small-scale magnetic field generation in dynamos, depending on the nature of the velocity field and the conditions imposed at the boundaries. The efficiency of a dynamo in converting the kinetic energy to magnetic energy, apart from the energy redistribution inside the domain, is found to depend on the kinematic and magnetic boundary conditions. In a small-scale dynamo with a turbulent velocity field, the turbulent kinetic energy converts to turbulent magnetic energy via small-scale magnetic field stretching. This term also represents the amplification of the turbulent magnetic energy due to work done by stretching the small-scale magnetic field lines owing to fluctuating velocity gradients. The stretching of the large-scale magnetic field plays a significant role in this energy conversion in a large-scale turbulent dynamo, leading to a broad range of energetic scales in the magnetic field compared with a small-scale dynamo. This large-scale magnetic field stretching becomes the dominant mechanism of magnetic energy generation in a weakly nonlinear dynamo. We also find that, in the weakly nonlinear dynamo, an upscale energy transfer from the small-scale magnetic field to the large-scale magnetic field occurs owing to the presence of a gradient of the mean magnetic field.

The geomagnetic field is sustained by thermochemical convection in Earth’s outer core. Crystallization of the solid inner core releases latent heat and light elements, providing both thermal and chemical buoyancy sources. Most geodynamo simulations use the codensity approach, ignoring the vastly different diffusivities and different boundary conditions for the thermal and chemical fields and thus cannot capture double-diffusive effects. In this study, we consider a numerical convection model of a Boussinesq mixture of light elements in a heavy fluid confined within a rotating spherical shell. The governing parameters are the Ekman number (𝐸 = 2 × 10−5), a non-dimensional measure of the rotation rate, the thermal and chemical flux Rayleigh numbers (𝑅𝑎𝑇 = 9 × 106 − 1.2 × 108 and 𝑅𝑎𝜉 = 3 × 106 − 5 × 1010), representing the non-dimensional thermal and chemical forcing, and the thermal and chemical Prandtl numbers (𝑃𝑟𝑇 = 1 and 𝑃𝑟𝜉 = 10), that are fluid properties. We have performed a detailed analysis of the force balance that emerges within these simulations. We find a transition from a thermal wind to a chemical wind balance with increasing chemical forcing in the azimuthally averaged ”mean” forces in the radial direction. The transition is found to occur at buoyancy ratio, Λ = (𝑅𝑎𝑇 /𝑃𝑟𝑇 )/(𝑅𝑎𝜉 /𝑃𝑟𝜉 ) ≃ 1. However, the corresponding ”fluctuating” balance is quasi-geostrophic in all directions. The analysis lets us locate the geophysically relevant ”rapidly rotating” regime in this parameter space.We proceed by imposing a laterally heterogeneous thermal flux at the core-mantle boundary (CMB) in our rapidly rotating double-diffusive simulations. Recent thermally-driven simulations with lateral variations in CMB heat flux produce local regions with a subadiabatic thermal gradient near the CMB (Mound et al., 2019), termed as regional inversion lenses (RILs). This may reconcile the conflicting inferences about the possibility of a globally stratified layer at the top of the core (Kaneshima 2018; Gastine et al. 2020), by accommodating the possibility of both stable and unstable regions. Our goal is to assess the effect of chemical buoyancy on the RILs. The parameter space now also includes the pattern and amplitude of lateral variation in the CMB heat flux. A standard ’tomographic’ pattern, as suggested by seismic measurements (Masters et al., 1996), has been used in these simulations. The amplitude is characterized as 𝑞∗ = (𝑞𝑚𝑎𝑥 − 𝑞𝑚𝑖𝑛)/𝑞𝑎𝑣𝑔 where 𝑞𝑚𝑎𝑥, 𝑞𝑚𝑖𝑛, and 𝑞𝑎𝑣𝑔 are the maximum, minimum and horizontally averaged heat flux through the CMB. We study the RILs by varying the lateral heterogeneity with 𝑞∗ = {1, 2.3, 5} and buoyancy ratios with Λ = 400-0.01. These RILs are characterized by their strength, measured by a characteristic Brunt-Väisälä frequency (𝑁). Their thickness (𝐿) is measured as the distance of the point of neutral stability from CMB, and the chemical anomaly (𝛿𝜉 ) represents the difference in chemical composition across the lenses. The scaling dependence of these quantities (Mound & Davies, 2020) on the chemical forcing has been explored to extrapolate their values for Earth-like parameters.

A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 10⁵ and 10⁷ while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.