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[SEM13-P08] Effects of driving mode of convection on a spherical dynamo action with a small inner core
Keywords:Dynamo, Convection, Core
Paleomagnetic studies suggest that the geodynamo has been working for ca. 4.2 billion years (Tarduno et al., 2020). During the long lifetime of the geodynamo it is often argued that the geomagnetic field is maintained without the solid inner core in the Hadean and Archean eons. Moreover, high electrical conductivity of the core material suggests a young age of the inner core (e.g., Ohta et al., 2016). Geomagnetic signature restored from paleomagnetic samples is possibly the only tool to infer the age of inner core nucleation based on observations (Biggin et al. 2016). However, we still have little knowledge how to properly interpret paleomagnetic data, which is, in part, ascribed to lack of the understanding of geodynamo behavior in an old era and the mechanisms controlling it. In order to enhance our understanding of the geodynamo, we have investigated basic features of convection and dynamos relying on numerical dynamo modeling. Also in this study, we will proceed along this line.
We focus on the buoyancy source distribution to drive convection in the Earth’s core. Light element ejection and latent heat release upon inner core growth fuels convection from the bottom, while various mechanisms such as uniformly distributed heat source, secular cooling of the core, iron-snow etc. provide negative buoyancy from the top. In fact, the geodynamo is driven by a mixture of the “bottom-up” and “top-down” buoyancy, strongly depending on the origin and evolution history of the Earth. Bearing the fact in mind, here we try to understand the effects of the individual driving mode on convection and magnetic field generation processes as a first step.
We consider a problem of an MHD dynamo in a rotating spherical shell, of which the inner to outer core radius ratio is 0.2. This geometry may suitably mimic that of the Earth’s core in the past well after inner core nucleation. The non-dimensional parameters are the Prandtl number (Pr = 1), the magnetic Prandtl number (Pm = 3), the Ekman number (E = 10-4), and the Rayleigh number (Ra) kept close to the threshold for maintaining the dynamo, which is searched by trial and error. Note that equatorial symmetry (anti-symmetry) is assumed for the velocity (magnetic) field. The present results would be compared with the full 3-dimensional simulations to elucidate non-linear coupling between different symmetries. As a result of the runs, it is found that the minimum Rayleigh number required for a successful dynamo in terms of the critical value for the onset of convection, Ra_c, is substantially different between the two modes. Dynamo is not maintained even at 20 Ra_c for the bottom-up mode, while lower supercriticality of 4.5 Ra_c is sufficient for the top-down mode. In both cases, dipolarity is not as high as the present geomagnetic field, suggesting importance of symmetry-breaking interaction in maintaining a dipole-dominant dynamo (Takahashi et al., 2019). Analysis of kinetic energy budget reveals that the zonal flows are dominantly powered by the Reynolds stress in most of the runs. Furthermore, magnetic field morphology and characteristic force balance will be compared and discussed.
Acknowledgements: This work was supported by JSPS KAKENHI Grant Number JP18K03808.
We focus on the buoyancy source distribution to drive convection in the Earth’s core. Light element ejection and latent heat release upon inner core growth fuels convection from the bottom, while various mechanisms such as uniformly distributed heat source, secular cooling of the core, iron-snow etc. provide negative buoyancy from the top. In fact, the geodynamo is driven by a mixture of the “bottom-up” and “top-down” buoyancy, strongly depending on the origin and evolution history of the Earth. Bearing the fact in mind, here we try to understand the effects of the individual driving mode on convection and magnetic field generation processes as a first step.
We consider a problem of an MHD dynamo in a rotating spherical shell, of which the inner to outer core radius ratio is 0.2. This geometry may suitably mimic that of the Earth’s core in the past well after inner core nucleation. The non-dimensional parameters are the Prandtl number (Pr = 1), the magnetic Prandtl number (Pm = 3), the Ekman number (E = 10-4), and the Rayleigh number (Ra) kept close to the threshold for maintaining the dynamo, which is searched by trial and error. Note that equatorial symmetry (anti-symmetry) is assumed for the velocity (magnetic) field. The present results would be compared with the full 3-dimensional simulations to elucidate non-linear coupling between different symmetries. As a result of the runs, it is found that the minimum Rayleigh number required for a successful dynamo in terms of the critical value for the onset of convection, Ra_c, is substantially different between the two modes. Dynamo is not maintained even at 20 Ra_c for the bottom-up mode, while lower supercriticality of 4.5 Ra_c is sufficient for the top-down mode. In both cases, dipolarity is not as high as the present geomagnetic field, suggesting importance of symmetry-breaking interaction in maintaining a dipole-dominant dynamo (Takahashi et al., 2019). Analysis of kinetic energy budget reveals that the zonal flows are dominantly powered by the Reynolds stress in most of the runs. Furthermore, magnetic field morphology and characteristic force balance will be compared and discussed.
Acknowledgements: This work was supported by JSPS KAKENHI Grant Number JP18K03808.