Abstract:
The formation of the main geomagnetic field is ensured by the hydromagnetic dynamo mechanism — the generation of a magnetic field by the movement of a conducting medium. The Earth's dynamo (geodynamo) is driven by the convection of liquid metal in the Earth's outer core. This mechanism is fundamentally nonlinear and three-dimensional, so solving the geodynamo equations is only possible numerically. Convection in the core is characterized by developed turbulence, and a direct numerical solution with resolution of all turbulent scales is impossible even on high-performance computing systems. One solution is to separate scales into large and small. At large scales, the geodynamo equations are solved using a suitable numerical method, but using turbulent values of the diffusion coefficients. These values are properties of the flow, not the medium, and therefore must be calculated based on small-scale movements. Small-scale dynamics can be described by a shell model of magneto convection. Combining two such models forms a multiscale geodynamo model. This paper derives equations for a complex shell model of magneto convection that satisfy the conservation laws of energy, cross-helicity, magnetic helicity, and temperature fluctuation energy in the dissipation-free limit. The model coefficients are consistent with the probabilities of interaction between scale shells. A scheme is described for coupling a large-scale spectral model of the geodynamo and a shell model of turbulent convection, which exchange information with each other. The spectral model determines the values of the phase variables of the largest scales in the shell model. Turbulent values of the diffusion coefficients for the spectral model are calculated from the phase variables of the shell model. Explicit expressions are obtained for calculating the parameters of one model from the phase variables of the other.
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