For instance, Christopher et al. ( 2010) showed that even would require at least days to calculate one single magnetic diffusion time on a -processor supercomputer, a formidable computational challenge from both the numerically stable schemes and reliable parallel solvers of the ill-conditioned linear system arising from the multiscale intrinsic nature of the geodynamo mechanism. A huge gap cannot be captured by limited supercomputing capacity. However, nowadays, geodynamo simulations have only been capable of operating down to in practice (Aubert et al., 2017). Numerical geodynamo simulations require massive parallel computers than currently available to solve the rapid rotation against the outer core's low viscosity (corresponding to the low value of ). Among the unsolved issues, the value space of controlling parameters, such as the Ekman number and the magnetic Prandtl number, differs dramatically from the realistic planetary parameters (Christensen & Aubert, 2006). Most models have four critical dimensionless parameters: the Rayleigh number, measures thermal driven force the Ekman number, measures the relative importance of viscous forces to Coriolis forces the Prandtl number, measures the ratio of viscosity to thermal diffusivity and the magnetic Prandtl number, measures the ratio of viscosity to magnetic diffusivity (Christensen et al., 1999). Nevertheless, the huge gap between the simulations' parameter and their expected values in the Earth's core still exists (Aubert, 2018 Schaeffer et al., 2017 Schwaiger et al., 2019). For those models, the magnetic field properties closely match the geomagnetic field in terms of spatial spectra and magnetic field morphology, secular variation, and occasionally the characteristics of dipole reversals (Aubert, 2020 Calkins et al., 2017 Wicht & Sanchez, 2019 Yadav et al., 2016). A couple of years later, numerous numerical geodynamo models emerged, for a comprehensive review see Christensen and Wicht ( 2007). The GR95 model showed that such models could describe and explain many basic properties of the geomagnetic field, including dipole-dominated morphology, reversals, and westward drift (Glatzmaiers & Roberts, 1995a).įurthermore, they studied viscous and electromagnetic coupling between the inner core and the outer core, which brought differential rotation of the inner core (Glatzmaiers & Roberts, 1995a). In 1995, there was a breakthrough in the numerical simulation of magnetohydrodynamic (MHD) flow by Glatzmaiers and Roberts, called GR95 (Glatzmaiers & Roberts, 1995b). From 1950 to 1990, the dynamo theory has shown that the principle of a homogeneous dynamo process is possible and has elucidated the parameter prerequisites and model constraints. As emerging from numerical simulations, details of these mechanisms achieve a self-sustaining magnetic field (Aubert, 2020 Buffett, 2000 Yadav et al., 2015). Earth's magnetic field is generated and maintained by a strongly coupled mechanism known as geodynamo (Roberts, 2007). Paleomagnetic records indicate that the Earth's geomagnetic field has existed for at least 3 billion years, with a roughly reversal rate of hundreds of thousands of years. Still, appropriate assumptions can be made to take this variation into account. Comparing with other scaling laws previous wisdom holds, we propose that the effect of viscosity diffusion is non-negligible for both existing weak and strong dynamo regimes. In a quasi-MAC regime, the Lorentz force instead of the inertial force enters into the first-order agostrophic force balance, though the viscous force still plays a role. Furthermore, we conducted a local force balance analysis and demonstrated that the balance shifts under different. The reason that increases with is essential that increasing breaks the Taylor-Proudman constraint and drops the critical Rayleigh number, but this kind of increase of does not give a stronger. The magnetic field does not change much with when the driving force is not too strong ( ) but decreases with by a scaling law of when geodynamo operates in a very vigorous mode ( ).

While in the strong field mode, varies very slowly by a scaling law of.

In the weak field mode, the fluid velocity varies with by a scaling law of. To boost these, taking the outer core viscosity, we studied its impacts on weak and strong field geodynamo outputs by varying in two orders of magnitudes. Existing scaling laws need to be tested by numerical simulations. Exploring geodynamo's scaling laws is of great importance when a tremendous gap still lies between realistic physics and estimated model parameters.

Viscosity for mac reviewa