Abstract
The mechanism by which the Earth’s magnetic field is generated is thought to be thermal convection in the metallic liquid iron core. Here we present results of a suite of self-consistent spherical shell computations with ultra-low viscosities that replicate this mechanism, but using diffusivities of momentum and magnetic field that are notably dissimilar from one another. This leads to significant scale separation between magnetic and velocity fields, the latter being dominated by small scales. We show a zeroth order balance between the azimuthally-averaged parts of the Coriolis and Lorentz forces at large scales, which occurs when the diffusivities of magnetic field and momentum differ so much, as in our model. Outside boundary layers, viscous forces have a magnitude that is about one thousandth of the Lorentz force. In this dynamo dissipation is almost exclusively Ohmic, as in the Earth, with convection inside the so-called tangent cylinder playing a crucial role; it is also in the “strong field” regime, with significantly more magnetic energy than kinetic energy (as in the Earth). We finally show a robust empirical scaling law between magnetic dissipation and magnetic energy.
Highlights
Earth’s dynamo is generally considered to be driven by cooling of the core and from latent heat and buoyancy associated with the crystallisation of the inner core
The core-mantle boundary (CMB) and a constant temperature inner core boundary (ICB); no-slip boundary conditions are applied at the ICB and CMB and the inner core is conducting and free to rotate
Fixed heat flux boundary conditions were suggested by Sakuraba and Roberts[8] as being more realistic boundary conditions for the core considering the overlying convecting mantle. They showed that the use of these boundary conditions affected the length scale of magnetic fields
Summary
The mechanism by which the Earth’s magnetic field is generated is thought to be thermal convection in the metallic liquid iron core. Viscous forces have a magnitude that is about one thousandth of the Lorentz force In this dynamo dissipation is almost exclusively Ohmic, as in the Earth, with convection inside the so-called tangent cylinder playing a crucial role; it is in the “strong field” regime, with significantly more magnetic energy than kinetic energy (as in the Earth). Fixed heat flux boundary conditions were suggested by Sakuraba and Roberts[8] as being more realistic boundary conditions for the core considering the overlying convecting mantle They showed that the use of these boundary conditions affected the length scale of magnetic fields. When the kinetic spectrum is modified by the presence of magnetic field, it fits a −4/3 slope in both Case S0 and Case S4
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