Scaling Laws for Planetary Dynamos

TL;DR

This paper introduces new power-law scaling laws for planetary dynamo properties, linking them to observable planetary parameters, and refines previous models by emphasizing the negligible inertial term in planetary cores.

Contribution

It presents modified scaling laws for planetary dynamos that account for the small Rossby number, improving upon previous models and aligning with numerical evidence.

Findings

Scaling laws relate dynamo properties to planetary dipole moment and rotation rate.

The inertial term is negligible in planetary cores, affecting the scaling exponents.

The proposed laws are consistent with numerical simulations.

Abstract

We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect ratio of the columnar convection cells are all predicted to be power-law functions of two observable quantities: the magnetic dipole moment and the planetary rotation rate. The resulting scaling laws constitute a somewhat modified version of the scalings proposed in Christensen & Aubert (2006) and Christensen (2010). The main difference is that, in view of the small value of the Rossby number in planetary cores, we insist that the nonlinear inertial term, (u.grad)u, is negligible. This changes the exponents in the power-laws which relate the various properties of the fluid dynamo to the planetary dipole moment and rotation rate. Our scaling laws are consistent with the available numerical evidence.