Transition between viscous dipolar and inertial multipolar dynamos

TL;DR

This study identifies a new three-term force balance involving inertial, viscous, and Coriolis forces that governs the transition from dipolar to multipolar dynamos, providing a unified parameter to describe this transition.

Contribution

It introduces a novel three-term force balance and a single parameter that accurately characterizes the transition in spherical rotating dynamos, resolving previous contradictions in the literature.

Findings

The transition is characterized by a three-term force balance.

The parameter ${ m Ro} { m E}^{-1/3}$ accurately describes the transition.

A unified framework resolves earlier conflicting theories.

Abstract

We investigate the transition from steady dipolar to reversing multipolar dynamos. The Earth has been argued to lie close to this transition, which could offer a scenario for geomagnetic reversals. We show that the transition between dipolar and multipolar dynamos is characterized by a three terms balance (as opposed to the usually assumed two terms balance), which involves the non-gradient parts of inertial, viscous and Coriolis forces. We introduce from this equilibrium the sole parameter ${{\rm Ro}}\,{{\rm E}}^{-1/3} \equiv {{\rm Re}}\,{{\rm E}}^{2/3}$, which accurately describes the transition for a wide database of 132 fully three dimensional direct numerical simulations of spherical rotating dynamos (courtesy of U. Christensen). This resolves earlier contradictions in the literature on the relevant two,terms balance at the transition. Considering only a two terms balance between the non-gradient part of the Coriolis force and of inertial forces, provides the classical ${{\rm Ro}}/{\ell_u}$ (Christensen and Aubert, 2006). This transition can be equivalently described by ${{\rm Re}} \, {\ell^{2}_u}$, which corresponds to the two terms balance between the non-gradient part of inertial forces and viscous forces (Soderlund {\it et al.}, 2012).