Solenoidal force balances in numerical dynamos

TL;DR

This paper introduces solenoidal force balances as a new method to analyze force interactions in numerical geodynamo simulations, revealing clearer insights especially at smaller scales, and emphasizing the importance of considering only solenoidal forces for accurate comparisons.

Contribution

It proposes and demonstrates the use of solenoidal force balances to better understand force dynamics in planetary dynamo models, highlighting differences from traditional analyses.

Findings

Solenoidal force balances provide a clearer picture of force interactions.

Differences between traditional and solenoidal analyses are significant at small scales.

Only the solenoidal parts of forces should be considered for meaningful force comparisons.

Abstract

Numerical simulations of the geodynamo (and other planetary dynamos) have made significant progress in recent years. As computing power has advanced, some new models claim to be ever more appropriate for understanding Earth's core dynamics. One measure of the success of such models is the ability to replicate the expected balance between forces operating within the core; Coriolis and Lorentz forces are predicted to be most important. The picture is complicated for an incompressible flow by the existence of the pressure gradient force which renders the gradient parts of all other forces dynamically unimportant. This can confuse the situation, especially when the scale dependence of forces are considered. In this work we investigate force balances through the alternative approach of eliminating gradient parts of each force to form `solenoidal force balances'. We perform a lengthscale dependent analysis for several spherical simulations and find that removal of gradient parts offers an alternative picture of the force balance compared to looking at traditional forces alone. Solenoidal force balances provide some agreement with the results of previous studies but also significant differences. They offer a cleaner overall picture of the dynamics and introduce differences at smaller scales. This has implications for geodynamo models purporting to have reached Earth-like regimes: in order to achieve a meaningful comparison of forces, only the solenoidal part of forces should be considered.