Solenoidal force balances in numerical dynamos

Teed, R. J. and Dormy, E. (2023) Solenoidal force balances in numerical dynamos. Journal of Fluid Mechanics, 964, A26. (doi: 10.1017/jfm.2023.332)

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 is 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 length-scale-dependent analysis for several spherical simulations and find that removal of gradient parts offers an alternative picture of the force balance compared with 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.

• Item Type: Articles
• Additional Information: This work was supported by DiRAC Project ACTP245.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Teed, Dr Robert
• Authors: Teed, R. J., and Dormy, E.
• Subjects: Q Science > QA Mathematics; Q Science > QC Physics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Fluid Mechanics
• Publisher: Cambridge University Press
• ISSN: 0022-1120
• ISSN (Online): 1469-7645
• Published Online: 01 June 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Journal of Fluid Mechanics 964:A26
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher