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arXiv · 2103.08091

Generation of momentum transport in weakly turbulent $\beta$-plane magnetohydrodynamics

R. A. Heinonen·P. H. Diamond·M. F. D. Katz·G. E. Ronimo
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Abstract

Magnetohydrodynamic (MHD) turbulence on a $\beta$-plane with an in-plane mean field, a system which serves as a simple model for the solar tachocline, is investigated analytically and computationally. We first derive two useful analytic constraints: we express the mean turbulent cross-helicity in terms of the mean turbulent magnetic energy, and then show that (for weak turbulence) the time-averaged momentum transport in the system can be expressed in terms of the cross-helicity spectrum. We then complete a closure of the system using weak turbulence theory, appropriately extended to a system with multiple interacting eigenmodes. We use this closure to perturbatively solve for the spectra at lowest order in the Rossby parameter $\beta$ and thereby show that the momentum transport in the system is $O(\beta^2)$, thus quantifying the transition away from Alfv\'enized turbulence. Finally, we verify our theoretical results by performing direct numerical simulations of the system over a broad range of $\beta$.

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R. A. Heinonen, P. H. Diamond, M. F. D. Katz, G. E. Ronimo. 2021-03-15. Generation of momentum transport in weakly turbulent $\beta$-plane magnetohydrodynamics. https://arxiv.org/abs/2103.08091

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