Eigenvalues of magnetohydrodynamic mean-field dynamo models: bounds and reliable computation

Boegli, Sabine; Tretter, Christiane (2020). Eigenvalues of magnetohydrodynamic mean-field dynamo models: bounds and reliable computation. SIAM journal on applied mathematics, 80(5), pp. 2194-2225. Society for Industrial and Applied Mathematics 10.1137/19M1286359

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This paper provides the first comprehensive study of the linear stability of three important magnetohydrodynamic (MHD) mean-field dynamo models in astrophysics, the spherically symmetric \alpha^2-model, the \alpha^2\omega -model, and the \alpha \omega -model. For each of these highly nonnormal problems, we establish upper bounds for the real part of the spectrum, prove resolvent estimates, and derive thresholds for the helical turbulence function \alpha and the rotational shear function \omega below which no MHD dynamo action can occur for the linear models (antidynamo or bounding theorems). In addition, we prove that interval truncation and finite section method, which are employed to regularize the singular differential expressions and the infinite number of coupled equations, are spectrally exact. This means that all spectral points are approximated and no spectral pollution occurs, thus confirming, for the first time, that numerical eigenvalue approximations for the highly nonnormal MHD dynamo problems are reliable.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

0036-1399

Publisher:

Society for Industrial and Applied Mathematics

Funders:

[4] Swiss National Science Foundation ; [UNSPECIFIED] Imperial College London ; [UNSPECIFIED] Early Postdoctoral Mobility grant

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

10 Feb 2021 14:57

Last Modified:

10 Feb 2021 14:57

Publisher DOI:

10.1137/19M1286359

Uncontrolled Keywords:

eigenvalues, approximation, magnetohydrodynamics, dynamo problem, spectral convergence, resolvent bounds

BORIS DOI:

10.48350/151245

URI:

https://boris.unibe.ch/id/eprint/151245

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