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Validity of sound-proof approximations for magnetic buoyancy

Lookup NU author(s): John Moss, Dr Toby Wood, Professor Paul BushbyORCiD

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Abstract

The presence of acoustic waves in models of compressible flows can present complications for analytical and numerical analysis. Therefore, several methods have been developed to filter out these waves, leading to various "sound-proof" models, including the Boussinesq, anelastic and pseudo-incompressible models. We assess the validity of each of these approximate models for describing magnetic buoyancy in the context of the solar interior. A general sound-proof model is introduced and compared to the fully compressible system in a number of asymptotic regimes, including both non-rotating and rotating cases. We obtain specific constraints that must be satisfied in order that the model captures the leading-order behaviour of the fully compressible system. We then discuss which of the existing sound-proof models satisfy these constraints, and in what parameter regimes. We also present a variational derivation of the pseudo-incompressible MHD model, demonstrating its underlying Hamiltonian structure.

Publication metadata

Author(s): Moss JB, Wood TS, Bushby PJ

Publication type: Article

Publication status: Published

Journal: Physical Review Fluids

Year: 2022

Volume: 7

Issue: 10

Online publication date: 07/10/2022

Acceptance date: 23/09/2022

Date deposited: 27/09/2022

ISSN (electronic): 2469-990X

Publisher: American Physical Society

URL: https://doi.org/10.1103/PhysRevFluids.7.103701

DOI: 10.1103/PhysRevFluids.7.103701

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