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Validity of sound-proof approximations for magnetic buoyancy

J. B. Moss*, T. S. Wood, and P. J. Bushby

  • School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom

  • *j.moss2@newcastle.ac.uk
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Phys. Rev. Fluids 7, 103701 – Published 7 October, 2022

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

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 pseudoincompressible 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 nonrotating and rotating cases. We obtain specific constraints that must be satisfied in order for the model to capture the leading-order behavior 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 pseudoincompressible magnetohydrodynamics model, demonstrating its underlying Hamiltonian structure.

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Phys. Rev. Fluids 7, 103701– Published 7 October, 2022
  • Received 28 October 2021
  • Accepted 23 September 2022
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