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Self-adjointness of sound-proof models for magnetic buoyancy

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

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Abstract

An ideal magneto-hydrodynamic fluid, whether fully compressible or incompressible, is a Hamiltonian system. This implies that the equations describing perturbations to any static state are self-adjoint, a fact that is useful in obtaining stability criteria. To describe weakly compressible flows, there are a number of ``sound-proof'' models that eliminate sound waves by making approximations to the governing equations. However, such approximations may violate the Hamiltonian structure of the system. In a recent work, we have introduced a very general sound-proof model and determined conditions under which it closely approximates the linear regime of magneto-buoyancy instability, motivated by conditions in the solar interior. In the present work we take a complementary approach, by deriving constraints under which the linearised sound-proof system is self-adjoint. We show that there is a unique set of self-adjoint sound-proof equations that conserves the same energy as the fully compressible system.

Publication metadata

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

Publication type: Article

Publication status: Published

Journal: Geophysical and Astrophysical Fluid Dynamics

Year: 2023

Volume: 117

Issue: 4

Pages: 263-277

Online publication date: 19/07/2023

Acceptance date: 05/07/2023

Date deposited: 05/07/2023

ISSN (print): 0309-1929

ISSN (electronic): 1029-0419

Publisher: Taylor & Francis

URL: https://doi.org/10.1080/03091929.2023.2234596

DOI: 10.1080/03091929.2023.2234596

ePrints DOI: 10.57711/0r3h-ay98

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