Particle relabelling symmetries and Noether's theorem for vertical slice models

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Title: Particle relabelling symmetries and Noether's theorem for vertical slice models
Authors: Cotter, CJ
Cullen, MJP
Item Type: Journal Article
Abstract: We consider the variational formulation for vertical slice models introduced in Cotter and Holm (Proc Roy Soc, 2013). These models have a Kelvin circulation theorem that holds on all materially-transported closed loops, not just those loops on isosurfaces of potential temperature. Potential vorticity conservation can be derived directly from this circulation theorem. In this paper, we show that this property is due to these models having a relabelling symmetry for every single diffeomorphism of the vertical slice that preserves the density, not just those diffeomorphisms that preserve the potential temperature. This is developed using the methodology of Cotter and Holm (Foundations of Computational Mathematics, 2012).
Issue Date: 1-Jun-2019
Date of Acceptance: 27-Sep-2018
ISSN: 1941-4889
Publisher: American Institute of Mathematical Sciences
Start Page: 139
End Page: 151
Journal / Book Title: Journal of Geometric Mechanics
Volume: 11
Issue: 2
Copyright Statement: © American Institute of Mathematical Sciences
Sponsor/Funder: Natural Environment Research Council (NERC)
Funder's Grant Number: NE/K012533/1
Publication Status: Published
Embargo Date: 2020-06-01
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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