Particle relabelling symmetries and Noether's theorem for vertical slice models
File(s)
Accepted version
Author(s)
Cotter, CJ
Cullen, MJP
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).
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).
Date Issued
2019-06-01
Date Acceptance
2018-09-27
Citation
Journal of Geometric Mechanics, 2019, 11 (2), pp.139-151
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
Natural Environment Research Council (NERC)
Grant Number
NE/K012533/1
Publication Status
Published