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@article{Cotter:2019:10.3934/jgm.2019007,
author = {Cotter, CJ and Cullen, MJP},
doi = {10.3934/jgm.2019007},
journal = {Journal of Geometric Mechanics},
pages = {139--151},
title = {Particle relabelling symmetries and Noether's theorem for vertical slice models},
url = {http://dx.doi.org/10.3934/jgm.2019007},
volume = {11},
year = {2019}
}

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TY  - JOUR
AB  - We consider the variational formulation for vertical slice models introduced in Cotter and Holm (Proc RoySoc,  2013).   These  models  have  a  Kelvin  circulation  theorem  that  holds  on  all  materially-transported  closedloops,  not  just  those  loops  on  isosurfaces  of  potential  temperature.   Potential  vorticity  conservation  can  bederived directly from this circulation theorem.  In this paper, we show that this property is due to these modelshaving a relabelling symmetry for every single diffeomorphism of the vertical slice that preserves the density, notjust those diffeomorphisms that preserve the potential temperature.  This is developed using the methodologyof Cotter and Holm (Foundations of Computational Mathematics, 2012).
AU  - Cotter,CJ
AU  - Cullen,MJP
DO  - 10.3934/jgm.2019007
EP  - 151
PY  - 2019///
SN  - 1941-4889
SP  - 139
TI  - Particle relabelling symmetries and Noether's theorem for vertical slice models
T2  - Journal of Geometric Mechanics
UR  - http://dx.doi.org/10.3934/jgm.2019007
UR  - http://hdl.handle.net/10044/1/65150
VL  - 11
ER  -

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