A variational formulation of vertical slice models
File(s)
Accepted version
Author(s)
Cotter, CJ
Holm, DD
Type
Journal Article
Abstract
A variational framework is defined for vertical slice models with three-dimensional velocity depending only on x and z. The models that result from this framework are Hamiltonian, and have a Kelvin–Noether circulation theorem that results in a conserved potential vorticity in the slice geometry. These results are demonstrated for the incompressible Euler–Boussinesq equations with a constant temperature gradient in the y-direction (the Eady–Boussinesq model), which is an idealized problem used to study the formation and subsequent evolution of weather fronts. We then introduce a new compressible extension of this model. Unlike the incompressible model, the compressible model does not produce solutions that are also solutions of the three-dimensional equations, but it does reduce to the Eady–Boussinesq model in the low Mach number limit. Hence, the new model could be used in asymptotic limit error testing for compressible weather models running in a vertical slice configuration.
Date Issued
2013-07-08
Date Acceptance
2013-04-18
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013, 469 (2155)
ISSN
1364-5021
Publisher
Royal Society, The
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
469
Issue
2155
Copyright Statement
© 2013 The Author(s). Published by the Royal Society. All rights reserved.
Sponsor
Natural Environment Research Council (NERC)
Grant Number
NE/I02013X/1
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
variational principles
slice models
Kelvin circulation laws
math.DS
physics.ao-ph
physics.flu-dyn
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
20120678
Date Publish Online
2013-07-08