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A variational formulation of vertical slice models

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Title: A variational formulation of vertical slice models
Authors: Cotter, CJ
Holm, DD
Item 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.
Issue Date: 8-Jul-2013
Date of Acceptance: 18-Apr-2013
URI: http://hdl.handle.net/10044/1/65447
DOI: https://dx.doi.org/10.1098/rspa.2012.0678
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/Funder: Natural Environment Research Council (NERC)
Funder's Grant Number: NE/I02013X/1
Keywords: 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
Online Publication Date: 2013-07-08
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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