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@article{Cotter:2013:10.1098/rspa.2012.0678,
author = {Cotter, CJ and Holm, DD},
doi = {10.1098/rspa.2012.0678},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
title = {A variational formulation of vertical slice models},
url = {http://dx.doi.org/10.1098/rspa.2012.0678},
volume = {469},
year = {2013}
}
TY - JOUR
AB - 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.
AU - Cotter,CJ
AU - Holm,DD
DO - 10.1098/rspa.2012.0678
PY - 2013///
SN - 1364-5021
TI - A variational formulation of vertical slice models
T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR - http://dx.doi.org/10.1098/rspa.2012.0678
UR - http://hdl.handle.net/10044/1/65447
VL - 469
ER -
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