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- Title
Variational formulations of sound-proof models.
- Authors
Cotter, C. J.; Holm, D. D.
- Abstract
We derive a family of ideal (non-dissipative) three-dimensional (3D) sound-proof fluid models that includes both the Lipps-Hemler anelastic approximation (AA) and the Durran pseudo-incompressible approximation (PIA). This family of models arises in the Euler-Poincaré framework involving a constrained Hamilton's principle expressed in the Eulerian fluid description. The derivation in this framework establishes the following properties of each member of the entire family: the Kelvin-Noether circulation theorem, conservation of potential vorticity on fluid parcels, a Lie-Poisson Hamiltonian formulation possessing conserved Casimirs, a conserved domain-integrated energy and an associated variational principle satisfied by the equilibrium solutions. Having set the stage with derivations of 3D models using the constrained Hamilton's principle, we then derive the corresponding 2D vertical slice models for these sound-proof theories.
- Subjects
THREE-dimensional imaging; APPROXIMATION theory; HAMILTON'S principle function; EULERIAN graphs; ANELASTIC relaxation
- Publication
Quarterly Journal of the Royal Meteorological Society, 2014, Vol 140, Issue 683, p1966
- ISSN
0035-9009
- Publication type
Article
- DOI
10.1002/qj.2260