2012/11/26 by Darryl D. Holm, Holm, Darryl D. · 1 citation
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #physics.class-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1211.5827
12 pages, rescuing and old draft for the arXiv that may be updated later. Comments welcome!
arxiv created 2012/11/26 · arxiv updated 2012/11/27
We show that the ideal (nondissipative) form of the dynamical equations for the Lipps-Hemler formulation of the anelastic fluid model follow as Euler-Poincaré equations, obtained from a constrained Hamilton's principle expressed in the Eulerian fluid description. This establishes the mathematical framework for the following properties of these anelastic equations: the Kelvin-Noether circulation theorem, conservation of potential vorticity on fluid parcels, and the Lie-Poisson Hamiltonian formulation possessing conserved Casimirs, conserved domain integrated energy and an associated variational principle satisfied by the equilibrium solutions. We then introduce a modified set of anelastic equations that represent the mean anelastic motion, averaged over subgrid scale rapid fluctuations, while preserving the mathematical properties of the Euler-Poincaré framework.