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O. Bokhove and M. Oliver,
A parcel formulation for Hamiltonian layer models,
Geophys. Astrophys. Fluid Dyn. 103 (2009),
423-442.
Abstract:
Starting from the three-dimensional hydrostatic primitive equations,
we derive Hamiltonian N-layer models with isentropic tropospheric
and isentropic or isothermal stratospheric layers. Our construction
employs a new parcel Hamiltonian formulation which describes the fluid
as a continuum of Hamiltonian ordinary differential equations bound
together by integral transport laws. In particular, we show that this
parcel Hamiltonian structure is compatible with the stacking of layers
under isentropic or isothermal constraints. The appeal of the parcel
formulation is the simplification of various calculations, in
particular the derivation of the continuum Poisson bracket and the
proof of the Jacobi identity. A comparison and connection is made
between the Hamiltonian dynamics of fluid parcels and the Hamiltonian
system of partial differential equations. The parcel formulation can
be seen as a precursor and tool for the study of Hamiltonian numerical
schemes.
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