A parcel formulation for Hamiltonian layer models

Onno Bokhove, M. Oliver

    Research output: Contribution to journalArticleAcademicpeer-review

    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.
    Original languageUndefined
    Pages (from-to)423-442
    Number of pages18
    JournalGeophysical and astrophysical fluid dynamics
    Volume103
    Issue number6
    DOIs
    Publication statusPublished - Dec 2009

    Keywords

    • EWI-17317
    • Atmospheric layer model
    • IR-65435
    • METIS-265776
    • Hamiltonian dynamics

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