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March 30, 2009 16:44 Geophysical and Astrophysical Fluid Dynamics gafdbo09 Geophysical and Astrophysical Fluid Dynamics
 

Summary: March 30, 2009 16:44 Geophysical and Astrophysical Fluid Dynamics gafdbo09
Geophysical and Astrophysical Fluid Dynamics
Vol. 00, No. 00, Month 200x, 1­19
A parcel formulation for Hamiltonian layer models
O. BOKHOVE
AND M. OLIVER1

Department of Applied Mathematics, University of Twente, The Netherlands
1
School of Engineering and Science, Jacobs University, 28759 Bremen, Germany
(January 2009)
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N­layer models with isentropic tropo-
spheric 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. 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.
1 Introduction
Compressible fluid mechanics has a well known Hamiltonian formulation in which all Eulerian fields--

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering