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O. Bokhove and M. Oliver,
Parcel Eulerian-Lagrangian fluid dynamics of
rotating geophysical flows,
Proc. R. Soc. Lond. A, in press.
Abstract:
Parcel Eulerian-Lagrangian Hamiltonian formulations have recently been
used in structure-preserving numerical schemes, asymptotic
calculations, and in alternative explanations of fluid parcel
(in)stabilities. A parcel formulation describes the dynamics of one
fluid parcel with a Lagrangian kinetic energy but an Eulerian
potential evaluated at the parcel's position. In this paper, we
derive the geometric link between the parcel Eulerian-Lagrangian
formulation and well-known variational and Hamiltonian formulations
for three models of ideal and geophysical fluid flow: generalized
two-dimensional vorticity-streamfunction dynamics, the rotating
two-dimensional shallow water equations, and the rotating
three-dimensional compressible Euler equations.
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