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-stream function dynamics, the rotating two-dimensional shallow-water equations and the rotating three-dimensional compressible Euler equations.
|Number of pages||16|
|Journal||Proceedings of the Royal Society A: mathematical, physical and engineering sciences|
|Publication status||Published - 8 Sep 2006|
Bokhove, O., & Oliver, M. (2006). Parcel Eulerian-Lagrangian fluid dynamics for rotating geophysical flows. Proceedings of the Royal Society A: mathematical, physical and engineering sciences, 462(2/2073), 2575-2592. [10.1098/rspa.2006.1656]. https://doi.org/10.1098/rspa.2006.1656