Multi-symplectic formulation of near-local Hamiltonian balanced models

作者：Delahaies Sylvain^*; Hydon Peter E

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2011, 467(2136): 3424-3442.

DOI：10.1098/rspa.2011.0147

• multi-symplectic system
• balanced models
• semigeostrophic theory

We transform near-local Hamiltonian balanced models (HBMs) describing nearly geostrophic fluid motion (with constant Coriolis parameter) into multi-symplectic (MS) systems. This allows us to determine conservation of Lagrangian momentum, energy and potential vorticity for Salmon's L(1) dynamics; a similar approach works for other near-local balanced models (such as the root 3-model). The MS approach also enables us to determine a class of systems that have a contact structure similar to that of the semigeostrophic model. The contact structure yields a contact transformation that makes the problem of front formation tractable. The new class includes the first local model with a variable Coriolis parameter that preserves all of the most useful geometric features of the semigeostrophic model.

• 出版日期2011-12-8