Two discrete models for semi-geostrophic dynamics

Journal article

We discuss two dynamical systems, each intended to represent a discrete analogue of the infinite-dimensional f-plane semi-geostrophic equations. The first model, the lattice model, gives rise to a Hamiltonian system for which the Hamiltonian vector field is discontinuous. This poses a problem with uniqueness of solutions. The second model, the doubly stochastic model, is a C 1 generalisation of the lattice model. We outline both models and completely solve both models in the simplest possible case. Finally, we discuss an interpretation of the dynamics of each model from the viewpoint of air parcels in an idealised atmosphere. Copyright © 1997 Elsevier Science B.V. All rights reserved.

Authors: Baigent, S; Norbury, J

• Publication status: Published
• Journal: PHYSICA D
• Volume: 109
• Issue: 3-4
• Pages: 333-342
• Publication date: 1997-11-15
• DOI: 10.1016/S0167-2789(97)00073-0
• ISSN: 0167-2789
• Language: English
• Keywords: proximation theory; Hamiltonian systems; semi-geostrophic theory