Zonal-meridional decomposition and the Hamiltonian description of planetary fluid dynamics

The basic properties of planetary flows are studied within the framework of the noncanonical Hamiltonian approach formulated by Morrison. A zonal-symmetric decomposition is applied in order to characterize the contributions of the different dynamical terms. Steady states and the Lorenz energy and angular momentum cycles are also written within the Lie–Poisson bracket formalism.

► We model the planetary fluid dynamics in terms of noncanonical Lie–Poisson brackets.
► Zonal-meridional decomposition for the momentum fields is introduced.
► Axisymmetric model and basic equilibria are characterized.
► Angular momentum cycle and Hide’s theorem are recovered in the Hamiltonian form.
► Lorenz energy cycle is written in terms of the noncanonical Lie–Poisson formalism.