Hamiltonian formulation of the baroclinic quasigeostrophic fluid equations

A Hamiltonian formulation using a noncanonical Poisson bracket is presented for the nonlinear dynamics of baroclinic quasigeostrophic fluid flow. Nonlinear integral invariants for the system are found to be in the kernel of the noncanonical Poisson bracket. A novel feature of this formulation is that dynamical boundary conditions are generated from the constrained energy Hamiltonian, via the noncanonical Poisson bracket.