Hamiltonian structure for drift waves and geostrophic flow

The equation (1−∇2)φt+J[φ, (1−∇2)φ−λ]=0 in the plane is put in Hamiltonian form with respect to a noncanonical Poisson bracket. If the function λ is a linear combination of x,y, and x2+y2, the equation can be transformed to a form very close to the vorticity equation for an ideal fluid. In particular, β-plane dynamics are transformed into f-plane dynamics.