On a possible mechanism of anomalous diffusion by Rossby waves

Abstract

We study the advection of passive tracers by traveling plane Rossby waves of finite amplitude. In distinction with previous studies the nonlinearity of the wave field is taken into account in the first order of perturbation theory by considering the Lagrangian transport by resonant wave triads. Using the waves’ phases as new dynamical variables we reduce the problem to the study of a specific one-and-a-half degree of freedom Hamiltonian system with nonharmonic modulation. By using a symplectic integrator we study this system numerically and find an interesting series of bifurcations of its phase portrait as the nonlinearity increases. As is standard in the systems of this type we commonly see a chaotic sea with elliptic islands in the phase space, which means that in the physical space the resonant triads give rise to chaotic mixing and ballistic transport, respectively. The relevance of these results to the transport properties of β-plane turbulence is discussed.