Hamiltonian chaos and transport in quasigeostrophic flows

Chaotic advective transport in quasigeostrophic flows is studied. Particular interest is to compare theory with recent rotating tank experiments. Ideas regarding chaotic advection are briefly reviewed. A derivation of the quasigeostrophic equation relevant to the tank experiments is given, from which a model for the stream function is extracted and compared to experimental data. Linear theory is shown to predict correctly the onset of observed sinuous Rossby waves. A model stream function, composed of a zonal flow equilibrium with linear eigenfunctions, is used to study chaotic transport. Upon applying the Chirikov overlap criterion to the model it is seen, in agreement with experiments, that banded chaos, i.e., regions of chaos bounded by invariant surfaces, is to be expected. It is also shown that global chaos, and hence transport across the zonal flow, is inconsistent with linear theory and in general requires resonances with phase velocities near the peak velocity of the zonal flow equilibrium. Speculations regarding the consistency of chaos and conservation of potential vorticity are made.