Chaos and mixing in a geostrophic flow

Abstract

Experiments on Rossby waves on an azimuthal jet in a rapidly rotating annular tank reveal a striking barrier to mixing across the jet. A model based on the experiments assumes a two‐dimensional incompressible flow described by a time‐dependent streamfunction consisting of azimuthally propagating waves on a narrow jet. When there is only one wave, all Lagrangian particle trajectories are closed in the appropriate reference frame. When two independent waves are present, some trajectories are chaotic, and the size of the chaotic sea grows as the amplitude of the second wave is increased; however, at least one barrier to global transport—an invariant surface—prohibits trajectories from crossing the jet. The addition of a third wave is found to break the barrier only if the wave amplitudes exceed the width of the jet. In the experiment, the wave amplitude is typically about one‐half the jet width, and the barrier to mixing persists even at the highest accessible Reynolds numbers.