Chaotic advection by Rossby-Haurwitz waves

We study the kinematics of the mixing of particles passively advected by linear wave solutions of Haurwitz [J. Marine Res. 3 (1940) 254] for an incompressible, inviscid, barotropic, horizontal flow on a sphere. We show, with the help of Poincaré maps, that the superposition of two waves is sufficient to produce chaotic trajectories in physical space. We use Lyapounov exponents to quantify the predictability of particle trajectories in the chaotic region. Whether the chaos is temporarily uniform or intermittent is inferred by calculating the local deviation from the Lyapounov exponent. Some typical correlation dimension calculations are presented to characterize the geometric evolution of a tracer cloud. The physical significance of the results is discussed in the context of tracer transport in the stratosphere during “sudden warmings”. The drawbacks of the present model and directions for further work are also pointed out.