Lobe dynamics in a kinematic model of a meandering jet. I. Geometry and statistics of transport and lobe dynamics with accelerated convergence

In geophysical fluid mechanics a meandering jet is a fundamental flow structure arising in a variety of diverse settings. In this paper we apply the method of lobe dynamics to study transport associated with a kinematic model of a meandering jet. We describe in detail the geometric structure of cross jet transport. In particular, we describe the mechanisms for particles to cross the jet, to enter the jet from a certain region and to leave it by exiting into the same region, and to escape from the jet, all in terms of lobe dynamics. Furthermore, we are able to derive a number of statistical quantities in terms of lobe dynamics, such as the average time to cross the jet for particles entering the jet and the average residence time for particles in the jet. These statistical quantities are expressed in terms of infinite series of areas of intersections of turnstile lobes. We develop a procedure for achieving “accelerated convergence” of these series which yields a good approximation to the exact result with a low order truncation of the series.