Institute for Mathematics and Its Applications
Patrick Miller , Stevens Institute of Technology
Larry Pratt, Woods Hole Oceanographic Institute
Geometric methods from dynamical systems are used to study Lagrangian transport in numerically-generated, time-dependent, two-dimensional (2D) flow fields. The first calculation involves an idealized model of the Gulf Stream consisting of an unstable jet. The instability has been allowed to develop to the point of saturation, leading to a nearly-periodic, meandering state. Calculation of the stable and unstable manifolds of hyperbolic trajectories allows a lobe analysis showing fluid passing between regions of predominantly retrograde, prograde, and recirculating motion. The volume transports are comparable to those observed for Gulf Stream rings, implying that this type of transport may be important for the mixing of the Gulf Stream with its surroundings. A similar analysis is carried out in connection with a wobbling recirculation gyre located on the eastern edge of an island. Here the object is to compare the lobe transport into and out of the gyre to the transport produced by the Ekman layer. A laboratory experiment will be presented in which the unstable manifold of the gyre is visualized with dye.