The Eulerian and Lagrangian Predictability of Oceanic Flows

To improve our capabilities and scientific knowledge concerning Lagrangian predictability in the ocean. Specific applications include search and rescue operations, the design of float and drifter experiments, and the understanding of stirring mechanisms. OBJECTIVES 1) To identify robust geometrical structures that help distinguish regions of inherent unpredictability (Lagrangian chaos) from predictable (regular) regions. 2) Also, to identify geographical regions in the ocean where such a separation is appropriate, i.e., where Lagrangian motion is controlled by chaotic advection and not by small-scale turbulence. APPROACH To achieve objective (1) we use idealized models of regions or processes to identify underlying geometrical structures. The geographical extent of the Lagrangian chaos and the associated stirring and transport processes are then analyzed by finding the stable manifolds of distinguish hyperbolic points in the flow field. With regard to objective (2), we calculate measures based on dynamical systems and turbulence theory that help one to distinguish between the chaotic advection regime and fully developed turbulence. These calculations are made from ocean data or from highly resolved regional ocean models. WORK COMPLETED We have made good progress in mapping out the underlying geometry and the corresponding chaotic advection fields for a number of different types of current systems. The simplest case involves a single recirculation gyre trapped to a boundary. Applications include the Alboran Gyre, the Great Whirl, and various island- and ridge-trapped eddies. The underlying heteroclinic geometry in this case is known in advance and our study (with P. Miller, K. Helfrich, and C.K.R.T. Jones) has concentrated on determining how much of the eddy is in a Lagrangian chaotic state. We have also looked into two situations in which the underlying geometry is not known in advance. The first deals with the deep western boundary current in the N. Atlantic, a flow that is now known t