The past two decades have seen significant advances in the development of dynamical systems (DS) theory and its use in the interpretation and quantification of stirring and transport processes in geophysical fluid dynamics, and also in the closely related field of Lagrangian data assimilation. Theory and application so far have been restricted to time-varying flows that are spatially 2D. We propose to extend the theory and analysis to time-varying velocity fields that exhibit the full three-dimensional spatial structure (3D+1) thought to be important within ocean mesoscale-to-submesoscale range (roughly 50km down to 1km or less). A team with a wide range of expertise, including applied mathematics, dynamical systems, data assimilation, statistics, geophysical fluid dynamics, ocean modeling, and ocean data analysis will collaborate on an organized plan to develop the concepts the methodology appropriate to 3D+1 space and to apply the methodology to ocean applications of interest to DoD. One subgroup will develop approaches for the construction of Lagrangian coherent structures in 3D+1; another will extend 2D+1 filters and algorithms for Lagrangian data assimilation to 3D+1. These efforts are linked by the fact that data assimilation benefits from knowledge of the location of stable and unstable manifolds. A third subgroup will explore idealized and realistic applications of each approach in an attempt to test the methodology, to determine the parameter space over which full 3D+1 analysis is necessary, to render 3D views of chaotic transport processes, and to explore dynamical processes such as the establishment of upper ocean stratification. Consequences for Navy forecast models and navigation of underwater vehicles in complex flow fields will also be considered.
|Effective start/end date||10/1/10 → 3/31/17|
- Woods Hole Oceanographic Institution