Trajectory and Invariant Manifold Computation for Flows in the Chesapeake Bay
Abstract
The field of mathematics known as dynamical systems theory has seen great progress in recent years. A number of techniques have been developed for computation of dynamical systems structures based on a data set of a given flow, specifically Distinguished Hyperbolic Trajectories (DHTs) and their invariant manifolds. In this project, algorithms in MATLAB have been successfully implemented and applied to a number of test problems, as well as to the Chesapeake Bay flow data generated by the QUODDY shallow-water finite-element model. A number of interesting discoveries have been made including instabilities of convergence of the DHT algorithm and evidence of lobe dynamics in the Chesapeake. Additionally, MATLAB code has been developed to compute Synoptic Lagrangian Maps (SLMs). When applied to an oceanographic flow, SLMs produce plots of the time that it takes particles in various regions to encounter the coast or escape to the open ocean. Such maps are of interest to the oceanography community. A new algorithm for SLM computation has been developed resulting in orders of magnitude increase in efficiency. Previously SLM computation for a week of flow data was a problem limited to massively parallel supercomputers. With the new algorithm, similar data is computed in a few days on a single processor machine. The development of platform-independent MATLAB implementation of the algorithms for computation of DHTs, invariant manifolds and SLMs should prove valuable tools for studying the dynamics of complex oceanographic flows.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 09, 2005
- Accession Number
- ADA437130
Entities
People
- Nathan F. Brasher
Organizations
- United States Naval Academy