Analysis of Lagrangian Coherent Structures of the Chesapeake Bay

Numerical lagrangian analysis of the Chesapeake Bay can reveal dynamical features not obtainable through analytical means. These features can indicate coherent structures within the Bay, revealing neighboring regions of fluid that have very different behaviors. Given the model-based discrete velocity data of the bay, obtained through the use of the Regional Ocean Modeling System (ROMS), we implement bilinear and bicubic spatial interpolation methods and a 3 order lagrangian polynomial to interpolate in time. This interpolation allows us to calculate trajectories of ∼1 million initial conditions, using a 5 order Runge Kutta Fehlberg method and a 4 order Runge Kutta method. From these trajectories, we apply both a deterministic method and a probabilistic method to identify coherent structures in the flow field. We validate interpolation methods against analytic functions and integration methods against ordinary differential equations with analytic solutions. The deterministic method is validated using the Duffing equation while the probabilistic method is validated using results from [7]. Lastly we apply our methods to a modeled flow field of the Chesapeake Bay and compare the results of the two methods.