Nonlinear dynamical systems as fluid flow exhibit complex behaviors. We develop mathematical methods and algorithms to identify coherent structures (CSs) that disentangle this complexity. CSs are distinct, low-dimensional surfaces that shape complex trajectory patterns, providing a simplified picture of the underlying dynamics. We show below two examples of CSs that reveal key features in oceanic dynamics and atmospheric science.

Attracting Objective Eulerian Coherent Structures (OECSs) reveal previously unknown transient attracting profiles (TRAPs) that provide critical information for search and rescue operations and oil spill containment. In collaboration with MIT, the Woods Hole Oceanographic Institution and the US Coast Guard, we verified these theoretical predictions in three ocean field experiments. 

The polar vortices play a crucial role in the formation of the ozone hole and can cause severe weather anomalies. Their boundaries, known as the vortex ‘edges’, are typically identi- fied via methods that are either frame-dependent or return non-material structures, and hence are unsuitable for assessing material transport barriers. Using two-dimensional velocity data on isentropic surfaces in the northern hemisphere, we show that elliptic Lagrangian Coherent Structures (LCSs) identify the correct outermost material surface dividing the coherent vortex core from the surrounding incoherent surf zone. Despite the purely kinematic construction of LCSs, we find a remarkable contrast in temperature and ozone concentration across the identified vortex boundary. We also show that potential vorticity-based methods, despite their simplicity, misidentify the correct extent of the vortex edge.

Collaborators: P. Sathe, Prof. F. Beron-Vera Prof. G. Haller                             

Uncovering the Edge of the Polar Vortex

Uncovering the hidden skeleton of environmental flows for hazards prediction and response

The goal of this project is to employ an integrated theoretical, computational and observational approach to develop, implement and utilize cutting-edge methods with data-driven modeling for the purpose of uncovering, quantifying and predicting key transport processes and structures during regional flow-based hazards in the ocean and atmosphere.

Joint with: MIT, UC Berkeley, Virginia Tech, WHOI &  U.S. Coast Guard

PIs and collaborators: Prof. T. Peacock (MIT) & Prof. P. Lermusiaux (MIT) 
Prof. G. Haller & P. Sathe