A New Mixing Diagnostic and Gulf Oil Spill Movement

TLDR

Chaotic advection, characterized by invariant attracting and repelling manifolds, serves as the paradigm for mixing in fluid flows with simple time dependence. The study develops a finite‑time theory for two‑dimensional incompressible fluid flows with arbitrary time dependence and introduces a new mixing diagnostic. The finite‑time theory defines a diagnostic that detects stretching events around invariant manifolds, identifies hyperbolic mixing zones, and enables forecasting of oil movement. Applying the diagnostic, the authors forecasted the spatial location and timing of oil washing ashore in Plaquemines Parish, Grand Isle, and Pensacola in May 2010, and the flow toward Panama City Beach in June 2010.

Abstract

Chaotic advection has served as the paradigm for mixing in fluid flows with simple time dependence. Its skeletal structure is based on analysis of invariant attracting and repelling manifolds in fluid flows. Here we develop a finite-time theory for two-dimensional incompressible fluid flows with arbitrary time dependence and introduce a new mixing diagnostic based on it. Besides stretching events around attracting and repelling manifolds, this allows us to detect hyperbolic mixing zones. We used the new diagnostic to forecast the spatial location and timing of oil washing ashore in Plaquemines Parish and Grand Isle, Louisiana, and Pensacola, Florida, in May 2010 and the flow of oil toward Panama City Beach, Florida, in June 2010.