A New Mixing Diagnostic and Gulf Oil Spill Movement

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.

A dynamical systems perspective for a real-time response to a marine oil spill

“…Another perspective is the direct computation of manifolds [13,14,15], which has also provided valuable insight into oceanic problems [16,17]. Other approaches in this field have been the geodesic 100 4 and variational theories of LCS [18,19], the trajectory complexity measures [20], mesohyperbolicity measures and ergodic partitions [21,22] and transfer operator methods [23,24]. Lagrangian tools have provided in the past interesting insights into oceanic problems related to oil spills and pollutant release.…”

“…Lagrangian tools have provided in the past interesting insights into oceanic problems related to oil spills and pollutant release. For instance, they have been applied to the release of organic contaminants in the 105 coast of Florida [25] or to the Gulf oil spill disaster after the Deepwater Horizon oil rig explosion in 2010 [22].…”

An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method

“…Further examples include population genetics, distribution of nutrients, oil spills and the prediction of the weather. [1][2][3][4][5][6] Spectral analysis has become popular for the investigation of scalar transport in such flows, as the governing advection-diffusion equation is linear and thus amenable to characterization in terms of the eigenvalues and eigenvectors of the evolution operator. 7 Analysis of its spectral structure has been performed in Cerbelli et al 8 and revealed an exponential decay of the scalar field towards a homogeneous asymptotic state.…”

New Lagrangian diagnostics for characterizing fluid flow mixing

“…Some of the Lagrangian characteristics present the resulting observable after a certain integration time, with no information regarding the intermediate time dynamics (e.g. the AD and RD fields depend only on the initial and final location of the particles), whereas some of the other Lagrangian characteristics use averaging or integration along the trajectories [3,17,26,[33][34][35]. These Lagrangian fields are commonly used to identify regions of small and enhanced stretching and, in particular, are used to identify the spatial position of dividing surfaces between different regions, the Lagrangian Coherent Structures (LCS) [2,26,27].…”

“…Visualizing and quantifying mixing in unsteady fluid flows is a magical and tricky business, with important practical implications including larval dispersion and population connectivity [1,2], oil spills [3,4], search and rescue [5,6], functioning of the marine ecological system [7] and more [8]. By now there are many tools to visualize and analyze mixing properties of flows and maps [9][10][11][12][13][14][15][16][17].…”