Integrated Computation of Finite Time Lyapunov Exponent During ...
Integrated Computation of Finite Time Lyapunov Exponent During ...
Integrated Computation of Finite Time Lyapunov Exponent During ...
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Introduction<br />
<strong>Finite</strong> <strong>Time</strong> <strong>Lyapunov</strong> <strong>Exponent</strong> (FTLE)<br />
Avg. stretching rate <strong>of</strong> initially adjacent tracers over finite time.<br />
Ridges show strong correspondence with Lagrangian coherent<br />
structures (LCS): Invariant transport barriers, skeleton <strong>of</strong> tracer<br />
patterns. [Haller, 2001, Shadden et al., 2005]<br />
Relatively modern FTLE/LCS theory contributed new understanding to<br />
many fields<br />
Typically computed via algorithmically simple, computationally<br />
expensive post-processing <strong>of</strong> experimental/numerical data<br />
Enormous number <strong>of</strong> particle advections<br />
Careful memory management.<br />
Fewer velocity fields ⇒ more uncertainty.<br />
Speedup possible: AMR [Miron et al., 2012], Ridge<br />
tracking [Lipinski and Mohseni, 2010], GPU<br />
acceleration [Conti et al., 2012],<br />
Repelling<br />
trajectories [Shadden et al., 2005]<br />
Atmospheric events [Lekien and Ross, 2010] Granular flow in a tumbler [Christov et al., 2011]<br />
Startup <strong>of</strong> a swimming<br />
fish [Conti et al., 2012]<br />
Finn & Apte FTLE & DNS Integration 2
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