Identifying dynamical boundaries and phase space transport using Lagrangian coherent structures

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dc.contributor.authorTallapragada, Phanindraen
dc.contributor.committeechairRoss, Shane D.en
dc.contributor.committeememberSchmale, David G. IIIen
dc.contributor.committeememberPaul, Mark R.en
dc.contributor.committeememberStremler, Mark A.en
dc.contributor.committeememberHendricks, Scott L.en
dc.contributor.departmentEngineering Science and Mechanicsen
dc.date.accessioned2014-03-14T20:15:59Zen
dc.date.adate2010-09-22en
dc.date.available2014-03-14T20:15:59Zen
dc.date.issued2010-08-24en
dc.date.rdate2010-09-22en
dc.date.sdate2010-09-07en
dc.description.abstractIn many problems in dynamical systems one is interested in the identification of sets which have qualitatively different fates. The finite-time Lyapunov exponent (FTLE) method is a general and equation-free method that identifies codimension-one sets which have a locally high rate of stretching around which maximal exponential expansion of line elements occurs. These codimension-one sets thus act as transport barriers. This geometric framework of transport barriers is used to study various problems in phase space transport, specifically problems of separation in flows that can vary in scale from the micro to the geophysical. The first problem which we study is of the nontrivial motion of inertial particles in a two-dimensional fluid flow. We use the method of FTLE to identify transport barriers that produce segregation of inertial particles by size. The second problem we study is the long range advective transport of plant pathogen spores in the atmosphere. We compute the FTLE field for isobaric atmospheric flow and identify atmospheric transport barriers (ATBs). We find that rapid temporal changes in the spore concentrations at a sampling point occur due to the passage of these ATBs across the sampling point. We also investigate the theory behind the computation of the FTLE and devise a new method to compute the FTLE which does not rely on the tangent linearization. We do this using the 925 matrix of a probability density function. This method of computing the geometric quantities of stretching and FTLE also heuristically bridge the gap between the geometric and probabilistic methods of studying phase space transport. We show this with two examples.en
dc.description.degreePh. D.en
dc.identifier.otheretd-09072010-235513en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-09072010-235513/en
dc.identifier.urihttp://hdl.handle.net/10919/28891en
dc.publisherVirginia Techen
dc.relation.haspartthesis4.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectpunctuated changesen
dc.subjectMaxey Riley equationen
dc.subjectinertial particles.en
dc.subjectLagrangian coherent structuresen
dc.subjectLyapunov exponentsen
dc.subjectphase space transporten
dc.subjectatmospheric transport barriersen
dc.titleIdentifying dynamical boundaries and phase space transport using Lagrangian coherent structuresen
dc.typeDissertationen
thesis.degree.disciplineEngineering Science and Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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