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dc.contributor.authorTallapragada, Phanindraen_US
dc.date.accessioned2014-03-14T20:15:59Z
dc.date.available2014-03-14T20:15:59Z
dc.date.issued2010-08-24en_US
dc.identifier.otheretd-09072010-235513en_US
dc.identifier.urihttp://hdl.handle.net/10919/28891
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_US
dc.publisherVirginia Techen_US
dc.relation.haspartthesis4.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectpunctuated changesen_US
dc.subjectMaxey Riley equationen_US
dc.subjectinertial particles.en_US
dc.subjectLagrangian coherent structuresen_US
dc.subjectLyapunov exponentsen_US
dc.subjectphase space transporten_US
dc.subjectatmospheric transport barriersen_US
dc.titleIdentifying dynamical boundaries and phase space transport using Lagrangian coherent structures.en_US
dc.typeDissertationen_US
dc.contributor.departmentEngineering Science and Mechanicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineEngineering Science and Mechanicsen_US
dc.contributor.committeechairRoss, Shane Daviden_US
dc.contributor.committeememberSchmale, David G. IIIen_US
dc.contributor.committeememberPaul, Mark R.en_US
dc.contributor.committeememberStremler, Mark A.en_US
dc.contributor.committeememberHendricks, Scott L.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-09072010-235513/en_US
dc.date.sdate2010-09-07en_US
dc.date.rdate2010-09-22
dc.date.adate2010-09-22en_US


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