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dc.contributor.advisorTumin, Anatoli M.en_US
dc.contributor.authorForgoston, Eric T.
dc.creatorForgoston, Eric T.en_US
dc.date.accessioned2011-12-06T14:08:10Z
dc.date.available2011-12-06T14:08:10Z
dc.date.issued2006en_US
dc.identifier.urihttp://hdl.handle.net/10150/195810
dc.description.abstractAn initial-value problem is formulated for a three-dimensional perturbation in a compressible boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature factor effects. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using the analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using a Gaussian model as well as the method of steepest descent. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation. Using the inverse Fourier transform computations, the development of the wave packet is studied, including effects due to Reynolds number, Mach number and temperature factor.
dc.language.isoENen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.titleInitial-Value Problem for Perturbations in Compressible Boundary Layersen_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.contributor.chairTumin, Anatoli M.en_US
dc.identifier.oclc137356327en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.contributor.committeememberBalsa, Thomas F.en_US
dc.contributor.committeememberBrio, Moyseyen_US
dc.contributor.committeememberKerschen, Edward J.en_US
dc.contributor.committeememberTumin, Anatoli M.en_US
dc.contributor.committeememberZackharov, Vladimiren_US
dc.identifier.proquest1513en_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.namePhDen_US
refterms.dateFOA2018-06-29T03:45:02Z
html.description.abstractAn initial-value problem is formulated for a three-dimensional perturbation in a compressible boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature factor effects. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using the analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using a Gaussian model as well as the method of steepest descent. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation. Using the inverse Fourier transform computations, the development of the wave packet is studied, including effects due to Reynolds number, Mach number and temperature factor.


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