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Riahi, Daniel N. Vonderwell, Mark Phillip 2011-05-07T13:18:55Z 2011-05-07T13:18:55Z 10000-01-01 1995 The roles of weakly nonlinear triad interactions and the self-interaction of primary instabilities in the transition-to-turbulence process in three-dimensional boundary layers are investigated. Resonant triad interactions are studied in the boundary layer on the leading edge of a swept wing under typical commercial jet cruise conditions. Both compressible and incompressible models are developed using the method of multiple scales and a spectral collocation numerical method. Detuning parameters for the wavenumbers and frequencies and the effects of the growth of the boundary layer are included in the modeling. The spatial and temporal growth of numerous triads consisting of different combinations of crossflow (CF) and Tollmein-Schlichting (TS) modes are studied for a specific laminar flow control wing. Calculations using the model indicate that the spatial evolution of the triad amplitudes is strongly dependent upon the initial spectrum of amplitudes and phases. Specific predictions are impossible without this information, but general conclusions regarding interaction strength are possible. Calculations indicate that triads consisting of three crossflow modes are abundant, but the interaction between the modes is relatively weak. Triads with two TS modes and one CF mode are also numerous and the interaction may strongly affect the CF mode. Comparison of results from the compressible and incompressible theories show significant differences in some cases. Compressibility is stabilizing to individual modes and usually weakens the interactions among them as well. Nonparallel effects are usually destabilizing according to both models and may significantly affect the evolution of the triad amplitudes. The self-interaction of disturbances is investigated in the three-dimensional boundary layer over a rotating disk. The method of multiple scales is used to model the weakly nonlinear growth of the critical stationary crossflow mode. The Landau constant is evaluated using a spectral collocation numerical method. Results indicate that nonlinearity is destabilizing, so subcritical instability and super-exponential growth is possible. Made available in DSpace on 2011-05-07T13:18:55Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543758.pdf: 5275573 bytes, checksum: 7509f056a04c4a1e85bd59ddf52701a1 (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:53:09Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:24:33-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9543758 (UMI)AAI9543758 http://hdl.handle.net/2142/21780 eng Copyright 1995 Vonderwell, Mark Phillip Applied Mechanics Engineering, Aerospace Wave interactions in three-dimensional boundary layers text Mechanical Science and Engineering Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign Dissertation Ph.D.