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Secondary instability in boundary-layer flowsThe stability of a secondary Tollmien-Schlichting wave, whose wavenumber and frequency are nearly one half those of a fundamental Tollmien-Schlichting instability wave is analyzed using the method of multiple scales. Under these conditions, the fundamental wave acts as a parametric exciter for the secondary wave. The results show that the amplitude of the fundamental wave must exceed a critical value to trigger this parametric instability. This value is proportional to a detuning parameter which is the real part of k - 2K, where k and K are the wavenumbers of the fundamental and its subharmonic, respectively. For Blasius flow, the critical amplitude is approximately 29% of the mean flow, and hence many other secondary instabilities take place before this parametric instability becomes significant. For other flows where the detuning parameter is small, such as free-shear layer flows, the critical amplitude can be small, thus the parametric instability might play a greater role.
Document ID
19790052388
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Nayfeh, A. H.
(Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
Bozatli, A. N.
(Virginia Polytechnic Institute and State University Blacksburg, Va., United States)
Date Acquired
August 9, 2013
Publication Date
May 1, 1979
Publication Information
Publication: Physics of Fluids
Volume: 22
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
AD-A074792
Accession Number
79A36401
Funding Number(s)
PROJECT: NR PROJECT 061-201
OTHER: NSG-1255
Distribution Limits
Public
Copyright
Other

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