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On the interaction of stationary crossflow vortices and Tollmien-Schlichting waves in the boundary layer on a rotating discThere are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete among themselves. The interaction is considered of two types of instability mode (at an asymptotically large Reynolds number) which can occur in the flow above a rotating disc. In particular, the interaction is examined between lower branch Tollmien-Schlichting (TS) waves and the upper branch, stationary, inviscid crossflow vortex whose asymptotic structure has been described by Hall (1986). This problem is studied in the context of investigating the effect of the vortex on the stability characteristics of a small TS wave. Essentially, it is found that the primary effect is felt through the modification to the mean flow induced by the presence of the vortex. Initially, the TS wave is taken to be linear in character and it is shown (for the cases of both a linear and a nonlinear stationary vortex) that the vortex can exhibit both stabilizing and destabilizing effects on the TS wave and the nature of this influence is wholly dependent upon the orientation of this latter instability. Further, the problem is examined with a larger TS wave, whose size is chosen so as to ensure that this mode is nonlinear in its own right. An amplitude equation for the evolution of the TS wave is derived which admits solutions corresponding to finite amplitude, stable, traveling waves.
Document ID
19900000691
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Bassom, Andrew P. (Institute for Computer Applications in Science and Engineering Hampton, VA, United States)
Hall, Philip (Institute for Computer Applications in Science and Engineering Hampton, VA, United States)
Date Acquired
September 6, 2013
Publication Date
May 1, 1989
Subject Category
Aerodynamics
Report/Patent Number
ICASE-89-34
NAS 1.26:181859
NASA-CR-181859
Accession Number
90N10007
Funding Number(s)
CONTRACT_GRANT: NAS1-18605
PROJECT: RTOP 505-90-21-01
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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