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On the Nonlinear Development of Görtler Vortices in a Compressible Boundary Layer
Author(s) -
Wadey P. D.
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1991854317
Subject(s) - vortex , compressibility , boundary layer , incompressible flow , compressible flow , instability , wavenumber , nonlinear system , flow (mathematics) , mathematics , bounded function , classical mechanics , physics , mechanics , boundary (topology) , mathematical analysis , optics , quantum mechanics
The nonlinear development of the Görtler instability in compressible boundary layers on curved walls is considered for vortices of asymptotically large wavenumber. The starting point for our calculations lies in the work of Hall and Lakin ( Proc. Roy. Soc. London Ser. A 415:421–444), where the incompressible results were formulated. Without neglecting downstream partial derivatives, the initial development of a vortex from the point where it first starts to grow is calculated. It is shown how the same basic structure that occurs in incompressible flow exists, where the disturbance is confined to a core region bounded above and below by thin shear layers, but that the flow in the core region is of more complicated form than that for incompressible flow.