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On the instabilities of supersonic mixing layers - A high-Mach-number asymptotic theoryThe stability of a family of tanh mixing layers is studied at large Mach numbers using perturbation methods. It is found that the eigenfunction develops a multilayered structure, and the eigenvalue is obtained by solving a simplified version of the Rayleigh equation (with homogeneous boundary conditions) in one of these layers which lies in either of the external streams. This analysis leads to a simple hypersonic similarity law which explains how spatial and temporal phase speeds and growth rates scale with Mach number and temperature ratio. Comparisons are made with numerical results, and it is found that this similarity law provides a good qualitative guide for the behavior of the instability at high Mach numbers. In addition to this asymptotic theory, some fully numerical results are also presented (with no limitation on the Mach number) in order to explain the origin of the hypersonic modes (through mode splitting) and to discuss the role of oblique modes over a very wide range of Mach number and temperature ratio.
Document ID
Document Type
Reprint (Version printed in journal)
Balsa, Thomas F. (Arizona, University Tucson, United States)
Goldstein, M. E. (NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
August 14, 2013
Publication Date
July 1, 1990
Publication Information
Publication: Journal of Fluid Mechanics
Volume: 216
ISSN: 0022-1120
Subject Category
Distribution Limits