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Tollmien—Schlichting wave/Dean vortex interactions in curved channel flow

Published online by Cambridge University Press:  26 April 2006

Bart A. Singer  and
Thomas A. Zang
Bart A. Singer
Affiliation:
High Technology Corporation, Hampton, VA 23666, USA
Thomas A. Zang
Affiliation:
NASA Langley Research Center, Hampton, VA 23665, USA
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Abstract

Evidence from direct numerical simulations and from a recent weakly nonlinear theory is presented which shows that the weakly nonlinear results of Daudpota, Hall & Zang (1988) make incorrect predictions for the influence of the Tollmien–Schlichting wave on the Dean vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 681 - 684
Copyright
© 1992 Cambridge University Press

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References

Bennett, J., Hall, P. & Smith, F. T. 1991 The strong nonlinear interaction of Tollmien—Schlichting waves and Taylor—Görtler vortices in curved channel flows. J. Fluid Mech. 223, 475–495.Google Scholar
Daudpota, Q. I., Hall, P. & Zang, T. A. 1988 On the nonlinear interaction of Görtler vortices and Tollmien—Schlichting waves in curved channel flows at finite Reynolds numbers. J. Fluid Mech. 193, 569–595 (referred to herein as DHZ).Google Scholar
Herbert, Th. 1980 Nonlinear stability of parallel flows by high-order amplitude expansions. AIAA J. 18, 243–248.Google Scholar
Herbert, Th. 1983 On perturbation methods in nonlinear stability theory. J. Fluid Mech. 126, 167–186.Google Scholar
Singer, B. A., Erlebacher, G. & Zang, T. A. 1992 A weakly nonlinear theory for wave—vortex interactions in curved channel flow. NASA Tech. Paper 3158.Google Scholar
Singer, B. A. & Zang, T. A. 1989 Direct numerical simulations of Tollmien—Schlichting/Dean interactions. NASA Tech. Paper 2919.Google Scholar
Stuart, J. T. 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behaviour in plane Poiseuille flow. J. Fluid Mech. 9, 353–370.Google Scholar
Watson, J. 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow. J. Fluid Mech. 9, 371–389.Google Scholar
Zang, T. A. 1991 On the rotation and skew-symmetric forms for incompressible flow simulations. Appl. Numer. Maths 7, 27–40.Google Scholar
Zang, T. A. & Hussaini, M. Y. 1986 On spectral multigrid methods for the time-dependent Navier Stokes equations. Appl. Math. Comput. 19, 359–372.Google Scholar