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Finite disturbance effect on the stability of a laminar incompressible wake behind a flat plate

Published online by Cambridge University Press:  29 March 2006

D. Ru-Sue Ko ,
T. Kubota  and
L. Lees
D. Ru-Sue Ko
Affiliation:
California Institute of Technology, Pasadena, California
T. Kubota
Affiliation:
California Institute of Technology, Pasadena, California
L. Lees
Affiliation:
California Institute of Technology, Pasadena, California
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Abstract

An integral method is used to investigate the interaction between a two-dimensional, single frequency finite amplitude disturbance in a laminar, incompressible wake behind a flat plate at zero incidence. The mean flow is assumed to be a non-parallel flow characterized by a few shape parameters. Distribution of the fluctuation across the wake is obtained as functions of those mean flow parameters by solving the inviscid Rayleigh equation using the local mean flow. The variations of the fluctuation amplitude and of the shape parameters for the mean flow are then obtained by solving a set of ordinary differential equations derived from the momentum and energy integral equations. The interaction between the mean flow and the fluctuation through Reynolds stresses plays an important role in the present formulation, and the theoretical results show good agreement with the measurements of Sato & Kuriki (1961).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 2 , 3 February 1970 , pp. 315 - 341
Copyright
© 1970 Cambridge University Press

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References

Gold, H. 1963 Stability of laminar wakes. Ph.D. Thesis, California Institute of Technology.
Goldstein, S. 1933 On the two-dimensional steady flow of a viscous fluid behind a solid body. Part. I. Proc. Boy. Soc. Lond. A 142, 545.Google Scholar
Kuwabara, S. 1967 Nonlinear instability of plane Couette flow. Phys. of Fluid. Supplement Copy on Boundary Layer and Turbulence 10: 9, Part II, S 115.Google Scholar
Landau, L. 1944 Stability of tangential discontinuity in compressible fluid. C.R. (Doklady) Acad. Sci. U.S.S.R. 44, 311.Google Scholar
McKoen, C. H. 1955 On the stability of a laminar wake. ARC CP 303.Google Scholar
Meksyn, D. & Stuart, J. T. 1951 Stability of viscous motion between parallel planes for finite disturbances. Proc. Roy. Soc. Lond. A 208, 517.Google Scholar
Sato, H. & Kuriki. K. 1961 The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11, 321.Google Scholar
Stuart, J. T. 1956 On the role of the Reynolds stresses in stability theory. J. Aero. Sci. 23, 86.Google Scholar
Stuart, J. T. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 1.Google Scholar
Stuart, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behaviour in plane Poiseuille flow. J. Fluid Mech. 9, 353.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. Lond. A 223, 289.Google Scholar
Watson, J. 1960 On the non-linear 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.Google Scholar
Watson, J. 1962 On spatially-growing finite disturbances in plane Poiseuille flow. J. Fluid Mech. 14, 211.Google Scholar