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Eigenvalues in trailing edge flows

Published online by Cambridge University Press:  09 April 2009

K. Capell
Affiliation:
Department of MathematicsUniversity of Queensland, Australia
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Abstract A wake similarity solution for symmetric uniform shear flows merging at the trailing edge of a flat plate has associated with it an eigenfunction problem which was overlooked by Hakkinen and O'Neil (1967). An asymptotic formula for large eigenvalues is obtained and compared with another such formula related to both the Goldstein (1930) inner wake solution and Tillett's (1968) similarity solution for a jet emerging from a two-dimensional channel.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

Antosiewicz, H. A. (1964), Bessel functions of fractional order, Handbook of mathematical functions with formulas, graphs and mathematical tables, 435578 (edited by Milton, Abramowitz and Irene, A. Stegun. National Bureau of Standards Applies Mathematics Series 55. United States Department of Commerce, 1964; reprinted Dover, New York, 1965).Google Scholar
Brown, S. N. (1968), ‘An asymptotic expansion for the eigenvalues arising in perturbations about the Blasius solution’. Appl. Sci. Res. 19, 111119.CrossRefGoogle Scholar
Brown, S. N. and Stewartson, K. (1965), ‘On similarity solutions of the boundary-layer equations with algebraic decay’, J. Fluid Mech. 23, 673687.CrossRefGoogle Scholar
Capell, K. (1972), ‘Asymptotic analysis of a linearized trailing edge flow’, Bull. Austral. Math. Soc. 6, 327347.CrossRefGoogle Scholar
Cole, J. D. (1968), Perturbation methods in applied mathematics. (Waltham, Massachusetts; Blaisdell).Google Scholar
Goldstein, S. (1930), ‘Concerning some solutions of the boundary layer equations in hydrodynamics’, Proc. Cambridge Philos. Soc. 26, 130.CrossRefGoogle Scholar
Hakkinen, R. J. and O'Neil, Elizabeth (1967), On the merging of uniform shear flows at a trailing edge, (Douglas Aircraft Co. Report DAC-60862).Google Scholar
Libby, P. A. and Fox, H. (1963), ‘Some perturbation solutions in laminar boundary-layer theory. Part 1. The momentum equation’, J. Fluid Mech. 17, 433449.CrossRefGoogle Scholar
Messiter, A. F. (1970), ‘Boundary-layer flow near the trailing edge of a flat plate’, SIAM J. Appl. Math. 18, 241257.CrossRefGoogle Scholar
Price, J. P. (1968), Ph. D. thesis, (University College, London (1968)).Google Scholar
Rott, N. and Hakkinen, R. J., (1965) Numerical solutions for merging shear flows, (Douglas Aircraft Co. Report SM-47809).Google Scholar
Stewartson, K. (1957), ‘On asymptotic expansions in the theory of boundary layers’, J. Math. and Physics 36, 173191.CrossRefGoogle Scholar
Stewartson, K. (1968), ‘On the flow near the trailing edge of a flat plate’, Proc. Roy. Soc. London Ser. A 306, 275290.Google Scholar
Stewartson, K. (1969), ‘On the flow near the trailing edge of a flat plat II’, Mathematika 16, 106121.CrossRefGoogle Scholar
Tillett, J. P. K. (1968), ‘On the laminar flow in a free jet of liquid at high Reynolds number’. J. Fluid Mech. 32, 273292.CrossRefGoogle Scholar