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The assimilation of a strong, two-dimensional laminar jet into an aligned uniform stream

Published online by Cambridge University Press:  14 November 2011

Graham Wilks  and
Roland Hunt
Graham Wilks
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
Roland Hunt
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
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Synopsis

A comprehensive appraisal of the title problem is presented in terms of a characterizing nondimensional co-ordinate ξ which is based upon the half excess of the momentum of the jet, J. Perturbation features of the problem appear as regular and singular boundary conditions in ξ upstream and downstream respectively. The conservation of momentum excess provides a monitor on the consistency of regular and singular perturbation series solutions. In particular the conservation constraint on the downstream singular perturbation solution confirms the inadequacy of expansions in inverse half powers of ξ and justifies formally the introduction of logarithmic terms.

The formulation provides the basis for a complete numerical integration over the semi-infinite region. Accordingly detailed knowledge of velocity excess along the axis of the jet is obtained and an undetermined coefficient in the asymptotic downstream perturbation solution may be estimated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 13 - 23
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Wygnanski, I.. The two-dimensional laminar jet in parallel streaming flow. J. Fluid Mech. 27 (1967), 431–43.CrossRefGoogle Scholar
2Stewartson, K.. On asymptotic expansions in the theory of boundary layers. J. Math. Phys. 36 (1957), 173–191.Google Scholar
3Hunt, R. and Wilks, G.. Continuous transformation computation of boundary layer equations between similarity regimes. J. Comput. Phys., to appear.Google Scholar
4Keller, H. B. and Cebeci, T.. Accurate numerical methods for boundary layer flows. I. Two dimensional laminar flows. Proc. Int. Conf. Numer. Math. Fluid. Dyn., 2nd, Berkeley, California, 1971. Lecture Notes in Physics 8 (New York: Springer, 1971).Google Scholar
5Keller, H. B.. Numerical methods in boundary layer theory. Annual Rev. Fluid Mech. 10 (1978), 417–433.CrossRefGoogle Scholar