Abstract
If the speed of the outer flow at the edge of the boundary layer does not depend on the time and is specified in the form of a power-law function of the longitudinal coordinate, then a self-similar solution of the boundary-layer equations can be found by integrating a third-order ordinary differential equation (see [1–3]). When the exponent of the power in the outerflow velocity distribution is negative, a self-similar solution satisfying the equations and the usually posed boundary conditions is not uniquely determinable [4], A similar result was obtained in [5] for flows of a conducting fluid in a magnetic field. In the present paper we study the behavior of non-self-similar perturbations of a self-similar solution, enabling us to provide a basis for the choice of a self-similar solution.
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Literature cited
N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydromechanics, Wiley (1964).
L. G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon (1966).
V. M. Falkner and S. W. Skan, Some Approximate Solutions of the Boundary Layer Equations, Aeronaut. Res. Committee, Repts. and Mem., No. 1314 (1930).
D. R. Hartree, “On an equation occurring in Falkner and Skan's [Approximate treatment of the equations of the boundary layer],∝ Proc. Cambr. Phil. Soc.,33, pt 1, 2 (1937).
A. V. Gotovtsev, “Separated self-similar flows in a laminar magnetohydrodynamic boundary layer with blowing and suction,∝ Izv. Akad. Nauk SSSR, Mekhan. Zhidk. Gaza, No. 3 (1972).
J. Heading, An Introduction to Phase Integral Methods, Wiley (1962).
A. G. Kulikovskii, “On the stability of homogeneous states,∝ Prikl. Matem. Mekhan.,30, No. 1 (1966).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–46, July–August, 1974.
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Kulikovskii, A.G., Slobodkina, F.A. Choice of a self-similar solution in boundary-layer theory. Fluid Dyn 9, 536–539 (1974). https://doi.org/10.1007/BF01031309
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DOI: https://doi.org/10.1007/BF01031309