Abstract
A study is made in the linear approximation, within the scope of the ideal fluid, of the asymptotic behavior of three-dimensional localized perturbations of the parameters of a shear flow which over considerable periods of time turn into growing and propagating wave packets. The behavior of the packets is studied in every possible system of coordinates moving with constant velocity parallel to the plane of the velocity shear. Mathematically, the problem reduces to using the method of steepest descent to study the asymptotic behavior of double Fourier integrals which depend parametrically on these velocities. The saddle points which determine this asymptotic behavior are found numerically. A region is indicated in a plane of flow parallel to the velocity shear which is moving and expanding linearly with time, and in which growing perturbations are found over long periods of time. The results obtained enabled us to write down the criteria for absolute and convective instability. This problem has been considered previously for flows of an ideal fluid with a shear discontinuity in the velocity [1, 2] and for flows in a wake [3].
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 8–14, March–April, 1987.
The author wishes to express his sincere gratitude to A. G. Kulikovskii for formulating the problem and for advice on numerous occasions.
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Shikina, I.S. Asymptotic behavior of localized perturbations in free shear layers. Fluid Dyn 22, 173–179 (1987). https://doi.org/10.1007/BF01052243
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DOI: https://doi.org/10.1007/BF01052243