Abstract
A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the stationary solution of a Rayleigh-type equation, which describes oscillations of the vertical velocity component in the classical boundary layer.
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References
V. G. Danilov and R. K. Gaydukov, “Vortexes in the Prandtl boundary layer induced by irregularities on a plate,” Russian J. Math. Phys. 22 (2) (2015).
V. G. Danilov and M. V. Makarova, “Asymptotic and numerical analysis of the flow around a plate with small periodic irregularities,” Russian J. Math. Phys. 2 (1) (1994).
L. Rayleigh, “On the stability or instability of certain fluid motions,” Proc. LondonMath. Soc. 11 (1880).
V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin–New York, 1989).
H. Schlichting and K. Gersten, Boundary Layer Theory (Springer-Verlag, Berlin–New York, 2000).
J. P. Boyd, “The Blasius function: ?omputations before computers, the value of tricks, undergraduate projects, and open research problems,” SIAM Review 50 (4) (2008).
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Borisov, D.I., Gaydukov, R.K. Existence of the stationary solution of a Rayleigh-type equation. Math Notes 99, 636–642 (2016). https://doi.org/10.1134/S0001434616050023
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DOI: https://doi.org/10.1134/S0001434616050023