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Three-dimensional analog of the Sokhotsky-Plemelj formulas and its application in the wing theory

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Abstract

A solution of a hydrodynamic problem of motion of an ideal incompressible fluid in a finite-thickness vortex layer is obtained. In the limiting case (infinitely thin layer), this layer transforms to a vortex surface. Formulas are derived for limiting values of the velocity vector of the fluid approaching this surface; these formulas extend the Sokhotsky-Plemelj formulas for a singular integral of the Cauchy type to a three-dimensional space. Three integral equations are derived on the basis of these formulas and the proposed method of modeling a finite-thickness wing by a closed vortex surface. It is shown that only one equation is left in the case of an infinitely thin wing, which corresponds to the condition of fluid non-penetration through the wing surface.

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Authors and Affiliations

  1. Omsk Department of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, 644099, Russia

    D. N. Gorelov

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  1. D. N. Gorelov
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Correspondence to D. N. Gorelov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 6, pp. 36–42, November–December, 2011.

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Gorelov, D.N. Three-dimensional analog of the Sokhotsky-Plemelj formulas and its application in the wing theory. J Appl Mech Tech Phy 52, 877–882 (2011). https://doi.org/10.1134/S0021894411060046

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  • DOI: https://doi.org/10.1134/S0021894411060046

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