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JOURNALS // Prikladnaya Mekhanika i Tekhnicheskaya Fizika // Archive

Prikl. Mekh. Tekh. Fiz., 2021 Volume 62, Issue 4, Pages 3–8 (Mi pmtf124)

Steady waves on the surface of a liquid of variable depth

T. A. Bodnar

Biysk Technological Institute, 659322, Biysk, Russia

Abstract: The Nekrasov integral equation is obtained which describes the steady flow of an ideal incompressible fluid with a free surface above an uneven bottom with a wavy profile. A numerical method has been developed for solving this equation at the coordinates of the bottom profile defined in the plane of the complex variable $z = x + iy$.

Keywords: steady waves on the surface of a liquid, integral equation, Laurent series, kernel of the Nekrasov equation, conformal mapping.

UDC: 517+532

Received: 04.02.2020
Revised: 17.10.2020
Accepted: 26.10.2020

DOI: 10.15372/PMTF20210401


 English version:
Journal of Applied Mechanics and Technical Physics, 2021, 62:4, 525–529

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© Steklov Math. Inst. of RAS, 2024