Abstract:
A solution of Nekrasov’s integral equation is obtained, and the range of its existence in the theory of steady nonlinear waves on the surface of a finite-depth fluid is determined. Relations are derived for calculating the wave profile and propagation velocity as functions of the ratio of the liquid depth to the wavelength. A comparison is made of the velocities obtained using the linear and nonlinear theories of wave propagation.
Keywords:
integral equation, nonlinear operator, bifurcations point, stream function, complex potential.
Citation:
T. A. Bodnar, “On steady periodic waves on the surface of a fluid of finite depth”, Prikl. Mekh. Tekh. Fiz., 52:3 (2011), 60–67; J. Appl. Mech. Tech. Phys., 52:3 (2011), 378–384
\Bibitem{Bod11}
\by T.~A.~Bodnar
\paper On steady periodic waves on the surface of a fluid of finite depth
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2011
\vol 52
\issue 3
\pages 60--67
\mathnet{http://mi.mathnet.ru/pmtf1481}
\elib{https://elibrary.ru/item.asp?id=16973530}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2011
\vol 52
\issue 3
\pages 378--384
\crossref{https://doi.org/10.1134/S0021894411030072}
Linking options:
https://www.mathnet.ru/eng/pmtf1481
https://www.mathnet.ru/eng/pmtf/v52/i3/p60
This publication is cited in the following 3 articles:
T. A. Bodnar, “Steady waves on the surface of a liquid of variable depth”, J. Appl. Mech. Tech. Phys., 62:4 (2021), 525–529
Nikolay Kuznetsov, Evgueni Dinvay, “Babenko's Equation for Periodic Gravity Waves on Water of Finite Depth: Derivation and Numerical Solution”, Water Waves, 1:1 (2019), 41
Troyan A. Bodnar, “The Conservation Laws and Stability of Fluid Waves of Permanent Form”, AM, 04:03 (2013), 486
Citation in format AMSBIB
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