T. A. Bodnar’, “Conservation Law of the Full Mechanical Energy and Stability of the Steady-State Waves on the Surface of a Fluid of Finite Depth,” In: IV All-Russian Conference with foreign participation on Free Boundary Problems: Theory, Experiment, and Applications, Biisk, 5-10 July 2011, pp. 18-19.

has been cited by the following article:

• TITLE: The Conservation Laws and Stability of Fluid Waves of Permanent Form

  AUTHORS: Troyan A. Bodnar

  KEYWORDS: Nekrasov Integral Equation; Kellogg Method; Successive Approximations Method; Wave Mechanical Energy; Wave Stability

  JOURNAL NAME: Applied Mathematics, Vol.4 No.3, March 21, 2013

  ABSTRACT: The solution of Nekrasov’s integral equation is described. By means of this solution the wave kinetic, potential, and full mechanical energies are defined as functions of fluid depth and wavelength. The wave obeys the laws of mass and energy conservation. It is found that for any constant depth of fluid the wavelength is bounded from above by a value denoted as maximal wavelength. At maximal wavelength 1) the maximum slope of the free surface of the wave exceeds 38o and the value 45o is supposed attainable,2) the wave kinetic energy vanishes. The stability of a steady wave considered as a compound pendulum is analyzed.