Fluid Dynamics

, Volume 10, Issue 5, pp 768–777 | Cite as

Composite steady waves in a gravity fluid stream of finite depth

  • V. S. Potapkin


The problem of plane steady gravitational waves of finite amplitude, caused by a periodically distributed pressure over the surface of an ideal incompressible gravity fluid stream of finite depth, is considered. It is assumed that these waves do not vanish as the pressure becomes constant, but become free waves, which exist at constant pressure and special values of the stream velocity. As in [1], where a stream of finite depth is considered, such waves will be designated composite as contrasted with forced waves which vanish together with the variable part of the pressure. A general method is given for computing the composite wave characteristics. The first three approximations are computed to the end. An approximate equation for the wave profile is found.


Constant Pressure Gravitational Wave Stream Velocity Wave Characteristic Approximate Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    Ya. I. Sekerzh-Zen'kovich, “On composite, steady gravitational waves of finite amplitude,∝ Prikl. Mat. Mekh.,33, No. 4 (1969).Google Scholar
  2. 2.
    A. I. Nekrasov, Exact Theory of Steady Waves on a Gravity Fluid Surface [in Russian], Izd. Akad. Nauk SSSR, Moscow (1951).Google Scholar
  3. 3.
    M. M. Vainberg and V. A. Trenogin, “Lyapunov and Schmidt methods in the theory of nonlinear equations and their further development∝, Usp. Mat. Nauk,17, No. 2 (1962).Google Scholar
  4. 4.
    Ya. I. Sekerzh-Zen'kovich, “On a kind of steady wave of finite amplitude,∝ Prikl. Mat. Mekhan.,32, No. 6 (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • V. S. Potapkin
    • 1
  1. 1.Moscow

Personalised recommendations