Finite-Amplitude Solitary Water Waves.
Abstract
This paper considers the existence problem for solutions of the free boundary value problem which arises from the question of the existence of solitary gravity waves, moving without changes of form, and with constant velocity, on the surface of ideal fluid in a horizontal canal of finite depth. The analysis imposes no restriction on either the slope or the amplitude of the wave, and we prove that there exists a connected set of solitary waves containing waves of all slope between 0 and pi/6. It is then proved that each of these solitary waves has finite mass, and, as a consequence, that F > 1, where F is the Froude number. This, in turn, tells us that the solitary wave decays faster than exp(-alpha abs.val.(x/h), where alpha is an element or (0, alpha-bar) and 1/alpha-bar tam(alph-bar) = f-squared. Finally, it is shown that, in a certain limit, these solitary waves converge to a solitary stokes wave of greatest height, and the validity of stokes' conjecture for solitary waves is considered, but not resolved. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1979
- Accession Number
- ADA079718
Entities
People
- C. J. Amick
- J. F. Toland
Organizations
- University of Wisconsin–Madison