Solitary and Periodic Gravity-Capillary Waves of Finite Amplitude.
Abstract
Two dimensional solitary and periodic waves in water of finite depth are considered. The wave propagate under the combined influence of gravity and surface tension. The flow, the surface profile, and the phase velocity are functions of the amplitude of the wave and parameters l = lambda/H and tau = T/g(H squared). Here lambda is the wavelength, H the depth, T the surface tension, rho the density and g the gravity. For small values of l and small values of the amplitude, the profile of the wave satisfies the Korteweg de Vries equation approximately. However, for tau close to 1/3 this equation becomes invalid. In the present paper a new equation valid for tau close to 1/3 is obtained. Moreover, a numerical scheme based on an integro-differential equation formulation is derived to solve the problem in the fully nonlinear case. Accurate solutions for periodic and solitary waves are presented. In addition, the limiting configuration for large amplitude solitary waves when tau > 1/2 is found analytically. Graphs of the results are included.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1982
- Accession Number
- ADA120984
Entities
People
- J. K. Hunter
- J.-m. Vanden-broeck
Organizations
- University of Wisconsin–Madison