DEFORMATION OF SOLITARY WAVES. PART II: SHOALING.
Abstract
This report investigates the properties of a solitary wave treated as a subregion of some fixed domain. By specifying trial boundary values on this larger domain, the velocity potential of a solitary wave can be approximated. For each trial potential function compatible with the symmetry of the fluid particle flow of the solitary wave, a family of possible wave surfaces can be derived from the differential equation of the kinematic boundary condition. The dynamic condition for the free surface is used to select that surface which most closely approximates the physical wave. It is found that McCowan's equations for the steady-state solitary wave are equivalent, in this procedure, to a single dipole field in the geometry of an infinite strip. The shape of the solitary wave undergoing deformation is obtained by mapping a generalized form of the kinematic condition from the domain of deformation to the infinite strip. The introduction of the Bergmann kernel function as a coefficient of the kinematic differential equation facilitates this transformation. This report also describes the application of the single dipole field approximation to the shoaling of a solitary wave on a 45 degree slope. Not only is the point of breaking determinable, but the entire continuous deformation of the solitary wave up to the point of breaking is accessible by the above method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 05, 1964
- Accession Number
- AD0600042
Entities
People
- N. R. Wallace
Organizations
- URS Corporation