On the Shore Singularity of Water-Wave Theory. Part 2. Small Waves Don't Break on Gentle Beaches.
Abstract
The model of gravitational surface waves on beaches of small slope formulated in and its mathematical theory are used to show how an incident-wave amplitude can be defined so that a bound on it guarantees solutions which respect the assumptions of the model everywhere and forever. The structure of those solutions far from shore is then compared with that predicted near shore by the classical, linear theory to remove the indeterminacies of both theories: Shore reflection is determined for the classical theory, and it is shown how the critical length scale and amplitude of the beach theory are related to the familiar wavelength and amplitude in deep water. These results indicate that the beach theory captures and elucidates the basic singularity structure underlying the shore behavior of gravitational surface waves. Keywords: Amplitude bounds; Beach erosion; Army Corps of Engineers. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1985
- Accession Number
- ADA163652
Entities
People
- R. E. Meyer
Organizations
- University of Wisconsin–Madison