A Unified Model for the Evolution of Nonlinear Water Waves.
Abstract
This paper gives details of a new model of water waves that describes wave propagation over long distances accurately, at low cost, and for a wide variety of physical situations. The analysis and numerical methods selected for computer solution are given in some detail. The model uses exact prognostic equations, and a high order expansion to relate variables at each time step. The accuracy of the model is demonstrated most completely for solitary wave propagation, where model results are compared to exact results. It is found that the model results are much more accurate for high solitary waves than are earlier, Boussinesq-type theories, and give good results for waves so high that they are almost breaking. The capability of the model to treat a variety of situations is demonstrated for colliding solitary waves, nonlinear dispersive wave trains, waves in channels of varying breadth, and undular bores. Formally, the model incorporates nonlinear long wave theory exactly, incorporates enough dispersion to describe linear waves with fourth-order precision, so that both shallow water waves and deep water waves are included, and describes accurately waves for which dispersive and nonlinear effects are both important. The factors that have made this development possible include use of a new theoretical conservation-of-velocity law and associated formalism that reduces the dimensionality of the calculations by one, while retaining nonlinear and dispersive effects to high order.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 30, 1982
- Accession Number
- ADA122822
Entities
People
- J. M. Witting
Organizations
- United States Naval Research Laboratory