Journal of Fluid Mechanics

Some exact solutions to the nonlinear shallow-water wave equations

William Carlisle  Thacker a1
a1 Sea-Air Interaction Laboratory, National Oceanographic and Atmospheric Administration, United States Department of Commerce

Article author query
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These exact solutions correspond to time-dependent motions in parabolic basins. A characteristic feature is that the shoreline is not fixed. It is free to move and must be determined as part of the solution. In general, the motion is oscillatory and has the appropriate small-amplitude limit. For the case in which the parabolic basin reduces to a flat plane, there is a solution for a flood wave. These solutions provide a valuable test for numerical models of inundating storm tides.

(Published Online April 20 2006)
(Received April 18 1980)
(Revised September 19 1980)