On the Behavior Near the Crest of Waves of Extreme Form.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This paper concerns waves of permanent form on the free surface of an ideal liquid which is in two-dimensional, irrotational motion under the action of gravity. We consider only extreme waves, often called waves of greatest height each of these is the end-member of a one-parameter family of waves, and is distinguished from other smaller members of the family by a sharp crest. Although this corner is physically unrealistic, oceanographers have given such idealized, extreme waves a great deal of attention since Stokes postulated their existence in 1880. One reason may be the physical importance of the smaller waves, and that scientists like to interpolate. The present paper is a contribution to the strict mathematical theory of extreme waves, which was emerged only since 1978. We derive rigorously an asymptotic series that describes the flow near the crest. This confirms and sharpens certain earlier exploratory results due to Grant and Norman. The series should play a useful part in numerical computations of extreme waves. Author
- Numerical Mathematics
- Fluid Mechanics