Comparison of model equations for small-amplitude long waves

✍ Scribed by Jerry L. Bona; Hongqiu Chen

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 166 KB
• Volume: 38
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(99)00100-5

✦ Synopsis

Consider a body of water of ÿnite depth under the in uence of gravity, bounded below by a at, impermeable surface. If viscous and surface tension e ects are ignored, and assuming that the ow is incompressible and irrotational, the uid motion is governed by the Euler equations together with suitable boundary conditions on the rigid surfaces and on the air-water interface. In special regimes, the Euler equations admit of simpler, approximate models that describe pretty well the uid response to a disturbance. In situations where the wavelength is long and the amplitude is small relative to the undisturbed depth, and if the Stokes number is of order one, then various model equations have been derived. Two of the most standard are the KdVequation