An intermediate wavelength, weakly nonlinear theory for the evolution of capillary gravity waves

作者：Rees Julia M^*; Zimmerman William B

来源：Wave Motion, 2011, 48(8): 707-716.

DOI：10.1016/j.wavemoti.2011.03.006

• Surface waves
• Evolution equation
• Dispersion relation
• Fredholm alternative theorem

A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid-air interface where the wave motion is induced by a harmonic forcing. Ins:ead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity.

• 出版日期2011-12