Journal of Fluid Mechanics



Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves


ELIEZER KIT a1 and LEV SHEMER a1
a1 Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel

Abstract

A spatial two-dimensional version of the Zakharov equation describing the evolution of deep-water gravity waves is used to derive two fourth-order evolution equations, for the amplitudes of the surface elevation and of the velocity potential. The scaled form of the equations is presented.

(Received August 5 2001)
(Revised September 11 2001)



Metrics