Dispersion of water waves

Abstract

The conspicuous ever-changing wave pattern of water waves is due mainly to frequency dispersion, according to which components of a group of waves with different frequencies are propagated with different velocities. Consequently, the group will move with a velocity, called the group velocity, generally different from the phase velocity of each component. The general problem of water waves is intrinsically nonlinear because, first, the kinematic and dynamic conditions on the free boundary are non-linear and, second, the disturbed water surface is always unknown in advance. Furthermore, the time dependence of the solution enters into the problem through the free surface boundary conditions.