A finite amplitude wave on a linear shear current

A numerical perturbation procedure is presented that generates water waves propagating over a vertically varying linear shear current. The water surface profile of these waves may be symmetric about the crest, with given height and period, or they may have an irregular water surface profile that has been measured in water of known depth. For waves of the same height the effect of the current is to cause a change in wavelength and hence the kinematics under the wave. Further, the shape of the wave profile is changed significantly.