Steady DeepWater Waves on a Linear Shear Current.
Abstract
The behavior of steady, periodic, deepwater gravity waves on a linear shear current is investigated. A weakly nonlinear approximation for the small amplitude waves is constructed via a variational principle. A local analysis of those large amplitude waves with sharp crests, called extreme waves, is also provided. To construct solutions for all waveheights (especially the limiting ones) a convenient mathematical formulation which involves only the wave profile and some constants of the motion is derived and then solved by numerical means. It is found that for some shear currents the highest waves are not necessarily the extreme waves. Furthermore a certain nonuniqueness in the sense of a fold is shown to exist and a new type of limiting wave is discovered.
 Publication:

Ph.D. Thesis
 Pub Date:
 1984
 Bibcode:
 1984PhDT.......121S
 Keywords:

 Physics: Fluid and Plasma