Simmen, Jeffrey Alan (1984) Steady deep-water waves on a linear shear current. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-01192007-153942
The behavior of steady, periodic, deep-water 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 non-uniqueness in the sense of a fold is shown to exist and a new type of limiting wave is discovered.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Engineering and Applied Science|
|Major Option:||Applied And Computational Mathematics|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||23 May 1984|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||30 Jan 2007|
|Last Modified:||26 Dec 2012 02:28|
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