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Steady Deep-Water Waves on a Linear Shear Current


Simmen, Jeffrey Alan (1984) Steady Deep-Water Waves on a Linear Shear Current. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/H88C-1G49.


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.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Saffman, Philip G.
Thesis Committee:
  • Whitham, Gerald Beresford (chair)
  • Wu, Theodore Yao-tsu
  • Ingersoll, Andrew P.
  • Kath, William L.
  • Saffman, Philip G.
Defense Date:23 May 1984
Funding AgencyGrant Number
Office of Naval Research (ONR)UNSPECIFIED
Record Number:CaltechETD:etd-01192007-153942
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:242
Deposited By: Imported from ETD-db
Deposited On:30 Jan 2007
Last Modified:21 Dec 2019 02:26

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PDF (Simmen_ja_1984.pdf) - Final Version
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