Citation
Rispin, Peter Paul Augustine (1967) A singular perturbation method for nonlinear water waves past an obstacle. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd09272002161056
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The method of matched singular perturbation expansions is used to solve the problem of a steady twodimensional flow of a perfect fluid with a free surface under the influence of gravity. A flat plate of length [...] is inclined at an angle [alpha] to the horizontal and its trailing edge is immersed to a depth h below the surface of an otherwise uniform stream of infinite depth, the velocity at upstream infinity being U. A parameter [...] (Froude number [...]) is assumed small so that the flow separates smoothly at the leading and trailing edges, giving rise to an upward jet and gravity waves in the downstream. An inner solution for the velocity field is obtained which is valid near the plate and an outer solution which holds far away. These are determined through the orders 1,[beta log beta], [beta], [beta^2 log^2 beta], [beta^2 log beta] up to order [beta^2], and are matched with one another to these orders. In contrast with linearized planing theory, the depth of submergence can be prescribed as a parameter. The lift coefficient is calculated for several values of [alpha], [...] and [beta]. The results reduce to known ones in certain limits.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Applied Mechanics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  24 August 1966 
Record Number:  CaltechETD:etd09272002161056 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd09272002161056 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3801 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  30 Sep 2002 
Last Modified:  26 Dec 2012 03:03 
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