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A Singular Perturbation Method for Non-Linear Water Waves Past an Obstacle


Rispin, Peter Paul Augustine (1967) A Singular Perturbation Method for Non-Linear Water Waves Past an Obstacle. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/D0P9-9109.


The method of matched singular perturbation expansions is used to solve the problem of a steady two-dimensional flow of a perfect fluid with a free surface under the influence of gravity. A flat plate of length ℓ 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 β = gℓ/U² (Froude number F = β-1/2) is assumed small so that the flow separates smoothly at the leading and trailing edges, giving rise to n 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, β log β, β, β² log² β, β² log β up to order β², 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 α, h/ℓ and β. The results reduce to known ones in certain limits.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wu, Theodore Yao-tsu
Thesis Committee:
  • Unknown, Unknown
Defense Date:24 August 1966
Record Number:CaltechETD:etd-09272002-161056
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3801
Deposited By: Imported from ETD-db
Deposited On:30 Sep 2002
Last Modified:03 Dec 2022 00:26

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