Publisher's Synopsis
Excerpt from The Dock Problem
Suppose one half-plane of an infinite water surface is covered with a rigid plate, the dock. How does this dock influence waves standing or traveling perpen dicularly to the edge of the dock on the free water sur face? This problem.may be considered as a special case of the problem of waves on a sloping beach, viz. For a beach with a slope angle of see the introductory report For beach angles which are an integer fraction of a right angle, cu the problem was solved by Miche Stoker, and Lewy for beach angles of the form 00 with relatively prime integers/p and q, the problem.was solved by Lewy in case p is odd. The present problem.corresponds to the case q l, p 2. Although it may be possible to make tend to the limit 1 and follow through.this passage to the limit in the explicit expressions for the waves, we attack the problem.differ ently, using a.method related to the Laplace transforma tion. It turns out that the problem permits a simple explicit solution Which offers the possibility of discussing the nature of the solution and of determining it numerically. We shall in particular discuss the behavior of the wave motion near the edge of the dock, i.e. Near the line along which the water surface and the dock meet. In addition, we shall show graphically the amplitudes of the waves on the free surface and of the pressure under the dock.
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