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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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Paperback. Zustand: New. Print on Demand. This book explores the hydrodynamic behavior of water waves in unique scenarios, including situations where waves interact with structures such as barriers and sloping beaches. The author presents an in-depth analysis of these interactions through mathematical modeling, uncovering the underlying phenomena and their impact on wave motion. The book delves into the mathematical complexities of wave behavior, particularly when waves encounter physical obstacles. It unveils how these interactions influence the velocity potential, wave amplitude, and pressure distribution, providing valuable insights into real-world applications such as coastal engineering and fluid dynamics. Through rigorous mathematical derivations and numerical simulations, the book illuminates the intricacies of wave behavior near edges, boundaries, and obstacles. It sheds light on the logarithmic singularity observed at the edge of a submerged structure, revealing the specific characteristics of wave motion in such regions. This book offers a comprehensive examination of water waves in unconventional environments, expanding our understanding of their dynamics and behavior. It is a valuable resource for researchers and practitioners in fluid mechanics, coastal engineering, and related fields, as it provides a deeper comprehension of wave phenomena and their practical implications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781333544690_0
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