Higher Approximation To Nonlinear Water Waves And The Limiting Heights Of Cnoidal Solitary And Stokes Waves

To obtain the first and second approximations to solitary and cnoidal waves the shallow water expansion method of Friedrichs and Keller is carried out to the fourth order. It is shown that the rigorous first approximation to these amplitude waves of permanent form is identical to the solution first given by Korteweg and deVries in 1895. The second approximation however results in some new expressions for predicting the behavior of long waves in shallow water. Limiting amplitude is found to be 8/11 of the free water depth for the solitary wave. The third approximation to Stokes waves in water of finite depth is verified by the use of the classical small-perturbation expansion method. For finite amplitude waves the series expansion is found to be in terms of a parameter most suitable for wavelengths shorter than 8 times the depth. Rather severe restrictions inherent in the well-known analogy between the nonlinear shallow water flow and two-dimensional perfect gas flow are pointed out. (Author).

The subject of hydrodynamics applied to offshore structures is vast. The topics covered in this book aim to help the reader understand basic principles while at the same time giving the designer enough information for particular designs. Thus, results are given with derivations, and applications are discussed with the aid of examples, with an overview of the advantages and limitations of the method involved. This makes the book suitable as a text for undergraduate and graduate students specializing in offshore and ocean engineering.