International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 625-652

Nonlinear diffraction of water waves by offshore stuctures

Matiur Rahman1 and Lokenath Debnath2

1Department of Applied Mathematics, Technical University of Nova Scotia, Halifax B3J 2X4, Nova Scotia, Canada
2Department of Mathematics, University of Central Florida, Orlando 32816-6990, Florida, USA

Received 8 January 1986; Revised 30 July 1986

Copyright © 1986 Matiur Rahman and Lokenath Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear) effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.