Master of Science (Hons.)
Department of Mathematics
Satravaha, Pornchai, Diffraction of nonlinear short-crested waves around a vertical circular cylinder, Master of Science (Hons.) thesis, Department of Mathematics, University of Wollongong, 1992. http://ro.uow.edu.au/theses/2845
In this thesis, a complete solution is presented in closed-form for the velocity potential, up to the second-order of wave amplitude, resulting from the diffraction of nonlinear short-crested waves around a vertical circular cylinder. Second-order analytical solutions are developed and expressed in the form of series and integrals. When numerical results are required, the Hankel transform is then employed to simplify the integrals in combination with other extensive numerical techniques employed to significantly reduce the computational effort. Hydrodynamic forces at second-order are examined by comparing with those obtained by the adoption of linear diffraction theory. Second-harmonic terms resulting from self-interaction of incident waves are found to play an important role in the solutions. It will be shown that second-order forces exerted by short-crested waves on solid structures can be up to two times greater than those by plane waves. The present nonlinear analysis will also show that the excess of forces from those predicted by linear diffraction theory can be as much as 45 %. This large increment is an important contribution toward the total wave-induced forces and therefore should be taken into consideration in offshore engineering design and operation processes.