Numerical Methods in Water-Wave Diffraction and Radiation

Abstract

The subject of diffraction and radiation of water wave s by natural boundarie s or man-made structure s i s of con siderable im portance in ocean engineering. A s a re sult of the ra pid growth of ocean e xploration and tran sportation, detailed knowledge of wave effect s i s now a virtual nece ssity for the safe de sign of co stly pro ject s such a s tanker s and their mooring s, off shore terminal s and drilling rig s, etc. Predicting the re spon se s to po ssible incident waves i s essential for the safe and economical o peration of exi sting and new harbor s. Effect s of t sunami s along a coa st line mu st be under stood in order to devi se mea sure s for protecting live s and pro pertie s. In di scu ssing wave effect s it i s im portant to di stingui sh between small and large bodie s (of ty pical dimen sion a) in com pari son with the characteri stic wave­ length (2n/k) and the wave am plitude (A). For small ka and large A/a [�0( 1)], vortex shedding and flow se paration are dominant, but diffraction i s in significant, i.e. while the body i s affected by the wave field near by, it doe s not materially alter the wave field at large. For small A/a and ka � 0(1 ), se paration become s in signi ficant while diffraction become s crucial. It i s to the latter category that thi s review i s addre ssed. In the conte xt of linearized theory, some analytical solution s are available for sim ple geometrie s by em ploying either re sult s that are known in cla ssical phy sic s (a circular vertical cylinder, a semi-in finite long breakwater, etc) or other exact technique s ( e.g., Dean 1945, Ur sell 1947, 1948, John 1948, Hein s 1948, Lewin 196 3, Mei 1966). A sym ptot ic theorie s for short or long wave s have al so been deve lo ped. Thi s review cover s numerical methods f or arbitrary geometrie s and frequencie s for which exten sive u se of the com puter i s nece ssary. It i s further re stricted to sim ple harmonic wave s. The more general ca se s of tran sient or random wave s can in princi ple be obtained by Fou rier integral s from the single-frequency re spon se calculated for all frequencie s (0 < W < CfJ). Direct calculation of tran sient problem s u sing tran sient Green function s ha s ju st begun ( see Shaw 197 5, Harten 197 5).