ABSTRACT

The numerical scheme developed by Huang et al. (1998) for solving the wave-making problem in a two-dimensional numerical wave tank was employed to generate different incident waves, including small- and finite- amplitude waves and solitary waves. To generate the small-amplitude waves, the displacement of the wavemaker was determined from the linear wavemaker theory. To generate relatively long finite- amplitude waves and to make sure that the generated waves have a permanent form, Madsen's second-order wave maker theory (Madsen, 1971) was applied to determine the wavemaker motion. The accuracy of the numerical results for the incident wave profiles and the associated boundary layer flows were verified by comparison with the analytical solutions.

INTRODUCTION

To date, the wave tank has been widely applied in laboratory studies on coastal structures, beach profiles, and other related coastal phenomena. Most of the wave generators built in wave tanks for hydraulics laboratories are either piston- or flap-type. The pistontype wavemaker is easier to generate shallow water waves, as the piston motion resembles more closely the water particle trajectories, while in deep water, the flap-type is more efficient (Dean and Dalrymple, 1984). Havelock (1929) derived analytical solutions for piston- and flap-type wavemaker from linear wave theory. Ursell et at. (1960) did experimental verification of the linear wavemaker theory for a piston motion. Hudspeth et al. (1981) performed experimental verification for the flap-type wave maker. If the motion of the piton-type wavemaker is set to be sinusoidal, the generated finite-amplitude waves will not have a permanent form. These waves will decompose into a primary and one or more secondary waves. The period of the primary wave will be the same as that of the wavemaker. However, the period of the secondary waves will be only half of the primary wave.

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