Ž . Coastal Engineering 43 2001 265–286 www.elsevier.comrlocatercoastaleng On the interaction of a solitary wave and a submerged dike Ching-Jer Huang ) , Chih-Ming Dong 1 Department of Hydraulics and Ocean Engineering, National Cheng Kung UniÕersity, 1 Dah Shyue Road, Tainan 70101, Taiwan Received 13 July 2000; received in revised form 26 February 2001; accepted 28 May 2001 Abstract The unsteady, two-dimensional Navier–Stokes equations and the exact free surface boundary conditions were solved to study the interaction of a solitary wave and a submerged dike. A piston-type wavemaker was set up in the computational domain to produce the incident solitary waves. The incident wave and the associated boundary layer flow in a wave tank with a flat bed were compared with the analytical solutions to verify the accuracy of this numerical scheme. Effects of the incident wave height and the size of the dike on the wave transformation, the flow fields, and the drag forces on the dike were discussed. Our numerical results showed that even though the induced local shear stress on the top surface of the dike is large at some particular locations, the resultant pressure drag is much larger than the friction drag. The primary vortex generated at the lee side of the dike and the secondary vortex at the right toe of the dike may scour the bottom and cause a severe problem for the dike. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Solitary wave; Submerged dike; Wavemaker; Vortex generation; Boundary layer flow; Drag 1. Introduction The interaction between water waves and a sub- merged marine structure has attracted more and more attention over the past decade. Not only is this topic related to many ocean and coastal engineering prob- lems, such as dike applications for preventing beach erosion, but also to the water waves propagation over coral reefs or continental shelf. With increasing available computational capability, the complex flow configurations near the submerged structure can be easily revealed, even using a personal computer. ) Tel.: q 886-6-2757575x63252; fax: q 886-6-2741463. Ž . E-mail addresses: cjhuang@mail.ncku.edu.tw C.-J. Huang , Ž . gimi@mail.tit.edu.tw C.-M. Dong . 1 Present address: Department of Environmental Resource Management, Transworld Institute of Technology, Yunlin, Tai- wan. This was difficult to imagine a decade ago when the expensive LDV or related techniques were thought as the only appropriate means to reach this goal. The main characteristics as water waves propagat- ing over a submerged structure are the generation of higher harmonics and vortices around the dike. The nonlinear shallow-water wave theories, such as the Boussinesq equations and KdV equation have been applied to predict the transformation of a solitary wave propagating over continental shelf or an iso- Ž lated obstacle Madsen and Mei, 1969; Seabra- . Santntos et al., 1987; Goring and Raichlen, 1990 . Ž . Beji and Battjes 1994 applied a similar approach to investigate the transformation of periodic waves passing over a bar. Since the derivation of the Boussinesq equations are based on the assumption of both weak non-linearity and weak dispersion, for strongly nonlinear problems the Laplace equation and the fully nonlinear free surface boundary condi- 0378-3839r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. Ž . PII: S0378-3839 01 00017-5