Yun-Ta Wu, Shih-Chun Hsiao, Guan-Shiue Chen


We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique was employed to measure instantaneous free surface displacements and velocity fields in the vicinity of the porous media. The porous media, consisted of uniform glass-made spheres, was mounted on the seafloor. Quantitative mean properties were obtained by ensemble averaging 30 repeated instantaneous measurements. In addition, two different numerical considerations are taken to simulate the experiments. One is to model an idealized volume-averaged porous media using a two-dimensional (2D) volume of fluid (VOF)-type model. This model is based on the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations coupled with the non-linear k-ε turbulence closure solver. The other is to model the real porous breakwater constructed by spheres using a three-dimensional (3D) VOF-type model. This model solves 3D incompressible Navier–Stokes equations with Large-eddy-simulation (LES) model. The comparisons were performed between measurements, 2D and 3D numerical results for the time histories of the free surface elevation, instantaneous free surface displacements and corresponding velocity properties around the permeable object. Fairly good agreements were obtained. The verified 3D numerical results were used to trace the trajectories of fluid particle around the porous media to help understand the possible sediment movements in suspended loads. Also, the 2D numerical model is used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.


solitary wave; submerged permeable breakwater; PIV; RANS model; LES model

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Adrian, R.J. 1991. Particle-imaging techniques for experimental fluid mechanics, Annual Review of Fluid Mechanics, 23, 261-304.

Chorin, A.J. 1968. Numerical solution of the Navier–Stokes equations, Mathematics of Computation, 22 (104), 745-762.

Hirt, C.W., and B.D. Nichols. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39, 201-225.

Hsu, H.-C., Y.-Y. Chen, and H.-H. Hwung. 2012. Experimental study of the particle paths in solitary water waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370 (1964), 1629-1637.


Hsu, T.-J., T. Sakakiyama, and P.L.F. Liu. 2002. A numerical model for wave motions and turbulence flows in front of a composite breakwater, Coastal Engineering, 46, 25-50.

Hu, K.-C., S.-C. Hsiao, H.-H. Hwung, and T.-R. Wu. 2012. Three-dimensional numerical modeling of the interaction of dam-break waves and porous media, Advances in Water Resources, 47, 14-30.

Huang, C.-J., H.-H. Chang, and H.-H. Hwung. 2003. Structural permeability effects on the interaction of a solitary wave and a submerged breakwater, Coastal Engineering, 49 (1-2), 1-24.

Lara, J.L., I.J. Losada, M. Maza, and R. Guanche. 2011. Breaking solitary wave evolution over a porous underwater step, Coastal Engineering, 58 (9), 837-850.

Lee, J.J., E. Skjelbreia, and F. Raichlen. 1982. Measurement of velocities in solitary waves, Journal of the Waterway, Port, Coastal and Ocean Division, 108 (2), 200-218.

Lin, P. 2004. A numerical study of solitary wave interaction with rectangular obstacles, Coastal Engineering, 51 (1), 35-51.

Lin, P., and S. Karunarathna. 2007. Numerical study of solitary wave interaction with porous breakwaters, Journal of Waterway, Port, Coastal, and Ocean Engineering, 352-363.

Lin, P., and P.L.F. Liu. 1998. A numerical study of breaking waves in the surf zone, Journal of Fluid Mechanics, 359, 239-264.

Liu, P.L.F., P. Lin, K.-A. Chang, and T. Sakakiyama. 1999. Numerical modeling of wave interaction with porous structures, Journal of Waterway, Port, Coastal, and Ocean Engineering, 322-330.

Lynett, P.J., P.L.F. Liu, I.J. Losada, and C. Vidal. 2000. Solitary wave interaction with porous breakwaters, Journal of Waterway, Port, Coastal, and Ocean Engineering, 126 (6), 314-322.

Raffel, M., C.E. Willert, and J. Kompenhans. 1998. Particle image velocimetry, Springer.

Synolakis, C.E., and E.N. Bernard. 2006. Tsunami science before and beyond Boxing Day 2004, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 364 (1845), 2231-2265.


Torres-Freyermuth, A., J.L. Lara, and I.J. Losada. 2010. Numerical modelling of short- and long-wave transformation on a barred beach, Coastal Engineering, 57 (3), 317-330.

van Gent, M.R.A. 1995. Wave interaction with permeable coastal structures, Ph.D. Thesis, Delft University of Technology.

Wu, T.-R. 2004. A numerical study of three-dimensional breaking waves and turbulence effects, Ph.D. Thesis, Cornell University.

Wu, Y.-T., S.-C. Hsiao, Z.-C. Huang, and K.-S. Hwang. 2012. Propagation of solitary waves over a bottom-mounted barrier, Coastal Engineering, 62, 31-47.