Abstract
In this study we develop a new extended Boussinesq model that predicts the propagation of water waves in porous media. The inertial and drag resistances are taken account into the model in which the results are the same with the extended Boussinesq equations of Madsen and Sorensen (1992) when these resistances are removed. The developed model introduces its simplicity in solving the matching conditions at the permeable breakwater interfaces. The whole computational domain can be involved by specifying the porosity equal to unity outside the breakwater and to a value below unity inside the breakwater. There is no need for using any matching conditions at the interface. Furthermore, the applications of this current developed model are also extended to the cases that waves propagate inside and/or over a porous layer. For verification of the developed model, the internal generation of wave technique is applied to simulate sinusoidal and cnoidal waves propagating inside porous media in shallow and deep waters and nonlinear cnoidal waves interacting with porous breakwater. Numerical results give a good agreement with analytical solutions. Transformation of solitary waves to porous breakwater is also carried out. Refraction and transmission of solitary waves to the porous breakwater are well captured and verified by available physical experimental dataReferences
Cho, Y.-S., 203. A note on estimation of the Jacobian elliptic parameter in cnoidal wave theory. Ocean Engineering 30, 1915-192.
Cruz, E.C., Isobe, M., Watanabe, A., 197. Boussinesq equations for wave transformation on porous beds. Coastal Engineering 30, 125-156.
del Jesus, M., Lara, J.L., Losada, I.J., 2012. Three-dimensional interaction of waves and porous coastal structures. Part I: Numerical model formulation. Coastal Engineering 64, 57-72.
Ergun, S., 1952. Fluid flow through packed columns. Chemical Engineering Progress 48, 89-94.
Forchheimer, P., 1901. Wasserbewegung durch boden. Z. Ver. Deutsch. Ing. 45, 1782-178.
Gu, Z., Wang, H., 191. Gravity waves over porous bottoms. Coastal Engineering 15, 497-524.
Hsiao, S.-C., Liu, P.L.-F., Chen, Y., 202. Nonlinear water waves propagating over a permeable bed. Proceeding of Royal Society of London A 458, 1291-132.
Hsiao, S.-C., Hu, K.-C., Hwung, H.-H., 2010. Extended Boussinesq equations for water-wave propagation in porous media. J. Engineering Mechanics 136(5), 625-640.
Kennedy, A.B., Chen, Q., Kirby, J.T., Dalrymple, R.A., 200. Boussinesq modeling of wave transformation, breaking, and runup. Part 1. J. Waterway, Port, Coastal and Ocean Engineering 126(1), 39-47.
Kirby, J.T., Wei, G., Chen, Q., Kennedy, A.B., Dalrymple, R.A., 198. Fully Nonlinear Boussinesq Wave Model. User's Manual. CACR Report no. 98-06. Center for Applied Coastal Research, Univ. of Delaware. Liu, P.L.-F., Wen, J., 197. Nonlinear diffusive surface waves in porous media. J. Fluid Mechanics 347,19-139.
Liu, P.L.-F., Lin, P., Chang, K.A., Sakakiyama, T., 199. Numerical modeling of wave interaction with porous structures. J. Waterway, Port, Coastal, and Ocean Engineering 125 (6), 32-30.
Liu, Y., Li, H.-J., 2013. Wave reflection and transmission by porous breakwaters: A new analytical solution. Coastal Engineering 78, 46-52.
Lynett, P.J., Liu, P.L.-F, Losada, I.J., 200. Solitary wave interaction with porous breakwaters. J. Waterway, Port, Coastal, and Ocean Engineering 126(6), 314-32.
Madsen, O.S., 1974. Wave transmission through porous structures. J. Waterways, Harbors and Coastal Engineering Division 10(WW3), 169-18.
Ma, G., Shi, F., Hsiao, S.,-C., Wu, Y.-T., 2014. Non-hydrostatic modeling of wave interactions with porous structures. Coastal Engineering 91, 84-98.
Madsen, P.A., Sørensen, O.R., 192. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry. Coastal Engineering 15, 371-38.
Madsen, P.A., Sørensen, O.R., Schäffer, H.A., 197. Surf zone dynamics simulated by a Boussinesq type model. Part 1. Model description and cross-shore motion of regular waves. Coastal Engineering 32, 25-287.
Nwogu, O., 193. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterways, Harbors and Coastal Engineering 19(6), 618-638.
Peregrine, D.H., 1967. Long waves on beach. J. Fluid Mechanics 27, 815-827.
Sollitt, C.K., Cross, R.H., 1972. Wave transmission through permeable breakwater. Proceeding of 13th International Conference on Coastal Engineering, ASCE 1827-1846.
Wang, K.-H., 193. Diffraction of solitary waves by breakwaters. J. Waterway, Port, Coastal, and Ocean Engineering 19(1) 49-69.
Wei, G., Kirby, J.T., Grill, S.T., Subramanya, R., 195. A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. J. Fluid Mechanics 294, 71-92.
Wei, G., Kirby, J.T., Sinha, A., 199. Generation of waves in Boussinesq models using a source function method. Coastal Engineering 36, 271-29.