ICCE 2018 Cover Image

How to Cite

Lee, C., Vu, V. N., Jung, T.-H., & Huynh, T. T. (2018). EXTENDED BOUSSINESQ EQUATIONS FOR WAVES IN TWO POROUS LAYERS. Coastal Engineering Proceedings, 1(36), papers.92. https://doi.org/10.9753/icce.v36.papers.92


In this study we continue the work of Vu et al. (2018) [Coastal Eng. 139, 85-97] to develop an extended Boussinesq model that predicts the propagation of water waves in two porous layers. The first and second layer can be a water layer or a porous layer. The inertial and drag resistances are considered in the developed model. After being successfully validated against the analytical solutions, the model is used to simulate waves propagating over a submerged triangular porous bar. The numerical results show good agreement with the physical experimental data of Hsiao et al. (1998) [Proc. Royal Society of London A 458, 1291-1322].


Burcharth, H.F., Andersen, O.H., 1995. On the one-dimensional steady and unsteady porous flow equations. Coastal Engineering 24, 233-257.

Cruz, E.C., Isobe, M., Watanabe, A., (1997). Boussinesq equations for wave transformation on porous beds. Coastal Engineering 30, 125-156.

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, 1782-1788.

Hsiao, S.-C., Liu, P.L.-F., Chen, Y., (2002). Nonlinear water waves propagating over a permeable bed. Proc. Royal Society of London A 458, 1291-1322.

Irmay, S., 1958. On the theoretical derivation of Darcy and Forchheimer formulas. Transactions, American Geophysical Union 39, 702-707.

Liu, P.L.-F., Wen, J., 1997. Nonlinear diffusive surface waves in porous media. J. Fluid Mechanics 347,119-139.

Sollitt, C.K., Cross, R.H., 1972. Wave transmission through permeable breakwater. Proc. 13th International Conference on Coastal Engineering, ASCE 1827-1846.

Van Gent, M.R.A., 1994. The modeling of wave action on and in coastal structures. Coastal Engineering 22, 311-339.

Vu, V.N., Lee, C., Jung, TH., (2018). Extended Boussinesq equations for waves in porous media. Coastal Engineering 139, 85-97.

Authors retain copyright and grant the Proceedings right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this Proceedings.