Abstract
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].
Highlights
There exist multiple porous layers in coastal area
Sand beach is composed of one porous layer on the land side from the coastline
The Boussinesq equations have been developed for two layers with upper non-porous water layer and lower porous layer (Cruz et al, 1997; Hsiao et al, 2002)
Summary
There exist multiple porous layers in coastal area. Submerged breakwaters are composed of two layers, i.e., upper non-porous water layer and lower porous layer. Sand beach is composed of one porous layer on the land side from the coastline It is composed of two layers with upper water and lower porous layers on the sea side. Liu and Wen (1997) developed conventional Boussinesq equations in shallow water for waves inside porous media including drag resistance but neglecting inertial resistance. The Boussinesq equations have been developed for two layers with upper non-porous water layer and lower porous layer (Cruz et al, 1997; Hsiao et al, 2002). These models cannot be applied for rubble mound breakwaters or sand beach. Since the porosity is uniform, the continuity equation inside the j th permeable layer is given by
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