Abstract
An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.
Highlights
Porous structures are constructed along coasts for shoreline protection and beach erosion prevention against wave attack
Sakakiyama and Kajima suggested extended Navier–Stokes equations, which include the impacts of porous medium by drag and inertia force components, and studied the wave transformation interacting with a permeable breakwater [15]
The numerical solution proposed by Karunarathna and Lin represents the fact that the flow resistance depends on the Reynolds number, which results in covering a wide range of flows [20]
Summary
Porous structures are constructed along coasts for shoreline protection and beach erosion prevention against wave attack. Huang et al developed a numerical model in order to study the solitary wave interaction with a submerged structure [19] They solved the unsteady Navier–Stokes equations for the flow outside the breakwater and another Navier–Stokes-based equation for solving the flow motion inside the structure. The numerical solution proposed by Karunarathna and Lin represents the fact that the flow resistance depends on the Reynolds number, which results in covering a wide range of flows [20] They applied their model to investigate wave behavior passing over a permeable bed. Wu and Hsiao studied the non-breaking solitary wave propagation over a permeable submerged structure using experimental and numerical models [22] They employed the particle image velocimetry (PIV) method for measuring free surface elevation and velocity fields around a permeable structure instantaneously. Testing of the model’s accuracy was performed by comparing the model results with experimental measurements for the surface displacement, velocity fields, as well as velocity profiles around the structure
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