A numerical model for wave motions and turbulence flows in front of a composite breakwater
Introduction
The stability of breakwater in coastal region has been studied extensively by many researchers using various methods. In numerical approach, armor layers that are employed to protect the breakwater are usually modeled as porous materials. The calculated pore water pressure distribution and velocity field are then used to evaluate the stability of individual armor unit as well as the integrity of the entire structure. Therefore, the modeling of flows within the porous media is an important component of the overall modelling effort.
The scouring in the vicinity of the toe of breakwater also plays an important role in breakwater stability. To estimate the sediment transport rate, accurate information on the local fluid velocity and turbulent intensity are crucial. Although significant advancement has been made in modeling breaking waves, an accurate prediction of turbulence under breaking waves is still an ongoing and challenging research subject. In studying the interaction between breaking waves and a coastal structure that is protected by layers of armor units, three kinds of turbulence generation mechanisms must be considered. The first is the wave breaking process, initiated by wave shoaling over a varying bathymetry and/or an inclined surface of the structure. The second is the turbulence generation inside the boundary layer near the sea bottom or the structure. The third mechanism is attributed to the turbulence flow in the porous media. In modeling a wave–structure interaction system, Liu et al. (1999) assumed that turbulence inside the porous media is negligible. The turbulence boundary layer adjacent to the porous wall was modified by including the effects of percolation velocity along the porous boundary. The small-scale turbulence inside a porous medium could be indeed very weak, if the permeability of the medium is very small, i.e. fine sands. However, there are strong experimental evidences that turbulence inside the protective armor layer could be significant under breaking waves when the size of the armor unit is relatively large (e.g., Losada et al., 2000, Sakakiyama and Liu, 2001).
In this paper, by taking a volume-average of the Reynolds Averaged Navier-Stokes (RANS) equations along with the k−ϵ turbulence closure model, a set of governing equations that can describe the flows both inside and outside the porous medium is first presented. In the absence of the porous medium, the present model becomes the same as that developed by Lin and Liu (1998). The proposed model is solved numerically and its performance is checked by the experimental data reported by Sakakiyama and Liu (2001). In Sakakiyama and Liu's experiments, the breakwater is a caisson concrete block protected by a thick layer of Tetrapods and supported by a rubble foundation (see Fig. 1).
The paper is organized in the following manner. The substantially improved model is presented in the following section. Although the details of the derivations of the governing equations are presented in Appendix A Volume-Averaged Reynolds Averaged Navier–Stokes Equations, Appendix B Turbulence damping function, the basic assumptions and resulting equations are summarized in the main text. The detailed comparisons between the numerical results and the laboratory measurements by Sakakiyama and Liu (2001) are then discussed. We conclude the paper by examining the discrepancies between the numerical predictions and experimental data and by suggesting future works.
Section snippets
Model equations
In studying water wave and porous-structure interactions, it is still not practical to resolve the intrinsic flow field inside pores, whose geometry is usually random. It is more manageable if the flow equations are averaged over a volume that is larger than the characteristic pore size and is much smaller than the scale of the spatial variation of the physical variables in the flow domain. If the Reynolds Averaged Navier–Stokes (RANS) equations are adequate in describing the intrinsic flow
Validation of the model
To find solutions for the velocity field, pressure field, free surface elevation, and the turbulent kinetic energy, the continuity and momentum , along with the 〈k〉−〈ϵ〉 equations , , are integrated numerically. Since the present model equations are similar to those for the free fluid flow (i.e., Lin and Liu, 1998), the same numerical algorithm is adopted. In the present model, the flow equations are solved by the two-step projection method on a staggard grid system. The movement of the free
Concluding remarks
By taking the volume-average of RANS equations and corresponding k−ϵ equations, a numerical model describing the flow both inside and outside porous media is developed. Based on the simulation of the experiments studied by Sakakiyama and Liu (2001), we conclude that for case A, in which waves directly collapse on the breakwater, the present model is capable of predicting the free surface, flow velocity, impact pressure, and turbulence information in the vicinity of the breakwater. Specifically,
Acknowledgements
The research reported here has been supported through NSF grants to Cornell University (CMS-9908392, CTS-9808542, CTS-0000675).
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