Abstract: The mathematical modeling of the interaction of water waves with porous coastal structures has continuously been among the most relevant challenges in coastal engineering research and practice. Finding a tool to better predict essential processes, relevant to the functionality and stability of breakwaters and jetties, and how they are affected by permeability, has been hampered by computational limitations that are being overcome. Over the last 60 years, the Journal of Waterway, Port, Coast, and Ocean Engineering has witnessed gradual developments leading from linearized solutions based on wave theories and constant friction coefficients to very sophisticated Eulerian or Lagrangian solvers of the Navier-Stokes (NS) equations, including turbulence within porous media. Today, although not without difficulty, the first steps are being made toward addressing the simulation of a fully three-dimensional interaction of complete sea states with porous structures at prototype scale. In this paper, after posing the mathematical foundations of the problem, the solution techniques available in the literature are reviewed. Linear solutions based on potential theory; depth-integrated solutions, including Boussinesq approximations; and solutions based on the NS equations, in both the Eulerian and Lagrangian frameworks, are covered. Then, turbulence modeling on porous media is discussed. Conclusions and a discussion of future research directions close the paper. It is shown that, after so many years, some fundamental questions still remain unanswered, leaving challenges open for future research.
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