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http://dx.doi.org/10.12652/Ksce.2015.35.5.1061

Derivation and Application of Boussinesq Equations for the Wave Field in Porous Media  

Chun, Insik (Konkuk University)
Min, Yongchim (Korea Institute of Ocean Science & Technology)
Lim, Hak-Soo (Korea Institute of Ocean Science & Technology)
Publication Information
KSCE Journal of Civil and Environmental Engineering Research / v.35, no.5, 2015 , pp. 1061-1071 More about this Journal
Abstract
In the present study, the Navier-Stokes (N-S) equations delineating water flows inside porous media were derived applying Reynolds transport theorem in order to provide a basis for analyzing water wave problems inside the porous media. Then, the derived N-S equations were compared with the same species of equations in existing researches. Based on the N-S equations, a set of Boussinesq equations was then derived in such a form that the dispersiveness and nonlinearity of water waves inside the porous media can be properly reproduced. Finally, numerical analyses were carried out to demonstrate the validity of the equations. The reflection and transmission coefficients of porous breakwaters were calculated and compared with the results of existing hydraulic experiments. The numerical results showed a rather sensitive dependency on the virtual mass coefficient of grains constituting the porous media. The selection of the coefficient with zero turned out to give nice agreements with numerical and experimental results.
Keywords
Porous media; Navier-Stokes equation; Boussinesq equation; Porous breakwater; Virtual mass coefficient; Reflection coefficient; Transmission coefficient;
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