대한토목학회논문집 (KSCE Journal of Civil and Environmental Engineering Research)

  • 제35권5호
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  • Pages.1061-1071
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  • 2015
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  • 1015-6348(pISSN)
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  • 2799-9629(eISSN)
대한토목학회 (Korean Society of Civil Engeneers)
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공극매체에서의 파동장에 대한 Boussinesq 방정식의 유도 및 적용

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

  • 투고 : 2015.04.22
  • 심사 : 2015.08.04
  • 발행 : 2015.10.01
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초록

공극매체에서의 파동장을 해석할 목적으로 공극매체 흐름에 대한 Reynolds 이송정리를 적용하여 공극매체에서의 Navier-Stokes 방정식을 유도하였으며 기존의 연구들과 비교하였다. 또한, 이 N-S 방정식을 이용하여 공극매체 내외에서 파동장의 비선형성과 분산성을 적절히 재현하기 위한 확장형 Boussinesq 방정식을 유도하였다. 이들 방정식의 정확도를 검증하기 위하여 공극방파제의 반사율과 투과율에 대한 수치해석을 수행하여 그 결과를 기존의 수리실험결과들과 비교하였다. 수치해석결과는 토립자의 가상질량계수에 민감하게 반응하였으며 계수를 영으로 처리했을 때 수리실험결과와 비교적 잘 일치하는 것으로 나타났다.

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.

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