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Explicit Solution of Wave Dispersion Equation Using Recursive Relation

순환 관계에 의한 파랑분산식의 양해

  • 이창훈 (세종대학교 토목환경공학과) ;
  • 장호철 (세종대학교 토목환경공학과)
  • Received : 2007.08.29
  • Accepted : 2007.11.13
  • Published : 2008.01.31

Abstract

Explicit solutions of the wave dispersion equation are developed using the recursive relation in terms of the relative water depth. We use the solutions of Eckart (1951), Hunt (1979), and the deep-water and shallow-water solutions for initial values of the solution. All the recursive solutions converge to the exact one except that with the initial value of deep-water solution. The solution with the initial value by Hunt converged much faster than the others. The recursive solutions may be obtained quickly and simply by a hand calculator. For the transformation of linear water waves in whole water depth, the use of the recursive solutions will yield more accurate analytical solutions than use of previously developed explicit solutions.

파랑의 분산관계식에서 상대수심이 반복적으로 표현되는 순환 관계를 이용하여 파랑분산식의 양해를 개발하였다. 순환 관계를 이용한 해의 초기값으로 Eckart(1951), Hunt(1979)의 해와 심해와 천해에서의 해를 사용했다. 순환해 가운데 심해에서의 해를 초기값으로 사용한 해를 제외하고는 모두 참값으로 수렴하였다. 특히, Hunt의 해를 초기값으로 사용한 해는 다른 해보다 더 빠르게 수렴했다. 순환해는 휴대용 계산기를 사용하여 손 쉽고 빠르게 구할 수 있는 장점이 있다. 선형파의 변형을 예측하기 위하여 해석 해를 사용할 경우 파랑분산식의 양해를 사용해야 하는 데 본 연구에서 개발한 순환해를 사용하면 기존의 양해를 사용한 것보다 더 정확한 해석 해를 도출할 것이다.

Keywords

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