급변해저면을 갖는 해역에 대한 수정 부시네스크 방정식

Abstract

We investigated the transformation of water waves over rapidly varying topographywhich is simulated by the extended Boussinesq equations. We found that mild-slopeassumption was made during their derivation. Thus, both the bottom curvature and squaredbottom slope terms are neglected in the equations of Madsen and Sørensen (1992) and thesquared bottom slope terms are neglected in the equations of Nwogu (1993). We developed anew model which extends the model of Madsen and Sørensen by including both the bottomcurvature and squared bottom slope terms. Numerical experiments were conducted to measurenumerical results of the reflection coefficient of waves over the Booij’s (1983) planar slopeby varying incident wave periods. Nwogu’s model results are accurate for a mild slope butinaccurate for a steep slope. Madsen and Sørensen’s model results are not accurate for all theslopes in the intermediate water depth. The new developed model results are accurate for amild slope but inaccurate for a steep slope in the intermediate water depth. The inaccuracy inthe intermediate water depth comes from that the long wave approximation was made inimproving the model’s dispersion characteristics. Numerical experiments were also conductedto measure the reflection coefficient of waves over the Davies and Heathershaw’s (1984)ripple. The solutions of both the Nwogu’s model and the developed model are accuratebecause these models include the bottom curvature terms. However, the solutions of Madsenand Sørensen are inaccurate due to the neglect of the bottom curvature terms.