Author(s): Gunwoo Kim; Changhoon Lee; Woo Sun Park; Kyung-Duck Suh
Linked Author(s):
Keywords: Extended Boussinesq equations; Higher-order bottom variation; Steep slope; Ripple; Numerical experiment
Abstract: We investigated the transformation of water waves over rapidly varying topography which is simulated by the extended Boussinesq equations. We found that mild-slope assumption was made during their derivation. Thus, both the bottom curvature and squared bottom slope terms are neglected in the equations of Madsen and Sorensen (1992) and the squared bottom slope terms are neglected in the equations of Nwogu (1993). We developed a new model which extends the model of Madsen and Sorensen by including both the bottom curvature and squared bottom slope terms. Numerical experiments were conducted to measure numerical results of the reflection coefficient of waves over the Booij’s (1983) planar slope by varying incident wave periods. Nwogu’s model results are accurate for a mild slope but inaccurate for a steep slope. Madsen and Sorensen’s model results are not accurate for all the slopes in the intermediate water depth. The new developed model results are accurate for a mild slope but inaccurate for a steep slope in the intermediate water depth. The inaccuracy in the intermediate water depth comes from that the long wave approximation was made in improving the model’s dispersion characteristics. Numerical experiments were also conducted to 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 accurate because these models include the bottom curvature terms. However, the solutions of Madsen and Sorensen are inaccurate due to the neglect of the bottom curvature terms.
Year: 2007