Extended Boussinesq Equations for Rapidly Varying Topography

Abstract

We developed a new Boussinesq-type model which extends the equations of Madsen and Sørensen (1992) by including both bottom curvature and squared bottom slope terms. Numerical experiments were conducted for wave reflection from the Booijs (1983) planar slope with different wave frequencies using several types of Boussinesq equations and extended mild-slope equation. Madsen and Sørensens model results are accurate in the whole slopes in shallow waters but inaccurate in intermediate water depths. Nwogus (1993) model results are accurate up to 1:1 (V:H) slope but significantly inaccurate for steep slopes. The present model results are accurate up to the slope of 1:1 but somewhat inaccurate for very steep slopes. Further, numerical experiments were conducted for wave reflections from a ripple patch and also a Gaussian shaped trench. For the two cases, the results of Nwogus model and the present model are accurate because these models include the bottom curvature term which is important for the cases. However, Madsen and Sørensens model results are inaccurate because this model neglects the bottom curvature term.