YeonKil Jung - Non-Linear Dispersive Wave Propagation and Reflection in Complicated Bottom Profiles

Non-Linear Dispersive Wave Propagation and Reflection in Complicated Bottom Profiles

YeonKil Jung
Applied Mathematics
University of Colorado at Boulder

In shallow water, both non-linearity and frequency dispersion are important. Boussinesq-type equations are much more adequate mathematical models to describe these in this region. However, the traditional Boussinesq-type equations can only be applied to very shallow water. Some of them become unstable when they are applied to intermediate depth.

The purpose of this research was to focus on the follows:

1. The modification of linear dispersion of Boussinesq equations by Chebyshev polynomial matching Pade expansion techniques. This significantly improves the linear dispersion of the Boussinesq-type equations, making them applicable to a wider range of water depths.
2. The development of a numerical model that can propagate waves from deep depth to shallow water including wave breaking. In order to examine the applicable limit of the numerical models, numerical computations based on one-dimensional time domain Boussinesq equations with improved dispersion characteristics are carried out to model unidirectional waves propagating over a submerged obstacle. Comparisons for non-breaking waves show good agreement between the numerical results and experimental results (by DELFT) in a wave flume with submerged trapezoidal bar.

The results demonstrate that the new form of Boussinesq-type equations can reasonably simulate several nonlinear effects of surface wave from deep to shallow water and have comparatively in good agreement with experimental results.