Verification of a Refined Boussinesq Equation by Using Vertical 2-D Numerical Analysis

Shinichiro ONDA, Takashi HOSODA, Ichiro KIMURA
The refinement on a depth-averaged model with effects of vertical acceleration was tested in this paper. A refined type equation is firstly derived with the iteration procedure to modify a vertical velocity distribution under irrotational condition, which is slightly different from the model by Madsen et al and Nwogu. The pressure distribution is determined by using the modified vertical velocity distribution. The way used by Madsen is further applied to the depth averaged momentum equation,
more » ... mentum equation, which is derived by substituting the modified vertical velocity and pressure distribution, to avoid the singularity in linear dispersion relation. To evaluate the model performance, the equation is applied to the free surface oscillation in a water tank and the relation of linear distribution is compared with the Airy wave. In addition, the non-linear approximate solution of the equation is analytically derived and the characteristics of the equation are examined through the comparison with the numerical solution by vertical 2-D CFD model.
doi:10.2208/prohe.46.589 fatcat:e2yfhs4hyncjdlo5wt6oqznxe4