Collision of Solitary Waves in Branching Channels

The collision of solitary waves in branching channels is investigated on the basis of the extended Boussinesq equations in terms of the velocity potential and the surface elevation. The equations are transformed into a generalized curvilinear coordinate system so that the numerical domain can be fitted to the channel boundaries of a complex geometry. The transformed equations are then solved numerically by using a high-order finite difference method. The merit of the potential formulation is described and it is confirmed that the computational efficiency can be significantly improved compared with a velocity formulation. A series of computations is carried out for two types of branching channels with basic shapes. The general features of the transformation and interaction of solitary waves near the branch are described, and the effects of the channel geometry on the maximum crest height are examined. It is shown that the influence of the channel geometry on wave transformations is significant and that the maximum crest height becomes almost three times as large as the incident wave amplitude in wide channels.