Various interaction patterns of free-surface flow over multiple bumps at the bottom topography

Abstract

The free-surface flow generated by multiple bumps at the bottom topography in a rectangular channel was considered, in the framework of the forced Korteweg-de Vries (fKdV) equation. The fKdV equationwill be solved numerically using pseudo-spectral method as an analytical solution could not be obtained due to the presence of forcing term and broken symmetry. Various interaction patterns of solitary waves with certain parameter regimes were observed and presented in various graphical forms. Interesting interaction patterns of the collision between uniformly forced solitons will provide us with a better understanding of the hindrance caused by multiple bumps at the uneven bottom topography and it will have a high impact on the water flow in a rectangular channel with uneven bottom topography.