WAVE GENERATION ON AN INCLINED OPEN CHANNEL WITH A BUMP

Abstract

A uniform flow on an open channel is studied in this paper. Shallow water equations are used
as the model by involving the bottom topography. In this problem, we focus on incline bottom and put a bump
on it, so that the flow generates a surface wave. The model is extended by energy dissipation through tangential
shear and the energy dissipation by shearing normal to the flow. In non-dimensional variables, the profile of
the fluid surface is observed as waves growing to split and propagating, depending on the type of the bump,
parameters angle of the channel, Froude number and Reynolds number. When the angle is not zero, we found
that the waves propagate downward and possible appearing secondary waves or undular bore, that does not
occur for zero angles but agrees to the model of Boussinesq equations. To get the accurate result with purely
showing the damping effect from the equation, the finite volume method has been applied on a staggered grid
that is free from damping error to solve the equations numerically.