Flows caused by rise of a rectangular bar partially immersed in shallow water

Abstract

The wave flows caused by the vertical rise of a rectangular bar partially immersed in shallow water filling a rectangular prismatic channel with a horizontal bottom are investigated. Such flows are modeled within the framework of the first approximation of the theory of shallow water disregarding the effect of drag, the viscosity of the fluid, and its surface tension. The case is considered when at the second stage of flow at which the edges of the lower surface of the bar start to come out from the water, the pressure in the region of contact of the bar with the fluid is less than atmospheric one. For this case, an explicit formula setting the law of motion of this boundary is obtained.