An Extended Mathematical Model for Shallow Water Flows in Vegetated Open Channels

Abstract

An extended mathematical model governing shallow water flows in vegetated open channels, referred to as the 1-D extended shallow water equations (1-D ESWEs), is presented in this paper as a physically more consistent alternative to the conventional 1-D SWEs. Emerged and submerged aquatic plants in channels are considered in the 1-D ESWEs as momentum sinks with appropriately defined water fractions. The 1-D ESWEs improve the double-counting problem on the momentum losses in the 1-D SWEs originating from the additivity assumption of the wall friction and vegetation drag forces without considering the water fraction. The 1-D ESWEs are applied to steady and unsteady numerical simulation of water flows in an agricultural drainage canal in Japan. The computational results demonstrate advantages of the 1-D EWSEs over the 1-D SWEs, reducing overestimation of the water depth. Impacts of the vegetation modeling on the flows in the canal are also assessed through the unsteady simulation.