Linear Stability Analysis of Lateral Motions in Compound Open Channels

Abstract

A linear stability analysis of lateral motions in shallow flow open channels with a free surface is presented. Unlike previous studies, this work does not employ the rigid-lid assumption. Computations revealed that the rigid-lid assumption works well for weak shear flows and/or small Froude numbers. However, the validity of the rigid-lid assumption is reduced as the Froude number increases. Also, when Reynolds numbers are larger than 1,000, the stability domain is insensitive to the Reynolds number for all Froude numbers. The size of the stability domain is found strongly affected by the velocity and length scales of base velocity and the shape of the velocity profile. The analysis shows that the stability domains obtained by the Manning formula are larger than those obtained by the Chézy formula for the same Froude number. The analysis shows that a compound channel, whose floodplain has larger flow resistance than the main channel does, has larger lateral transport of flow mass, momentum, and energy.