Author(s): Man Yue Lam; Mohamed S. Ghidaoui
Keywords: Compound channels; Shear instability; Roll waves; Gravity waves; Froude number
Abstract: The effects of gravity waves on shear instability in compound channels are investigated. Scale analysis of the shallow water equations shows that the shear instability depends on the two Froude numbers: the stream Froude number Frs defined with the streamwise velocity, and the convective Froude number Frc. Frs corresponds to the destabilizing effect of gravity waves due to the reduction of bed frictional force by water depth perturbations. Frc corresponds to the effect of wave radiation. To quantify the effects of Frc and Frs on the shear instability respectively, linear stability analysis is performed numerically with a shooting procedure instead of the pseudospectral collocation method in order to account for the wave radiation from the shear layer. Initial results show that Frc stabilize the shear instability and Frs destabilize the instability in compound channels with bed friction. The future work will be on the linear stability analysis of shear instability in compound channels under more different S and Frc values, and the study of roll wave instability.