ABSTRACT
Bed-friction is an effect of significance on the instability of high-speed shear flow in shallow waters. Chu et al. (1991) examined the effect using a rigid-lid approximation. Without the waves, bed-friction is a stabilizing influence. The role of the waves was investigated recently by Karimpour & Chu (2016) ignoring the effect of the bed-friction. When bed-friction were ignored, the waves also was a stabilizing influence. In this paper, the instability is analyzed for the combined effect of the waves and the bed-friction over the full range of bed-friction number and convective Froude number. We find the solution to the eigenvalue problem of the instability by the shooting method and then verified by the pseudo-spectrum collocation method. The two methods have produced identical modes of shear instability that (i) reconfirm the previous results by Chu et al. (1991) and Karimpour & Chu (2016), and (ii) show the bed friction is a significant destabilizing effect leading to wave-like instability in the high-speed shear flow on steep channel.
