Stability of Transverse Shear Flows in Shallow Open Channels

Abstract

The bed‐friction effect on the stability of transverse shear flows in shallow open channels is examined using a linear and “inviscid” theory. Numerical calculations are conducted for four groups of parallel flows with inflection‐point velocity profiles. The necessary conditions for the transverse shear flows to become unstable, so that the large‐scale transverse motion may coexist with the small‐scale bed‐generated turbulence, are determined from the calculations. The results are correlated with two dimensionless parameters: a bed‐friction number and an ambient‐velocity parameter. The bed‐friction number quantifies the stabilizing effect of the bed‐friction. The ambient‐velocity parameter characterizes the changes in depth and roughness across the open‐channel flows. In the limiting case of a weak transverse shear flow, when the change in velocity across the flow is small, the bed‐friction number becomes the only dimensionless parameter governing the stability of the transverse shear flows. The critical values of this bed‐friction number for the weak transverse shear flows with hyperbolic‐tangent and hyperbolic‐secant velocity profiles, are 0.120 and 0.145, respectively.