STABILITY OF TRANSVERSE-SHEAR FLOWS IN SHALLOW OPEN CHANNELS

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.