Minimum channel length for roll-wave generation

The initial phase of roll-wave development is investigated by means of spatial linear stability analysis using the St. Venant equations, subject to a pointwise time-varying oscillating disturbance. The predicted spatial growth is compared with both Vedernikov's results and those computed with a fully non-linear model. It is shown that for large values of the channel slope Vedernikov's theory systematically overpredicts the roll waves spatial growth rate, whereas the present analysis yields significant improvements. A modification of Montuori's criterion for the minimum channel length prediction is finally proposed, which agrees with available experimental data independently of the channel slope.