Author(s): M. S. Ghidaoui; A. A. Kolyshkin
Linked Author(s): Mohamed S. Ghidaoui
Keywords: Roll waves; Stability of a gradually varying flow; Shallow water
Abstract: Flow instabilities in the form of roll waves, surges and bores are ubiquitous in shallow water flows. For example, surges and bores are commonly observed during rising flood and tida waves. In addition, roll waves are a common occurrence in overland flow, street surface flow partially fully sewer flow, gutter flow and slope drainage flow. Stability analysis is crucial fo determining the physical mechanisms and the condition for the formation of roll waves, surges and bores. To this end, stability of a gradually varying flow in an inclined open channel with a constan slope is studied in this paper. Stability criteria are obtained for Chezy and Manning resistance formulae. It is shown that momentum correction coefficient has a strong stabilizing influence on the stability boundary for supercritical flows (F r< /sbu> > 1). The method of multiple scales is used in order to derive nonlinear amplitude equation. Results of numerical calculations are presented.