GROWTH OF ALTERNATE BARS IN UNSTEADY-FLOW

A theoretical model is formulated to investigate the development of the amplitude of alternate bars in unsteady flows. The problem is tackled by means of a weakly nonlinear analysis developed in a neighborhood of the threshold conditions for bar formation. Bar response to unsteady flow is found to depend on a parameter U-triple-over-dot that is a measure of the ratio between the time scale of the basic flow and the time scale of bar growth. The present theory shows that if U-triple-over-dot is O(1), as often occurs in nature, flow unsteadiness affects the instantaneous growth rate and phase of bar perturbations and controls the final amplitude reached by the bed configuration. A procedure for determining the final amplitude for a given flood event is proposed. Flume experiments were performed to test the main theoretical results. The bed response to unsteady flow was measured for different values of the period of the flood. The observed temporal behavior of the bar amplitude proves to be strongly affected by the unsteady character of the flow for U-triple-over-dot of O(1), as predicted by the theory.