Shock fitting of aggradational profiles due to backwater

Depositional deltas form in the headwaters of most reservoirs. The deltas are characterized by a developing foreset slope that eventually approaches the submerged angle of repose. Deltas extend both upstream and downstream; downstream growth seriously depletes reservoir storage, while upstream evolution raises local ground-water levels and increases flood frequency. Flow separates as it passes downstream over the delta lip into the deeper part of the reservoir. Because of this flow separation and attendant recirculation, traditional finite difference modeling approaches are invalid near the steep foreset slope and cannot model delta growth accurately. A method of numerically fitting a vertical shock face to the evolving delta is developed and illustrated. Conditions upstream of the shock are described with the traditional St. Venant equations; downstream conditions are constant. A one-dimensional mobile-bed computer model is developed and compared to a simulated reservoir in a laboratory flume. The simulated delta closely matches the growth and propagation rate of the observed delta.