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On nonlinear simple waves in alluvial river flows: a theory for sediment bores

An increase in the upstream sediment discharge rate in an otherwise uniform alluvial flow often leads to the formation of a stable, propagating sediment bore. In this paper we study discontinuous simple wave solutions of the integral conservation laws governing flows in alluvial rivers or channels. We obtain a family of solutions, parametrized by the upstream sediment discharge rate, qL, and the downstream Eroude number, FO,which represent stable sediment bores. It is shown that the solutions exist only in a restricted region of the(FO, qL) plane, and within this region, their properties are derived. A sediment bore is generated experimentally in a flume and measurements are made. The agreement between the measurements and the predictions of the theory is encouraging.