Scaling and Self-Similarity of One-Dimensional Suspended Sediment Transport Equations

Abstract

The governing physical process of sediment transport can be represented in a scale model without the simplifying assumptions required in numerical modeling, making scale modeling a considerable complement to numerical simulations. However, the current methods utilized in scaling sediment transport in unsteady openchannel flow result in a number of model and scale effects, which decrease the accuracy and applicability of scale models. These model and scale effects may be reduced, and model applicability may be increased, by determining the conditions under which the governing equation for non-equilibrium sediment transport in unsteady flows are self-similar and require no scaling of sediment diameter and density. Conditions for self-similarity and unscaled sediment properties, for nonequilibrium sediment transport could be identified by applying the one-parameter Lie group of point scaling transformations. When coupled with one-parameter Lie group scaling of the Saint Venant equations for unsteady open channel flow, the scale effects of physical models could be reduced further. This article describes briefly the methodology of Lie-group scaling transformations and leaves the derivation of the self-similarity conditions of one-dimensional suspended sediment transport equations to later studies.