Scaling and Self-Similarity of One-Dimensional Unsteady Suspended Sediment Transport with Emphasis on Unscaled Sediment Material Properties

Abstract

Current methods utilized in scaling sediment transport in unsteady open-channel flow result in a number of model and scale effects, decreasing the accuracy and applicability of scale models. Identifying the conditions under which the governing equations of sediment transport are self-similar, and require no sediment diameter or density scaling, can reduce scale effects and increase model applicability. Conditions for self-similarity of one-dimensional unsteady suspended sediment transport are identified by applying the one-parameter Lie group of point scaling transformations, both for the general case and with unscaled sediment diameters. Under the scaling ratio relations found when holding sediment diameter to be unscaled, sediment diameter, density, critical and total shear, porosity, kinematic viscosity, and particle Reynolds number are all unscaled. It is shown that under Lie group scaling, the unsteady one-dimensional suspended sediment transport process as an initial-boundary value problem in the prototype domain can be self-similar with that of a variety of different scaled domains. The scaled values of sediment variables at specified temporal and spatial locations can then be upscaled to the corresponding values in the prototype domain.