Investigations of Self-Similarity and Scale Invariance of One-Dimensional Unsteady Bedload Transport

Self-similarity conditions and scale invariance of unsteady one-dimensional bedload sediment transport are investigated through the application of the one-parameter Lie group of point scaling transformations. Determining the suitability of scaling bedload transport equations has been plagued by empiricism. Two bedload transport equations are investigated to determine a representation of the transport regime that will be self-similar and scale invariant at a variety of different scaled domains. Furthermore, one-parameter Lie group point scaling transformations required to physically scale the transport process without scaling the sediment material properties are investigated. By applying the Lie group scaling method to the governing equations for one-dimensional non-equilibrium bedload sediment transport, a simplified approach to bedload sediment transport modeling is sought. The proposed scaling approach carries the advantage of identifying the self-similarity conditions due to the initial and boundary conditions of the corresponding initial and boundary value problem along with those due to the governing equations, expanding scaling of transport to unsteady, non-equilibrium conditions.