Scale Invariance and Self-Similarity of 1-Dimensional Non-equilibrium Bedload Sediment Transport

The conditions under which the governing equation for non-equilibrium one-dimensional bedload sediment transport in unsteady flows is scale-invariant and self-similar are examined by applying the one-parameter Lie group of point scaling transformations. Self-similarity conditions imposed due to initial and boundary conditions are also examined. Furthermore, one-parameter Lie group point scaling transformations required to physically scale the transport process without scaling the sediment material properties are investigated. Under Lie group scaling, the unsteady bedload sediment transport process, as an initial-boundary value problem in the prototype domain, can be self-similar with that of a variety of scaled spatial and temporal domains. By applying the Lie group scaling method to the Saint-Venant equations as well as the governing equation for one-dimensional non-equilibrium bedload sediment transport, a simplified approach to bedload sediment transport modeling is created. The proposed scaling approach carries the advantage of identifying the self-similarity conditions due to the initial and boundary conditions of the IBVP along with those due to the governing equations, expanding scaling of sediment transport to unsteady, non-equilibrium conditions.