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

Abstract:

The conditions under which the governing equation for non-equilibrium one-dimensional suspended 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 identified and investigated. Preserving sediment density and diameter is believed to eliminate some of the scale errors encountered in traditional scaling methods. Under these conditions, not only are sediment diameter and density unscaled, but so too are the critical and total shear, kinematic viscosity and particle Reynolds number. The similarity of suspended sediment transport is increased through more accurate representation of suspended sediment concentration and carrying capacity of flow. The proposed method meets the needs of modelers by; maintaining the benefits found from distortion such as reduced cost, space, and model run-time; removing the need to apply scaled sediment or surrogate sediment; avoiding some of the scale effects and resulting errors of traditional flow and sediment transport scaling.