Self-Similarity in One-Dimensional Unsteady Open Channel Flow through Irregular Channel Cross-Sections

Geophysical processes could be self-similar under certain similarity transformations at certain time and space dimensions. In this study, the conditions under which the Saint Venant equations system for unsteady open channel flow through irregular channel cross-sections becomes self-similar under various time and space scales are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the initial and boundary conditions are also investigated thoroughly in addition to the conditions due to the governing equations. The proposed scaling relations may provide additional spatial, temporal, and economical flexibility in setting up physical hydraulic models.