Topological and fractal aspects of the main hydraulic parameters

Abstract

The traditional concept of wetted cross-section, wetted perimeter and hydraulic radius seems fairly simple and clear, especially in the case of smooth boundaries of the flow. However, for the rough boundary surface covered with randomly arranged roughness the definition of the wetted cross-section as a normal to all elementary streams becomes notably problematic. More controversial seems the concept of wetted perimeter. This issue is of particular importance for the beds with high-dimensional roughness for which the geometric dimensions of the flow and the roughness elements are of the same order. The article shows that topological features of the boundary surfaces for the natural channels allow definitely refer them to fractals. Further study of the bed roughness based on its fractal nature can form a new approach to methodological soundness of main hydraulic parameters and open up new opportunities for their description.