Morphology of Dune-Like Relief in Rivers

Abstract

Linearized equations of two-dimensional hydraulics have been analyzed by the method of small perturbations within a wide range of alluvial features sizes at large values of Froude numbers and hydraulic resistance. The preservation of three-dimensional effects in depth-averaged equations of motion, continuity, and deformation enabled the authors to identify domains with combinations of flow hydraulic characteristics that correspond to alluvial features of different size and morphology. The study confirmed the results of the earlier analysis for subcritical flows with small hydraulic resistance and showed new types of relationships between alluvial features morphology and the hydraulic characteristics of flow for flows with large Froude numbers and high hydraulic resistance. In addition, a relationship between the length of two-dimensional ultramicroforms and hydraulic resistance has been established. A new class of macroforms—two-dimensional macroforms—have been identified. The verification of the results of theoretical analysis by measurements data on the morphology of channel formations and hydraulic characteristics of the flow has shown that the analysis of linearized equations of two-dimensional hydrodynamics by small-perturbation method can be used to determine the morphology and dimensions of channel forms in both subcritical and supercritical streams. The step–pool systems in torrential streams in mountain rivers are analogues of antidunes (in supercritical flows) and ripples (in subcritical flows), obtained in large flumes with sand alluvium. Three-dimensional macroforms are most common in rivers. If such macroforms are well developed in wide channels (at flow width greater than the half-width of the macroform), their length is determined by channel depth. Macroforms in narrower channels cannot develop completely, and their lengths are limited by channel width and can be calculated only through this width.