Growth of natural dams by deposition from steady supersaturated shallow flow

Abstract

The frequent occurrence in nature of dams or terraces deposited from supersaturated flows prompted the hypothesis that wavelike but quasi‐steady solid profile shapes may develop after sufficient time has elapsed. Dressler's (1978) approximate equations are used to describe steady fluid flow over a curved accreting surface, including a Chezy term to represent flow resistance. The case of a transition from subcritical to supercritical flow is treated, which leads to solutions for dams but excludes terraces. It is assumed that deposition is controlled principally by the diffusive resistance of the laminar sublayer, the thickness of which is almost inversely proportional to the flow velocity, lag effects being neglected on the assumption of large length scale/depth ratios. From the equations, the length scale of both the fluid flow and the solid profile is fixed by flow depth, and is relatively unaffected by slow temporal variations of the degree of supersaturation. The depth is defined by an upstream boundary condition on flow rate. This is taken constant as the surface grows, so that for selfsimilarity the profile moves in uniform translation. The direction of growth (“growth angle”) of the profile is expected to be nonhorizontal and is not known a priori. Here it is determined by the requirements of the geometrical boundary condition needed to satisfy the quasisteady growth assumption. The profile shape can be calculated from predetermined conditions, e.g., known values of the Froude number and drag coefficient. In applications involving the inverse problem, theoretical profiles have been fitted to photographs of natural dams with apparent success, and values of the Froude number and drag coefficient have been deduced. The study of these systems may be relevant to problems of mineral deposition.