Shear-Stress and Sediment Distribution in a Meander Bend

Abstract

A one-meter wide, meandering flume with movable sand bed was utilized in these experiments. Uniform flow was established at discharges of 20, 35, and 50 l/sec. Velocities near the bed, the distribution of sediment in transport, bed geometry, and strength of secondary flow were determined at each discharge . Bed shear stress was assumed to be proportional to the square of the velocity near the bed. Bed shear stresses were also measured with a Preston Tube in a uniform 35 l/sec flow over a dune-free stabilized bed. The stabilized bed was molded to the geometry produced by the same flow over sand. The zone of maximum bed shear stress and maximum sediment discharge is on the point bar in the upstream part of the bend. It crosses the channel centerline in the middle or downstream part of the bend, and follows the concave or down-valley bank to the next point bar downstream. With increasing discharge, secondary currents increase in strength. Consequently the zone of maximum bed shear stress and sediment discharge remains closer to the inside bank across the point bar, and crosses the channel centerline somewhat lower in the bend. Secondary currents were also stronger in the 35 l/sec over the stabilized bed than in the same flow over sand, apparently because no dunes were present to break up secondary flow in the former. The zone of maximum bed shear stress was consequently closer to the inside bank in the stabilized-bed run. It appears that bed geometry is adjusted to provide, at each point on the bed, precisely the shear stress necessary to transport the sediment load supplied. For example the gradual decrease in depth along the down-valley side of the channel from the deep in one bend to the point bar in the next results in a continual acceleration of the flow, and hence in shear stresses here which are higher than average for the channel. For many combinations of discharge, sediment discharge, and sediment character, straight channels are unstable in nature, and the commonly observed meander geometry is stable. To understand why this meander geometry is stable, we consider how displacements from the stable geometry set up forces tending to restore that geometry, From work done to date, it is hypothesized that channel width, W, is determined by cohesiveness of bank materials. The radius of curvature of the bend, R, is then determined by the fact that separation occurs when R/W=