Abstract
In this research, the secondary current theory is used in investigating the role of phase shift angle between the secondary current and the channel axis displacement in stability analysis of a river channel. To achieve this, a small-perturbation stability analysis is developed for investigation of the role of the secondary current accompanying channel curvature in the initiation and early development of meanders in open channels. The secondary currents are generating in planes perpendicular to the primary direction of motion. The secondary currents form a helical motion in which the water in the upper part of the river is driven outward, whereas the water near the bottom is driven inward in a bend. Force-momentum equations for longitudinal and transverse direction in open channel bends were utilized. Assuming that the transverse force contributed by the bed is negligible, the pressure force associated with the transverse surface inclination is balanced by the centripetal force. Existing equations of the transverse velocity profile were analyzed. Since the magnitude of the vertical velocity is negligible compared to the transverse velocity in secondary currents, this study concentrates on the transverse velocity which is the radial component of the secondary current. This formulation leads to a linear differential equation which is solved for its orthogonal components which give the rates of meander growth and downstream migration. It is shown that instability increases with decrease in phase shift angle. Transition from straight to meandering and then from meandering to braiding occurs when phase shift angle is reduced.
Highlights
[1] presented a quantitative basis for differentiating straight, meandering, and braided channel patterns based on relationships between slope and discharge. [2] noted that an increase in the ratio of bed material load to total sediment load with a corresponding increase in channel gradient leads to a decrease in stability and causing channel patterns to shift from a meandering to braided channel form. [3] argued that the pattern of a river channel changes from meandering to braiding with increasing flow strength. [4] observed that the lower limit of sinuosity of a meandering river is 1.5 and larger width-depth ratios characterize braided rivers
Instability was observed to increase with decrease in phase shift angle
This is due to the fact that secondary currents are more directed on the river banks and causing more erosion on the concave bank and more deposition on the convex bank at small phase shift angle
Summary
[1] presented a quantitative basis for differentiating straight, meandering, and braided channel patterns based on relationships between slope and discharge. [2] noted that an increase in the ratio of bed material load to total sediment load with a corresponding increase in channel gradient leads to a decrease in stability and causing channel patterns to shift from a meandering to braided channel form. [3] argued that the pattern of a river channel changes from meandering to braiding with increasing flow strength. [4] observed that the lower limit of sinuosity of a meandering river is 1.5 and larger width-depth ratios characterize braided rivers. [3] argued that the pattern of a river channel changes from meandering to braiding with increasing flow strength. Secondary currents represent circulation of fluids around the axis of the primary flow [11] This leads to movement of fluid particles on a circular path which referred to as spiral motion. Angle of the secondary current from the channel axis displacement plays a critical role in determining meander pattern and stability of a river channel. Based on secondary current theory, there is no mathematical model that has been generated to classify river channels using the width-depth ratio and the phase shift angle. It’s shown that river channel changes from straight to meandering and from meandering to braiding as the phase shift angle reduces. Instability increases with decrease in phase shift angle and meander growth dominates downstream meander migration at small phase shift angle and vice versa
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