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.
Cite this paper
K. Njenga, K. Kioko and G. Wanjiru, "Secondary Current and Classification of River Channels," Applied Mathematics
, Vol. 4 No. 1, 2013, pp. 70-78. doi: 10.4236/am.2013.41013
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