Upstream influence in erodible beds

Abstract

Abstract We tackle the problem of the morphodynamic influence in river meandering on the basis of a quasi 3-D model for flow field and bottom topography in arbitrary curved channels. A linearized treatment of the depth-averaged equations allows for an exact analytical solution which shows that the morphodynamics of a meandering river is determined, in general, by the distribution of centerline curvature. The latter gives rise both to a local effect and to some history effects which allow evaluation of the morphodynamic influence of the upstream and/or downstream reaches on the given cross section. We find that river morphodynamics is mainly downstream influenced provided the width ratio of the channel (β) does not exceed the resonant value (βR) of Blondeaux and Seminara (1985). Upstream influence dominates when β exceeds βR. These features were implicit in previous work, but don't seem to have been pointed out before. The theory is applied to the process of overdeepening occurring in erodible channels consisting of sequences of straight reaches and curved reaches with constant curvature and fixed banks. Struiksma et al. (1985) observed that a series of longitudinally damped oscillations of the bed surface is localized downstream of the cross section where the discontinuity of channel curvature occurs (downstream overdeepening); our theoretical results well compare with experimental results concerning this case, while experimental testing of the upstream overdeepening phenomenon is now being pursued. The theory is then set as the basis of a simulation model of planimetric development of river meanders. Along with the classical evolutive scenario of the Kinoshita (1961) type, we emphasize the possibility of a reversal in skewing and in direction of migration of meander loops, and point out a variety of realistic meandering patterns which do not seem to have been pointed out before.