4 results
Interaction between curvature-driven width oscillations and channel curvature in evolving meander bends
- F. Monegaglia, M. Tubino, G. Zolezzi
-
- Journal:
- Journal of Fluid Mechanics / Volume 876 / 10 October 2019
- Published online by Cambridge University Press:
- 09 August 2019, pp. 985-1017
-
- Article
- Export citation
-
We study the morphodynamics of channel width oscillations associated with the planform development of river meander bends. With this aim we develop a novel planform evolution model, based on the framework of the classical bend theory of river meanders by Ikeda et al. (J. Fluid Mech., vol. 112, 1981), that accounts for local width changes over space and time, tied to the local hydro-morphodynamics through a two-way feedback process. We focus our attention on ‘autogenic’ width variations, which are forced by flow nonlinearities driven by channel curvature dynamics. Under the assumption of regular, sinusoidal width and curvature oscillations, we obtain a set of ordinary differential equations, formally identical to those presented by Seminara et al. (J. Fluid Mech., vol. 438, 2001, pp. 213–230), with an additional equation for the longitudinal oscillation of the channel width. The proposed approach gives insight into the interaction between autogenic width variations and curvature in meander development and between forcing and damping effects in the formation of width variations. Model outcomes suggest that autogenic width oscillations mainly determine wider-at-inflection meandering river patterns, and affect their planform development particularly at super-resonant aspect ratios, where the width oscillation reaches its maximum and reduces meander sinuosity and lateral floodplain size. The coevolution of autogenic width oscillation and curvature occurs through temporal hysteresis cycles, whereby the peak in channel curvature lags behind that of width oscillation. Width oscillation amplitudes predicted by the model are consistent with those extracted from remotely sensed data.
Free instability of channel bifurcations and morphodynamic influence
- M. Redolfi, G. Zolezzi, M. Tubino
-
- Journal:
- Journal of Fluid Mechanics / Volume 799 / 25 July 2016
- Published online by Cambridge University Press:
- 28 June 2016, pp. 476-504
-
- Article
- Export citation
-
Channel bifurcations are a fundamental element of a broad variety of flowing freshwater environments worldwide, such as braiding and anabranching rivers, river deltas and alluvial fans. River bifurcations often develop asymmetrical configurations with uneven discharge partition and a bed elevation gap between the downstream anabranches. This has been reproduced by one-dimensional (1-D) analytical theories which, however, rely on the empirical calibration of one or more parameters and cannot provide a clear and detailed physical explanation of the observed dynamics. We propose a novel two-dimensional (2-D) solution for the flow and bed topography in channel bifurcations based on an innovative application to a multi-thread channel configuration of the 2-D steady linear solution developed decades ago to study river bars and meandering in single thread river settings. The resonant value of the upstream channel aspect ratio, corresponding to the theoretical resonance condition of regular river meanders (Blondeaux & Seminara, J. Fluid Mech., vol. 157, 1985, pp. 449–470) is the key parameter discriminating between symmetrical and asymmetrical bifurcations, in quantitative agreement with experimental observations and numerical simulations, and qualitatively matching field observations. Only when the aspect ratio of the upstream channel of the bifurcation exceeds resonance, is the bifurcation node able to trigger the upstream development of a steady alternate bar pattern, thus creating an unbalanced configuration. Ultimately, the work provides an analytical explanation of the intrinsic legacy between bifurcation asymmetry and the phenomenon of 2-D upstream morphodynamic influence discovered by Zolezzi & Seminara (J. Fluid Mech., vol. 438, 2001, pp. 183–211).
Downstream and upstream influence in river meandering. Part 2. Planimetric development
- G. ZOLEZZI, G. SEMINARA
-
- Journal:
- Journal of Fluid Mechanics / Volume 438 / 10 July 2001
- Published online by Cambridge University Press:
- 05 July 2001, pp. 183-211
-
- Article
- Export citation
-
Perturbations of channel geometry (like variations of channel curvature or channel width) in meandering rivers give rise to morphodynamic effects which display themselves through the development of large-scale perturbations of bottom topography in the form of stationary bars developing in the longitudinal direction. The latter may then drive the lateral migration of the channel by enhancing bank erosion at bar pools: through this mechanism local perturbations of channel geometry may affect the planimetric development of meandering rivers on large timescales. The problem tackled herein is whether such morphodynamic influence is invariably felt downstream as the commonly employed model of river meandering would suggest.
In order to solve this problem, we derive the exact solution of the linearized form of the mathematical problem of river morphodynamics. Linear analysis had pointed out the existence of a resonance phenomenon: in a linear (hence ideal) context, resonance occurs when the meander wavenumber and the width ratio of the channel take values (λR and βR, respectively) such as to force free spatial modes of the system consisting of free bars which neither grow nor decay either in time or in space. Channels characterized by values of the width ratio β larger (smaller) than βR are called super- (sub-)resonant. The present solution, which applies to channels with constant width and arbitrary curvature distribution, shows that two distinct scenarios may occur: downstream influence is associated with sub-resonant channels and vice versa dominant upstream influence occurs in super-resonant channels. Small-amplitude waves of bottom topography are shown to migrate downstream in the former case and may migrate upstream in the latter, as resonance also defines the threshold conditions below (above) which small-amplitude alternate bar perturbations (may) migrate downstream (upstream).
These results have several implications. In the present paper we examine the overdeepening phenomenon whereby abrupt variations of channel curvature, as in sequences of straight and constant curvature reaches, lead to sequences of stationary alternate bars with amplitude decaying in the longitudinal direction. We show that, along with downstream overdeepening, an upstream overdeepening scenario is predicted in the super-resonant regime.
Implications of the upstream influence on planimetric development of meandering rivers are investigated in Part 2.
Downstream and upstream influence in river meandering. Part 2. Planimetric development
- G. SEMINARA, G. ZOLEZZI, M. TUBINO, D. ZARDI
-
- Journal:
- Journal of Fluid Mechanics / Volume 438 / 10 July 2001
- Published online by Cambridge University Press:
- 05 July 2001, pp. 213-230
-
- Article
- Export citation
-
The exact solution of the problem of river morphodynamics derived in Part 1 is employed to formulate and solve the problem of planimetric evolution of river meanders. A nonlinear integrodifferential evolution equation in intrinsic coordinates is derived. An exact periodic solution of such an equation is then obtained in terms of a modified Fourier series expansion such that the wavenumbers of the various Fourier modes are time dependent. The amplitudes of the Fourier modes and their wavenumbers satisfy a nonlinear system of coupled ordinary differential equations of the Landau type. Solutions of this system display the occurrence of two possible scenarios. In the sub-resonant regime, i.e. when the aspect ratio of the channel is smaller than the resonant value, meandering evolves according to the classical picture: a periodic train of small-amplitude sine-generated meanders migrating downstream evolve into the classical, upstream skewed, train of meanders of Kinoshita type. Evolution displays all the experimentally observed features: the meander growth rate increases up to a maximum and then decreases, while the migration speed decreases monotonically. No equilibrium solutions are found. In the super-resonant regime the picture is essentially reversed: downstream skewing develops while meanders migrate upstream.
Numerical solutions of the planimetric evolution equation are obtained for the case when the initial channel pattern exhibits random small perturbations of the straight configuration. Under these conditions, the evolution displays the typical features of solutions of the Ginzburg–Landau equation, in particular, the occurrence of spatial modulations of the meandering pattern which organizes itself in the form of wavegroups. Furthermore, multiple loops develop in the advanced stage of meander growth.