Instability of Weakly-curved Meandering Channels

The hydrodynamics of a meandering channel fascinates researchers. It plays an important role in governing river morphodynamics, environmental management systems, streambed reclamation and many others. The hydrodynamics of a meandering channel is associated with the primary instability of the mobile interface lying between the fluid and the erodible boundary. Ikeda et al. (1981) performed a stability analysis to examine the conditions for the lateral migration of a sinusoidal channel bend, considering bank erosion. Later, Blondeaux and Seminara (1985) examined the behavior of a meandering channel to be identical to that of a linear oscillator that performs a resonance phenomenon for some key variables. The primary variables for the occurrence of resonance phenomenon were deemed to be the meander wavenumber and the channel aspect ratio. Therefore, it is interesting to study that how the other relevant flow variables affect the instability of a meandering channel. In addition, in most of the previous studies, the instability of a meandering channel was primarily examined for a hydraulically rough flow regime. Therefore, little is known about the role of key flow variables towards the instability mechanism.

In this study, the turbulent flow driven instability of weakly-curved meandering channels is presented. The depth-averaged flow continuity and momentum equations together with the Exner equation govern the physical system, in addition to appropriate fluid and granular closure relationships. The governing equations are then linearized, employing a regular expansion of the basic variables. The evolutions of resonance phenomenon with Shields parameter, channel aspect ratio, relative roughness and shear Reynolds number are studied. The variations of azimuthal velocity perturbation, bed topography perturbation, bend amplification rate and meander migration speed with meander wavenumber are analyzed for different characteristic variables. The mathematical analysis reveals that the channel instability in different flow regimes is primarily governed by the frictional resistance and the volumetric sediment transport rate. The variations of resonant wavenumber with Shields parameter, channel aspect ratio and relative roughness are also analyzed.

Key Words: Fluvial Hydraulics, Turbulent Flow, Meandering Channels, Sediment Transport

References

Blondeaux, P. and Seminara, G. (1985). A unified bar–bend theory of river meanders. Journal of Fluid Mechanics, 157, 449–470.

Ikeda, S., Parker, G. and Sawai, K. (1981). Bend theory of river meanders. Part 1. Linear development. Journal of Fluid Mechanics, 112, 363–377.