Hydrodynamic instability of meandering channels

Abstract

In this paper, we explore the hydrodynamic instability of meandering channels driven by the turbulent flow. The governing equations of channel dynamics with suitable boundary conditions are closed with the fluid and granular constitutive relationships. A regular expansion of the fundamental variables is employed to linearize the parent equations by superimposing the perturbations on the basic unperturbed flow. The channel dynamics reveal a resonance phenomenon which occurs when the key variables fall in the vicinity of the distinct critical values. The resonance phenomenon preserves its distinctive signature in different flow regimes which are guided by the characteristic values of the shear Reynolds number. The hydrodynamic analysis indicates that the fluid friction and the volumetric sediment flux play a decisive role to characterize the channel instability in different flow regimes. The growths of azimuthal velocity perturbation in phase with curvature, bed topography perturbation, bend amplification rate, and meander propagation speed in different flow regimes are investigated by varying the meander wavenumber, Shields number, channel aspect ratio, and relative roughness number. The analysis is capable to capture the effects of grain size on azimuthal velocity perturbation, bed topography perturbation, bend amplification rate, and meandering propagation speed over a wide range of shear Reynolds numbers. The variations of resonant wavenumbers in different flow regimes with the Shields number, channel aspect ratio, and relative roughness number are addressed. For a specific flow regime, the upstream and downstream migrations of meandering channels are typically governed by the Shields number, channel aspect ratio, and relative roughness number.