Numerical modelling of alternate bars in shallow channels

A code for the numerical solution of two-dimensional shallow-water equations over a movable bed is developed in order to reproduce the generation, growth and migration of alternate bars in a straight, rectangular channel. Many studies suggest that alternate bar formation may be related to hydrodynamic instability of a cohesionless bed. Such a phenomenon is reproduced by numerical simulations, which are carried out with both supercritical and subcritical uniform flow as the initial reference condition. The instability of the bed is generated by a localized bed disturbance. The evolution of the bed from this initial disturbance is modelled until a dynamic equilibrium of bed topography is achieved, characterized by alternate bars with a defined space-time evolution. Particular attention is devoted to the analysis of gravity effects due to the transverse bed slope on the equilibrium values of the geometric and kinematic bar characteristics. The simulated equilibrium values of bar height and bar length are compared with semi-empirical, experimental and numerical results from the literature.