Alternate bars of finite amplitude: spatial analysis

Federici & Seminara (2003) have recently shown that the nature of bar instability is convective rather than absolute. This implies that bar evolution observed either in nature or in the laboratory is due to the spatial amplification of perturbations that are permanently present in the initial cross-section of the channel. In the present paper, we report the results of numerical simulations on the fully nonlinear equations governing the morphodynamical problem, imposing boundary conditions appropriate to the convective nature of the bar instability mechanism. The results show that the bars evolve spatially and reach an equilibrium amplitude, i.e. an amplitude constant in space, only at some wavelength from the initial cross-section of the domain. This aspect may be relevant in the design of laboratory experiments because the length of the experimental facility could be not enough to allow for the full development of perturbations. A comparison with experimental observations of Fujita & Muramoto (1985) was also performed.