| Weakly nonlinear analysis was adapted to the hydraulic experiments in order to clarify the mechanisms of mode reduction process of sand bars. Hydraulic conditions of this analysis were set large width-depth ratio. The following facts became clear by this research. Initial bar growth rate must be calculated precisely when the mode reduction process is considered. The bar wavelength which passes through the mode reduction process of bar formation can be calculate by the linear stability analysis. The weakly nonlinear analysis can predict the mode reduction process of bars when the perturbation parameter is less than 1. This analysis shows good agreement on the contribution of each bar mode element to the bed formation.Although the growth rate expansion method has a mathematical problem applying to the multiple bar formation process、 this analysis shows good agreement on the hydraulic experimental results. |
