Abstract
The application of the existing weakly nonlinear theories of sand bars with the use of the growth rate expansion method, in which the growth rate of perturbations is taken as a small parameter for expansion, is limited to the vicinity of the minimum critical aspect ratio (width/depth); the theory is only applicable to the case of alternate bars. In this study, weakly nonlinear analysis with the use of the amplitude expansion method, in which the amplitude of perturbations is taken as a small parameter for expansion, is presented in order to extend theories to the case of multiple bars. It is shown that the reasonably good agreement between experimental and theoretical results of bar wavelength and height.
