5. Conclusion
A linear stability analysis of bar formation with the use of the vertically averaged and moment equations is per-formed. The results show that the present theory has a capability to investigate bar formation with smaller as-pect ratio that cannot be studied by the previous analysis using the St. Venant equations. Most of wavelengths estimated by the present theory give shorter wavelengths than the fully developed wavelength from the experi-ments, in which it should be caused by the nonlinear ef-fect. This hypothesis is supported with the conclusion from experiments that bar wavelength increases during its propagation.