Uniform flow on a relatively steep channel is known to be unstable to evolve into a wave train, which is termed roll waves. Though roll waves have long been studied, their wavelength cannot be theoretically determined. In this study, a linear stability analysis on the wavelength of fully-developed roll waves is performed. It is found that the instability of the fully-developed roll waves is maximized when the wavelength is 0.1-1, and roll waves with infinitely long or infinitesimally short wavelengths are neutrally stable. In order to study the development of roll waves and to verify the theory, numerical simulation is performed. As the distance from the inlet increase, roll waves tend to increase in the wavelength, and to approach a constant wavelength asymptotically.
