On the evolution of roll waves

An amplitude evolution equation is derived for roll waves that occur in a uniform open-channel flow down an incline. A periodic series of roll waves, which is a manifestation of the instability of high-velocity turbulent flow, is shown to be itself unstable to subharmonic disturbances. These disturbances develop into longer and higher roll waves. In this way roll waves tend to increase in size as time goes on, in agreement with experimental evidence.