Roll waves in channels with an active gas phase

A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and supports a self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude, which move in the same direction, are found. It is shown that the structure of the waves is similar to that of roll waves in open channels.