Roll waves in an annular channel

The goal of this study is to analytically construct periodic wind perturbations in an annular channel that are numerically produced by a regularized model. R. Dressler’s technique in the shallow water approximation is used to prove the nonexistence of smooth periodic solutions, and discontinuous solutions related to roll waves on inclined surfaces are constructed. The constraints on the accelerating and dissipating forces are obtained under which periodic solutions can exist. A numerical analysis of the problem is carried out, and a qualitative comparison of the numerical and theoretical results is presented.