This article is cited in 1 paper

Roll waves in an annular channel

M. A. Istomina^a, E. V. Yushkov<sup>b

a</sup> Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
^b Faculty of Physics, Moscow State University, Moscow, 119992, Russia

Abstract: 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.

Key words: annular channel, shallow water equations, solitary waves, regularized model, existence of periodic solutions.

UDC: 519.634

Received: 01.08.2013

DOI: 10.7868/S0044466914010086

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:1, 123–134

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