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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 1, Pages 114–125 (Mi zvmmf9978)  

Roll waves in an annular channel

M. A. Istominaa, E. V. Yushkovb

a 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. DresslerТs 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.

DOI: https://doi.org/10.7868/S0044466914010086

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

Bibliographic databases:

UDC: 519.634
Received: 01.08.2013

Citation: M. A. Istomina, E. V. Yushkov, “Roll waves in an annular channel”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 114–125; Comput. Math. Math. Phys., 54:1 (2014), 123–134

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