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Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane. / Chesnokov, Alexander.

In: Wave Motion, Vol. 106, 102799, 11.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Chesnokov, A 2021, 'Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane', Wave Motion, vol. 106, 102799. https://doi.org/10.1016/j.wavemoti.2021.102799

APA

Chesnokov, A. (2021). Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane. Wave Motion, 106, [102799]. https://doi.org/10.1016/j.wavemoti.2021.102799

Vancouver

Chesnokov A. Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane. Wave Motion. 2021 Nov;106:102799. doi: 10.1016/j.wavemoti.2021.102799

Author

Chesnokov, Alexander. / Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane. In: Wave Motion. 2021 ; Vol. 106.

BibTeX

@article{4361e29123f14ffea681812928196a2d,
title = "Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane",
abstract = "A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied within the framework of both two-dimensional governing equations of a power-law fluid and its depth-averaged hyperbolic simplification. The conditions of the existence of roll waves for these models are formulated in terms of the Whitham criterion. A free surface evolution and the development of roll waves are numerically calculated. The amplitude of roll waves obtained by the 2D equations is slightly larger than that for the 1D model. Moreover, for certain flow parameters, the small perturbations of the basic solution grow for the 2D equations and decay for the depth-averaged model. A two-parameter class of exact piecewise-smooth solutions of the 1D model is obtained and a comparison with a numerical solution is made. In the region of these parameters, diagrams of the roll waves existence are constructed.",
keywords = "Hyperbolic equations, Power-law fluid, Roll waves, Thin films",
author = "Alexander Chesnokov",
note = "Funding Information: This work is supported by the Russian Foundation for Basic Research (Project No. 19-01-00498 ). The author thanks S.L. Gavrilyuk, V.Yu. Liapidevskii and I.V. Stepanova for fruitful discussions. Publisher Copyright: {\textcopyright} 2021 Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = nov,
doi = "10.1016/j.wavemoti.2021.102799",
language = "English",
volume = "106",
journal = "Wave Motion",
issn = "0165-2125",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane

AU - Chesnokov, Alexander

N1 - Funding Information: This work is supported by the Russian Foundation for Basic Research (Project No. 19-01-00498 ). The author thanks S.L. Gavrilyuk, V.Yu. Liapidevskii and I.V. Stepanova for fruitful discussions. Publisher Copyright: © 2021 Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/11

Y1 - 2021/11

N2 - A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied within the framework of both two-dimensional governing equations of a power-law fluid and its depth-averaged hyperbolic simplification. The conditions of the existence of roll waves for these models are formulated in terms of the Whitham criterion. A free surface evolution and the development of roll waves are numerically calculated. The amplitude of roll waves obtained by the 2D equations is slightly larger than that for the 1D model. Moreover, for certain flow parameters, the small perturbations of the basic solution grow for the 2D equations and decay for the depth-averaged model. A two-parameter class of exact piecewise-smooth solutions of the 1D model is obtained and a comparison with a numerical solution is made. In the region of these parameters, diagrams of the roll waves existence are constructed.

AB - A laminar flow of a thin layer of mud down an inclined plane under the action of gravity is considered. The instability of a film flow and the formation of finite amplitude waves are studied within the framework of both two-dimensional governing equations of a power-law fluid and its depth-averaged hyperbolic simplification. The conditions of the existence of roll waves for these models are formulated in terms of the Whitham criterion. A free surface evolution and the development of roll waves are numerically calculated. The amplitude of roll waves obtained by the 2D equations is slightly larger than that for the 1D model. Moreover, for certain flow parameters, the small perturbations of the basic solution grow for the 2D equations and decay for the depth-averaged model. A two-parameter class of exact piecewise-smooth solutions of the 1D model is obtained and a comparison with a numerical solution is made. In the region of these parameters, diagrams of the roll waves existence are constructed.

KW - Hyperbolic equations

KW - Power-law fluid

KW - Roll waves

KW - Thin films

UR - http://www.scopus.com/inward/record.url?scp=85109538331&partnerID=8YFLogxK

U2 - 10.1016/j.wavemoti.2021.102799

DO - 10.1016/j.wavemoti.2021.102799

M3 - Article

AN - SCOPUS:85109538331

VL - 106

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

M1 - 102799

ER -

ID: 29129891