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Evolution of nonlinear perturbations for a fluid flow with a free boundary. Exact results Full article

Journal Journal of Fluid Mechanics
ISSN: 0022-1120
Output data Year: 2022, Volume: 953, Article number : A1, Pages count : 22 DOI: 10.1017/jfm.2022.918
Tags nonlinear instability
Authors Karabut E.A. 1 , Zhuravleva E.N. 1 , Zubarev N.M. 2 , Zubareva O.V. 2
Affiliations
1 Lavrentyev Institute of Hydrodynamics
2 Institute of Electrophysics of the Ural Branch of the Russian Academy of Sciences

Funding (1)

1 Министерство науки и высшего образования Российской Федерации FWGG-2021-0001

Abstract: The problem of a plane unsteady potential flow of an ideal incompressible fluid bounded by free boundary segments with a constant pressure and by solid walls moving in accordance with a known law is considered. External forces are absent, and capillary forces are neglected. An approach to constructing exact solutions for this type of problem is proposed. The corresponding solutions can be treated as nonlinear perturbations of a certain base flow. As an example of the application of this approach, nonlinear perturbations in a known problem of a fluid flow with a linear velocity field in the region bounded by a straight-line free boundary and parallel approaching or receding solid walls are considered. It is demonstrated that perturbations grow, which leads to variants of the formation of singularities on the free surface of the fluid within a finite time: formation of droplets, bubbles or cusps. A solution describing the collapse of a bubble in a fluid layer bounded by two approaching solid walls has also been found and studied. Thus, a new method of studying nonlinear stability of complicated unsteady fluid flows with combined boundary conditions is proposed and tested.
Cite: Karabut E.A. , Zhuravleva E.N. , Zubarev N.M. , Zubareva O.V.
Evolution of nonlinear perturbations for a fluid flow with a free boundary. Exact results
Journal of Fluid Mechanics. 2022. V.953. A1 :1-22. DOI: 10.1017/jfm.2022.918 WOS Scopus РИНЦ OpenAlex
Dates:
Published print: Dec 2, 2022
Identifiers:
Web of science: WOS:000912569000001
Scopus: 2-s2.0-85143709409
Elibrary: 58780948
OpenAlex: W4311185210
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