ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Sennitskii V. L. Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 2, pp. 197-208. DOI: 10.18500/0869-6632-003091, EDN: SMOTDZ

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Language: 
Russian
Heading: 
Innovations in applied physics
Article type: 
Article
UDC: 
532.516, 532.517, 517.928
DOI: 
10.18500/0869-6632-003091
EDN: 
SMOTDZ

Peculiarities of the dynamics of a viscous liquid with a free boundary under periodic influences

Autors: 
Sennitskii Vladimir Leonidovich,
Abstract: 

Purpose of the work is revealing and researching of peculiarities of a motion of a viscous liquid having a free boundary and undergoing periodic in time influences which are characterized by the absence of a predominant direction in space.

Methods. The analytic investigation methods of non-linear problems, of boundary problems for the system of Navier– Stokes and continuity equations are used that are the method of perturbations (the method of a small parameter) the method of Fourier (the method of a separation of variables), an averaging, a construction and studying of asymptotic formulas.

Results. A new problem on the motion of a viscous liquid is formulated and solved. Asymptotic representations of the found solution are constructed and explored. New hydromechanical effects are revealed.

Conclusion. The work is fulfilled in the development of a perspective direction in liquid mechanics that is of researching the dynamics of hydromechanical systems under periodic influences. The obtained results can be used in particular in further investigations of a non-trivial dynamics of hydromechanical systems, under working for the methods of a control of hydromechanical systems.

Key words: 
viscous liquid
free boundary
periodic in time influences
predominant direction in space
stationary motion
Reference: 
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Received: 
29.08.2023
Accepted: 
23.10.2023
Available online: 
08.02.2024
Published: 
29.03.2024
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