Abstract: Purpose of the work is the revealing and the researching of peculiarities of the dynamics of a viscous liquid which is undergoing by periodic in time influences possessing no predominant direction in space under possible simplest hydro-mechanical conditions (which are able to provide non-trivial behavior of the liquid). Methods. The analytic investigational methods for boundary problems for Navier–Stokes and continuity equations are used that are the method of perturbations, the method of Fourier. Results. A new problem on the flow of a viscous liquid is formulated and solved. The hydro-mechanical system consists of an incompressible viscous liquid and a moving absolutely solid wall which creates periodic influences to the liquid. A new peculiarity of the viscous liquid dynamics is revealed consisting in that in simplest hydro-mechanical conditions the liquid in the background of oscillations (in average of time) performs a motion of a new type — a stationary fading with the distance from the wall motion which is characterized by the presence of a laminate structure. A physical interpretation of the formulation of the problem under consideration is given. Conclusion. The obtained results can be used in particular in a scientific search of ways to control hydro-mechanical systems, under a developing methods of a creation of prescribed flows of liquid media.

Cite: Sennitskii V.L.
On the structure of a viscous liquid flow under periodic influences which have no predominant direction in space
Известия высших учебных заведений. Прикладная нелинейная динамика. 2025. V.33. N4. P.531-539.

Original: Сенницкий В.Л.
О структуре течения вязкой жидкости при периодических воздействиях, не имеющих выделенного направления в пространстве
Известия высших учебных заведений. Прикладная нелинейная динамика. 2025. Т.33. №4. С.531-544. DOI: 10.18500/0869-6632-003163 Scopus

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