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SUPERPOSITION OF TWO NONSTEADY ONE-DIMENSIONAL SHEARS IN A PLANE VISCOUS LAYER
- Authors: Georgievskii D.V.1,2
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Affiliations:
- Lomonosov Moscow State University
- Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences
- Issue: Vol 524, No 1 (2025)
- Pages: 59-62
- Section: МЕХАНИКА
- URL: https://bakhtiniada.ru/2686-7400/article/view/356213
- DOI: https://doi.org/10.7868/S3034508125050092
- ID: 356213
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Abstract
The stability of the unsteady flow of a Newtonian viscous medium, which is a superposition of two one-dimensional orthogonal shears in a layer between parallel planes, relative to the three-dimensional picture of kinematic perturbations, is investigated. Using the method of integral relations, sufficient integral estimates of the development of initial disturbances and their non-growth over an infinite time interval are derived. The cases of stationary main motion, acceleration and deceleration in different directions are considered.
About the authors
D. V. Georgievskii
Lomonosov Moscow State University; Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences
Email: georgiev@mech.math.msu.su
Moscow, Russia
References
- Georgievskii D.V. Sufficient energy estimates of stability of unsteady combined shear flows in a cylindrical layer // Izv. RAN. MZhG. 2024. № 6. P. 51–59.
- Kozyrev O.R., Stepanyan Yu.A. Method of integral relations in the linear theory of hydrodynamic stability // Itogi nauki i tekhniki. Ser. Mekhanika zhidkosti i gaza. M.: VINITI, 1991. V. 25. P. 3–89.
- Georgievskii D.V. Selected problems of continuum mechanics. 2nd ed. M.: URSS, 2020. 560 p.
- Georgievskii D.V., Putkaradze V.G. Energy-based stability estimates for incompressible media with tensor-nonlinear constitutive relations // Continuum Mechanics and Thermodynamics. 2023. V. 35. № 4. P. 1403–1415.
- Martynyuk A.A., Lakimshkin V., Lila S. Stability of motion: method of integral inequalities. Kiev: Nauk. dumka, 1989. 272 p.
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