Geodesic
Vortex models of shear laminar and turbulent flows
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Tome 239 (2025), pp. 32-42

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We discuss a mathematical model of laminar and turbulent shear flows of liquids and gases in rectangular channels based on a system of differential equations describing the longitudinal motion and rotation of vortex tubes. We show that in the case of a plane steady flow, this system of equations has two-parameter analytical solutions for velocity distributions in the cross-section of the channel, which are in good agreement with known experimental data and the results of numerical simulations. Model approximations of velocity profiles of laminar flows of non-Newtonian liquids and developed turbulent flows of liquids and gases in rectangular channels are discussed as examples.
Keywords: equation of vortex flows, non-Newtonian liquid, Reynolds tensor, eddy viscosity
Mots-clés : turbulence 
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     author = {V. L. Mironov and S. V. Mironov},
     title = {Vortex models of shear laminar and turbulent flows},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {32--42},
     publisher = {mathdoc},
     volume = {239},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2025_239_a3/}
}
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V. L. Mironov; S. V. Mironov. Vortex models of shear laminar and turbulent flows. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Tome 239 (2025), pp. 32-42. http://geodesic.mathdoc.fr/item/INTO_2025_239_a3/