Email this article 
ENSTROPHY DYNAMICS FOR FLOW PAST A SOLID BODY WITH NO-SLIP BOUNDARY CONDITION
- Authors: Gorshkov A.V1
-
Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Issue: No 4 (2025)
- Pages: 17-29
- Section: Articles
- URL: https://ogarev-online.ru/1024-7084/article/view/375892
- DOI: https://doi.org/10.7868/S3034534025040027
- ID: 375892
Cite item
Open Access
Access granted
Subscription Access
Abstract
In the paper we study the impact of the boundary vorticity distribution on the dynamics of enstrophy for flows around streamlined bodies. A new energy identity is derived in the article, which includes the boundary values of the vortex function. For the Stokes system the dissipativity of enstrophy is proved. For the Navier–Stokes system a new equation of the enstrophy dynamics is obtained.
Keywords
About the authors
A. V Gorshkov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: alexey.gorshkov.msu@gmail.com
Moscow, Russia
References
- Baiesi M., Maes C. Enstrophy dissipation in two-dimensional turbulence // Phys. Rev. E. 2005. V. 72.№5. P. 056314. https://doi.org/10.1103/PhysRevE.72.056314
- Matharu P., Protas B., and Yoneda T. On Maximum Enstrophy Dissipation in 2D Navier–Stokes Flows in the Limit of Vanishing Viscosity // Physica D: Nonlinear Phenomena. 2022. V. 441. P. 133517. https://doi.org/10.1016/j.physd.2022.133517
- Wu J.Z., Wu J.M. Interactions between a solid surface and a viscous compressible flow field // J. Fluid Mech. 1993. V. 254. P. 183–211. https://doi.org/10.1017/S0022112093002083
- Weiss J. The dynamics of enstrophy transfer in two-dimensional hydrodynamics// Physica D: Nonlinear Phenomena. 1991. V. 48.№2–3. P. 273–294. https://doi.org/10.1016/0167-2789(91)90088-Q
- Wu J.Z. A theory of three-dimensional interfacial vorticity dynamics // Phys. Fluids. 1995. V. 7.№10. P. 2375–2395.
- Chen T., Liu T., and Wang L.P. Features of surface physical quantities and temporal-spatial evolution of wall-normal enstrophy flux in wall-bounded flows // Phys. Fluids. 2021. V. 33№12. P. 125104.
- Foias C., Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations // Journal of Functional Analysis. 1989. V. 87. P. 359–369.
- Doering C.R., Gibbon J.D. Applied Analysis of the Navier-Stokes Equations. Cambridge University Press, New York, 1995. 240 p.
- Tennekes H., Lumley J.L. A First Course in Turbulence. The MIT Press, 1972. 310 p.
- Wang Z., Luo K., Tan J., Li D., and Fan J. Similarity of dissipation and enstrophy in particle-induced small-scale turbulence // Phys. Rev. Fluids. 2020. V. 5.№1. P. 014301. https://doi.org/10.1103/PhysRevFluids.5.014301
- Бэтчелор Дж. Введение в динамику жидкости. М.: Мир, 1973. 778 с.
- Zhu Y.U., Antonia R.A. On the Correlation between Enstrophy and Energy Dissipation Rate in a Turbulent Wake // Appl. Sci. Research. 1997. V. 57. P. 337–347.
- Koh Y.M. Vorticity and viscous dissipation in an incompressible flow // KSME Journal. 1994. V. 8. P. 35–42. https://doi.org/10.1007/BF02953241
- Karman Th. von. The fundamentals of the statistical theory of turbulence // J. Aeronaut. Sc. 1937. V. 4. № 4. P. 131–188. https://doi.org/10.2514/8.350
- Taylor G.I. Production and Dissipation of Vorticity in a Turbulent Fluid // Proc. Roy. Soc. 1938. V. 164. № 916. P. 15–23.
- Горшков А.В. Об однозначной разрешимости задачи дивергенция-ротор в неограниченных областях и энергетических оценках решений // ТМФ. 2024. Т. 221.№2. С. 240–254.
- Горшков А.В. Специальное преобразование Вебера с ненулевым ядром // Матем. заметки. 2023. Т. 114.№2. С. 212–228.
- Лионс Ж.-Л., Мадженес Э. Неоднородные граничные задачи и их приложения. М.: Мир, 1971. 371 с.
- Calderon A.P., Zygmund A. On singular integrals. American Journal of Mathematics // The Johns Hopkins University Press. 1956. V. 78.№2. P. 289–309.
Supplementary files
