Generalized Brenier Principle and the Closure Problem of Landgren–Monin–Novikov Hierarchy for Vorticity Field

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Resumo

Brenier’s concept – a representation of solutions to the equations of ideal incompressible fluids in terms of probability measures on the set of Lagrangian trajectories in the case of their stochasticity, is a generalization of Arnold’s principle of least action of finding smooth solutions of Euler’s equations. In this work, the variational generalized Brenier principle (Brenier, J. Am. Math. Soc. 1989) is used to close the infinite chain of Landgren–Monin–Novikov equations for the n-point probability density functions fn of the vortex field of two-dimensional turbulence. In addition, within the framework of the statistical approach, an approximation of the variational problem with conditions at the ends posed by Shnirelman (Mat. Sat. 1985) for the Euler equation is proposed.

Sobre autores

V. Grebenev

Federal Research Center for Information and Computational Technologies

Autor responsável pela correspondência
Email: vngrebenev@gmail.com
Rússia, Novosibirsk

A. Grishkov

University of Sao Paulo

Email: grishkov@ime.usp.br
Brasil, Sao Paulo

Bibliografia

  1. Friedrich R., Daitche A., Kamps O., Lülff J., Michel Voß kuhle M., Wilczek M. The Lundgren–Monin–Novikov hierarchy: Kinetic equations for turbulence // C.R. Physique. 2012. V. 13. P. 929–953.
  2. Lundgren T.S. Distribution functions in the statistical theory of turbulence // Phys. Fluids. 1967. V. 10. P. 969–975.
  3. Монин А.С. Уравнения турбулентного движения // Прикладная математика и механика. 1967. Т. 31. № 6. С. 1057–1068.
  4. Новиков Е.А. Кинетические уравнения для поля вихря // ДАН. 1967. Т. 177. № 2. С. 299–301.
  5. Friedrich R. Statistics of Lagrangian velocities in turbulent flows // Phys. Rev. Lett. 2003. V. 90. P. 084501.
  6. Friedrich J. Closure of the Lundgren-Monin-Novikov Hierarchy in Turbulence via a Markov Property of Velocity Increments in Scale. Dissertation: Doktor der Naturwissenschaften. Bochum, 2017.
  7. Wacławczyk M., Staffolani N., Oberlack M., Rosteck A., Wilczek M., Friedrich R. Statistics of Lagrangian velocities in turbulent flows // Phys. Rev. E. 2014. V. 90. P. 013022.
  8. Brenier Y. The least action principle and the related concept of generalized flows for incompressible perfect fluids // J. Am. Math. Soc. 1989. V. 2. P. 225–255.
  9. Шнирельман А.И. О геометрии группы диффеоморфизмов и динамике идеальной несжимаемойжидкости // Матем. сб. 1985. Т. 170. № 1. С. 82–109.
  10. Thalabard S., Bec J. Turbulence of generalised flows in two dimensions // J. Fluid Mechan. 2020. V. 883. P. A49.
  11. Arnold V.I. Sur la geom’etrie diff’erentielle des groupes de lie de dimension infinie et ses applicationsa l’hydrodynamique des fluides parfaits // Ann. Inst. Fourier. 1966. V. 16. P. 319–361.
  12. Гребенёв В.Н., Гришков А.Н., Оберлак М. Симметрии уравнений Лангрена–Монина–Новикова для распределения вероятности поля вихря // Доклады РАН. Физика, технические науки. 2023. Т. 509. №. 1. С. 50–55.
  13. Гребенёв В. Н., Гришков А.Н., Медведев С.Б. Преобразования симметрии статистики поля вихря в оптической турбулентности // Теоретическая и математическая физика. 2023. Т. 217. № 2. С. 438–451.
  14. Grebenev V.N., Oberlack M., Grishkov A.N. Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence // Z. Angew. Math. Phys. 2013. V. 64. P. 599–620.
  15. Фалькович Г. Конформная инвариантность в гидродинамической турбулентности // Успехи мат. наук. 2007. Т. 62. Вып. 3(375). С. 193–206.
  16. Friedrich R. Lagrangian probability distributions of turbulent flows. arXiv:physics/0207015v1. 2018

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