Vol. 36, issue 01, article # 2

Abstract:

The paper is dedicated to the memory of V.I. Tatarsky (1929–2020); however, it is not personalia. We present, as a brief review of our scientific works, the experimental and theoretical proofs of the E. Hopf's conjecture (1948) about the structure of turbulence as a space-time chaos of a finite number of interacting coherent structures. This review is the result of our many years research in the theory of turbulence. The theory of turbulence is a scientific direction that the authors have chosen under the scientific influence of V.I. Tatarsky.

Keywords:

Hopf, Tatarsky, chaos, turbulence, coherent structures

Figures:

References:

1. Tatarskij V.I. Rasprostranenie voln v turbulentnoj atmosfere. M.: Nauka, 1967. 548 p.
2. Klyatskin V.I., Tatarskij V.I. Priblizhenie diffuzionnogo sluchajnogo protsessa v nekotoryh nestatsionarnyh statisticheskih zadachah fiziki // Uspekhi fiz. nauk. 1973. V. 10, N 8. P. 499–536. DOI: 10.3367/UFNr.0110.197308b.0499.
3. Monin A.S., Yaglom A.M. Statisticheskaya gidromekhanika. V. 1. SPb.: Gidrometeoizdat, 1992. 696 p.
4. Monin A.S., Yaglom A.M. Statisticheskaya gidromekhanika. V. 2. SPb.: Gidrometeoizdat, 1996. 742 p.
5. Nosov V.V., Grigor'ev V.M., Kovadlo P.G., Lukin V.P., Nosov E.V., Torgaev A.V. Astroklimat spetsializirovannyh pomeshchenij Bol'shogo solnechnogo vakuumnogo teleskopa. Part 2 // Optika atmosf. i okeana. 2008. V. 21, N 3. P. 207–217.
6. Nosov V.V., Lukin V.P., Nosov E.V., Torgaev A.V., Grigoriev V.M., Kovadlo P.G. The Solitonic Hydrodynamical Turbulence // Proc. VI Int. Conf. Solitons, Collapses and Turbulence: Achievements Developments and Perspectives / V.E. Zakharov (ed.). Novosibirsk, 2012. P. 108–109. URL: http://conf.nsc.ru/sct2012/en/reportlist (last access: 22.08.2022).
7. Nosov V.V., Grigor'ev V.M., Kovadlo P.G., Lukin V.P., Nosov E.V., Torgaev A.V. Kogerentnye struktury – elementarnye sostavlyayushchie atmosfernoj turbulentnosti // Izv. vuzov. Fizika. 2012. V. 55, N 9/2. P. 236–238.
8. Nosov V.V., Lukin V.P., Kovadlo P.G., Nosov E.V., Torgaev A.V. Opticheskie svojstva turbulentnosti v gornom pogranichnom sloe atmosfery. Novosibirsk: Izd-vo SO RAN, 2016. 153 p.
9. Lukin V.P., Nosov V.V., Nosov E.V., Torgaev A.V. Causes of non-Kolmogorov turbulence in the atmosphere // Appl. Opt. 2016. V. 55, N. 12. P. B163–B168. DOI: 10.1364/AO.55.00B163.
10. Nosov V.V., Lukin V.P., Nosov E.V., Torgaev A.V. Modelirovanie kogerentnyh struktur (topologicheskih solitonov) v zakrytyh pomeshcheniyah putem chislennogo resheniya uravnenij gidrodinamiki // Optika atmosf. i okeana. 2015. V. 28, N 2. P. 120–133.
11. Nosov V.V., Lukin V.P., Nosov E.V., Torgaev A.V. Struktura turbulentnosti nad nagretymi poverhnostyami. Chislennye resheniya // Optika atmosf. i okeana. 2016. V. 29, N 1. P. 23–30; Nosov V.V., Lukin V.P., Nosov E.V., Torgaev A.V. Turbulence structure over heated surfaces: Numerical solutions // Atmos. Ocean. Opt. 2016. V. 29, N 3. P. 234–243.
12. Nosov V.V. Atmospheric turbulence in the anisotropic boundary layer /// Optical Waves and Laser Beams in the Irregular Atmosphere / N. Blaunshtein, N. Kopeika (eds.). London, New York: CRC Press, 2018. Chap. 3. P. 67–180. DOI: 10.1201/9780203732960.
13. Nosov V.V., Lukin V.P., Kovadlo P.G., Nosov E.V., Torgaev A.V. Peremezhaemost' kolmogorovskoj i kogerentnoj turbulentnosti v gornom pogranichnom sloe (obzor) // Optika atmosf. i okeana. 2021. V. 34, N 9. P. 726–749; Nosov V.V., Lukin V.P., Kovadlo P.G., Nosov E.V., Torgaev A.V. Intermittency of Kolmogorov and coherent turbulence in the mountain atmospheric boundary layer (review) // Atmos. Ocean. Opt. 2022. V. 35, N 3. P. 266–287.
14. Nosov V.V., Lukin V.P., Nosov E.V., Torgaev A.V., Bogushevich A.Ya. Measurement of atmospheric turbulence characteristics by the ultrasonic anemometers and the calibration processes // Atmos. 2019. V. 10, N 8. P. 1–15. DOI: 10.3390/atmos10080460.
15. Hopf E. A mathematical example displaying features of turbulence // Commun. Pure Appl. Math. 1948. V. 1, N 4. P. 303–322. DOI: 10.1002/CPA.3160010401.
16. Hopf E. Statistical hydromechanics and functional calculus // J. Ratio. Mech. Analys. 1952. V. 1. P. 87–123. URL: http://www.jstor.org/stable/24900259.
17. Van Dyke M. An Album of Fluid Motion. Stanford: Parabolic Press, 1982. 176 p.