Proof of Hopf's conjecture on the structure of turbulence (Tatarsky's memory)
V.V. Nosov1, V.P. Lukin1, P.G. Kovadlo2, E.V. Nosov1, A.V. Torgaev1
1V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
2Institute of Solar-Terrestrial Physics of the Siberian Branch of the RAS, Irkutsk, Russia
Keywords: Hopf, Tatarsky, chaos, turbulence, coherent structures
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.
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