ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Saichev I. S., Saichev A. I. Fluctuations of contours of passive tracer equal concentration in turbulent medium. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 5, pp. 15-22. DOI: 10.18500/0869-6632-2000-8-5-15-22

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2000no5p015.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
532.591
DOI: 
10.18500/0869-6632-2000-8-5-15-22

Fluctuations of contours of passive tracer equal concentration in turbulent medium

Autors: 
Saichev Irina Semenovna, Lobachevsky State University of Nizhny Novgorod
Saichev Alexandr Ivanovich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

In view of problems of atmosphere and ocean physics, statistical properties of contours length of passive tracer equal concentration and of the concentration field total gradient in chaotically moving incompressible medium are studied. Expressions for statistical moments of these processes and also the probability distribution of total gradient are derived. It is shown that moments grow exponentially in time and distribution tends to logarithmically normal one.

Key words: 
-
Acknowledgments: 
The work was supported by the grant INTAS № 97-11134, grant RFBR № 00-02-16167, grant «Leading scientific schools of Russia» № 00-15-96619, and grant from the Royal Swedish Academy of Sciences.
Reference: 
  1. Csanady G.T. Turbulent diffusion in the environment. Boston: Reidel; 1980. 249 p. DOI: 10.1007/978-94-010-2527-0.
  2. Careta A, Sagues F, Ramirez-Piscina L, Sancho JM. Effective diffusion in a stochastic velocity field. J. Stat. Phys. 1993;71:235-242. DOI: 10.1007/BF01048097.
  3. Crisanty А, Vulpiani А. On the effects оf noise аnd drift on diffusion in fluids. J. Stat. Phys. 1993;70(1-2):197-211. DOI: 10.1007/BF01053963.
  4. Dokuchaev VP. Method of dispersion ratios for average concentration in the theory of turbulent diffusion of passive impurity. Izvestiya, Atmospheric and Oceanic Physics. 1995;31(2):275-281. (in Russian).
  5. Zhukova IS, Saichhev AI. On the probability properties of the density gradient of a randomly moving incompressible medium. Radiophysics and Quantum Electronics . 1996;39(5):398-404. DOI: 10.1007/BF02124696.
  6. Klyatskin VI. Statistical description of the diffusion of a passive tracer in a random velocity field. Physics-Uspekhi. 1994;37:501-513. DOI: 10.1070/pu1994v037n05abeh000110.
  7. Saichev AI, Woyczynski WA. Probability distributions of passive tracers in randomly moving media. In: Molchanov SA, Woyczynski WA, editors. Stochastic Models in Geosystems. The IMA Volumes in Mathematics and its Applications. Vol. 85. New York : Springer; 1997. P. 359-400. DOI: 10.1007/978-1-4613-8500-4_17.
  8. Avellaneda M, Majda А. Mathematical models with exact renormalization for turbulent transport. Comm. Math. Phys. 1990;131:381-429. DOI: 10.1007/BF02161420.
  9. Papanicolaou GC. Wave propagation in one—dimensional random medium. SIAM J. Appl. Math. 1971;21(1):13-18. DOI: 10.1137/0121002.
  10. Kesten H, Papanicolaou GC. A limit theorem for turbulent diffusion. Comm. Math. Phys. 1979;65:97-128. DOI: 10.1007/BF01225144.
Received: 
26.08.2000
Accepted: 
21.12.2000
Published: 
07.02.2001
  • 126 reads