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Clustering and diffusion of particles and passive tracer density in random hydrodynamic flows


A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation

The diffusion of particles and conservative, passive tracer density fields in random hydrodynamic flows is considered. The crucial feature of this diffusion in a divergent hydrodynamic flow is the clustering of the conservative, passive tracer density field (in the Euler description) and occasionally of the particles themselves (in the Lagrange description) — a coherent phenomenon which occurs with probability unity and should arise in almost all dynamic scenarios of the process. In the present paper, statistical clustering parameters are described in statistical topography terms. Because of their inertial properties, particles and their concentration field can also cluster in random divergence-free velocity fields, the divergence of the particle velocity field itself being a crucial aspect of such a diffusion. The delta-correlated in time velocity field for fluctuating flow (as, e.g., in the Fokker-Planck diffusion equation for low-inertia particles) is in principle an invalid approximation for the statistical description of particle dynamics, and the diffusion approximation accounting for the finite time correlation radius should instead be used for this purpose.

PACS: 02.50.−r, 05.40.−a, 05.45.−a (all)
DOI: 10.1070/PU2003v046n07ABEH001600
URL: https://ufn.ru/en/articles/2003/7/a/
Citation: Klyatskin V I "Clustering and diffusion of particles and passive tracer density in random hydrodynamic flows" Phys. Usp. 46 667–688 (2003)
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Оригинал: Кляцкин В И «Кластеризация и диффузия частиц и плотности пассивной примеси в случайных гидродинамических потоках» УФН 173 689–710 (2003); DOI: 10.3367/UFNr.0173.200307a.0689

References (74) Cited by (23) Similar articles (20) ↓

  1. V.I. Klyatskin, D. Gurarie “Coherent phenomena in stochastic dynamical systems42 165 (1999)
  2. V.I. Klyatskin “Electromagnetic wave propagation in a randomly inhomogeneous medium as a problem in mathematical statistical physics47 169–186 (2004)
  3. A.S. Mikhailov, I.V. Uporov “Critical phenomena in media with breeding, decay, and diffusion27 695–714 (1984)
  4. V.I. Klyatskin “Integral characteristics: a key to understanding structure formation in stochastic dynamic systems54 441–464 (2011)
  5. Ya.B. Zel’dovich, S.A. Molchanov et alIntermittency in random media30 353–369 (1987)
  6. V.S. Anishchenko, T.E. Vadivasova et alStatistical properties of dynamical chaos48 151–166 (2005)
  7. A. Loskutov “Fascination of chaos53 1257–1280 (2010)
  8. V.V. Uchaikin “Fractional phenomenology of cosmic ray anomalous diffusion56 1074–1119 (2013)
  9. K.V. Koshel, S.V. Prants “Chaotic advection in the ocean49 1151–1178 (2006)
  10. S.I. Vainshtein, Ya.B. Zel’dovich “Origin of Magnetic Fields in Astrophysics (Turbulent ’Dynamo’ Mechanisms)15 159–172 (1972)
  11. A.B. Medvinskii, S.V. Petrovskii et alSpatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics45 27–57 (2002)
  12. V.V. Uchaikin “Self-similar anomalous diffusion and Levy-stable laws46 821–849 (2003)
  13. A.P. Gerasev “Nonequilibrium thermodynamics of autowave processes in a catalyst bed47 991–1016 (2004)
  14. E.A. Vinogradov, I.A. Dorofeyev “Thermally stimulated electromagnetic fields of solids52 425–459 (2009)
  15. V.P. Budaev, S.P. Savin, L.M. Zelenyi “Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features54 875–918 (2011)
  16. O.G. Bakunin “Stochastic instability and turbulent transport. Characteristic scales, increments, diffusion coefficients58 252–285 (2015)
  17. V.I. Klyatskin, V.I. Tatarskii “Diffusive random process approximation in certain nonstationary statistical problems of physics16 494–511 (1974)
  18. V.K. Vanag “Waves and patterns in reaction-diffusion systems. Belousov-Zhabotinsky reaction in water-in-oil microemulsions47 923–941 (2004)
  19. V.V. Lobzin, V.R. Chechetkin “Order and correlations in genomic DNA sequences. The spectral approach43 55–78 (2000)
  20. Yu.G. Rudoi, A.D. Sukhanov “Thermodynamic fluctuations within the Gibbs and Einstein approaches43 1169–1199 (2000)

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