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Variability of anomalous transport exponents versus different physical situations in geophysical and laboratory turbulence

  • Part 1: Lévy Flights in Fluids
  • Conference paper
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Lévy Flights and Related Topics in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 450))

Abstract

Geophysical turbulent flows are characterized by large Reynolds numbers. Therefore, it has been a common expectation that universal relations (such as energy spectrum E(k) ∼ k −5/3, passive scalar spectrum E c (k) ∼ k −5/3,diffusivity K ∼ ℓ 4/3 should be valid in such flows as well as their “two-dimensional” analogs in quasi-two-dimensional situations.

We present an overview of results of observations in the atmosphere, ocean and laboratory (including those used by Richardson in his famous paper in 1926) which can be interpreted in terms of anomalous diffusion of passive scalar in turbulent flows, i.e. not obeying the above universal relations.

One of the natural candidates among the possible reasons for the deviations from the Richardson law is the phenomenon of spontaneous breaking of statistical isotropy (rotational and/or reflectional) symmetry, locally or globally.

An attempt is made to provide a quantitative explanation of anomalous diffusion in terms of this phenomenon.

Some of the results are of speculative nature and further analysis is necessary to validate or disprove the claims made, since the correspondence with the experimental results may occur for the wrong reasons as happens from time to time in the field of turbulence.

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Authors and Affiliations

  1. Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    A. Tsinober

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Micheal F. Shlesinger George M. Zaslavsky Uriel Frisch

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Tsinober, A. (1992). Variability of anomalous transport exponents versus different physical situations in geophysical and laboratory turbulence. In: Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (eds) Lévy Flights and Related Topics in Physics. Lecture Notes in Physics, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59222-9_23

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  • DOI: https://doi.org/10.1007/3-540-59222-9_23

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