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Russian Mathematical Surveys, 2007, Volume 62, Issue 3, Pages 497–510
DOI: https://doi.org/10.1070/RM2007v062n03ABEH004417
(Mi rm6118)
 

This article is cited in 17 scientific papers (total in 17 papers)

Conformal invariance in hydrodynamic turbulence

G. Falkovich

Weizmann Institute of Science
References:
Abstract: This short survey is written by a physicist. It contains neither theorems nor precise definitions. Its main content is a description of the results of numerical solution of the equations of fluid mechanics in the regime of developed turbulence. Due to limitations of computers, the results are not very precise. Despite being neither exact nor rigorous, the findings may nevertheless be of interest for mathematicians. The main result is that the isolines of some scalar fields (vorticity, temperature) in two-dimensional turbulence belong to the class of conformally invariant curves called SLE (Scramm–Löwner evolution) curves. First, this enables one to predict and find a plethora of quantitative relations going far beyond what was known previously about turbulence. Second, it suggests relations between phenomena that seemed unrelated, like the Euler equation and critical percolation. Third, it shows that one is able to get exact analytic results in statistical hydrodynamics. In short, physicists have found something unexpected and hope that mathematicians can help to explain it.
Received: 05.10.2006
Bibliographic databases:
Document Type: Article
UDC: 517.54+517.957+517.958:531.32
MSC: Primary 60K35, 76F55; Secondary 35Q35, 60J65, 76F05, 76F25, 81T40, 82B27, 82C05
Language: English
Original paper language: Russian
Citation: G. Falkovich, “Conformal invariance in hydrodynamic turbulence”, Russian Math. Surveys, 62:3 (2007), 497–510
Citation in format AMSBIB
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\by G.~Falkovich
\paper Conformal invariance in hydrodynamic turbulence
\jour Russian Math. Surveys
\yr 2007
\vol 62
\issue 3
\pages 497--510
\mathnet{http://mi.mathnet.ru//eng/rm6118}
\crossref{https://doi.org/10.1070/RM2007v062n03ABEH004417}
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\zmath{https://zbmath.org/?q=an:05295355}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2007RuMaS..62..497F}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35648976211}
Linking options:
  • https://www.mathnet.ru/eng/rm6118
  • https://doi.org/10.1070/RM2007v062n03ABEH004417
  • https://www.mathnet.ru/eng/rm/v62/i3/p193
  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:915
    Russian version PDF:412
    English version PDF:24
    References:45
    First page:9
     
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