PMID: 11308763Apr 20, 2001Paper

Anomalous scaling in two models of passive scalar advection: effects of anisotropy and compressibility

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
N V Antonov, J Honkonen

Abstract

The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian, delta correlated in time, and scales with a positive exponent epsilon. Explicit inertial-range expressions for the scalar correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal anomalous exponents (dependent only on epsilon and alpha, the compressibility parameter). The complete set of anomalous exponents for the pair correlation functions is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to O(epsilon(2)) using the renormalization group. As in the incompressible case, the exponents exhibit a hierarchy related to the degree of anisotropy: the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. As the degree of compressibility increases, the corrections become closer to the leading terms. Th...Continue Reading

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Citations

Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L T AdzhemyanA N Vasil'ev
Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L T AdzhemyanA V Runov
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Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·O G ChkhetianiM Repasan
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E Jurcisinová, M Jurcisin
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E JurcisinováR Remecký
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Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A V GladyshevP Zalom
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N V Antonov, M M Kostenko
Oct 9, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L Ts AdzhemyanJ Honkonen
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N V AntonovMarian Jurcisin

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