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Corrections to fully developed turbulent spectra due to compressibility of the fluid

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Abstract

We construct the regular expansion at small compressibilities for the theory of fully developed turbulence of an isotropic homogeneous compressible fluid with MSR-type action. The parameter of the expansion is the Mach numberMa. For the inertial range of a compressible fluid, we study the infrared singularities determined by the transverse fields, which are used in the theory of incompressible fluids. These singularities are connected with the composite operators of transverse fields that are investigated by the quantum field renormalization group method. As a result, it is shown that the transverse fields induce scaling behavior with theMa scaling dimension equal to 1/3 (i.e.,Ma k−1/3 is the dimensionless scaling parameter of the correlation functions in the inertial range).

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Authors and Affiliations

  1. St. Petersburg State University, USSR

    D. Y. Volchenckov & M. Y. Nalimov

Authors
  1. D. Y. Volchenckov
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  2. M. Y. Nalimov
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Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 3, pp. 375–389, March, 1996.

Translated by L. O. Chekhov.

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Volchenckov, D.Y., Nalimov, M.Y. Corrections to fully developed turbulent spectra due to compressibility of the fluid. Theor Math Phys 106, 307–318 (1996). https://doi.org/10.1007/BF02071475

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  • DOI: https://doi.org/10.1007/BF02071475

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