Abstract:
A model of the fully developed turbulence of a compressible fluid based on the stohastic Navier–Stokes equation is considered by means of the field theoretic renormalization group. It is proved that the model is multiplicatively renormalizable in terms of the variables “velocity – logarithm of the pressure”. The scaling dimensions of the fields and parameters are calculated in the first order of the $\epsilon$-expansion. The dependence of the effective sound velocity and the Mach number on the integral turbulence scale $L$ is studied.
Citation:
N. V. Antonov, M. Yu. Nalimov, A. A. Udalov, “Renormalization group in the problem of the fully developed turbulence of a compresible fluid”, TMF, 110:3 (1997), 385–398; Theoret. and Math. Phys., 110:3 (1997), 305–315
\Bibitem{AntNalUda97}
\by N.~V.~Antonov, M.~Yu.~Nalimov, A.~A.~Udalov
\paper Renormalization group in the problem of the fully developed turbulence of a compresible fluid
\jour TMF
\yr 1997
\vol 110
\issue 3
\pages 385--398
\mathnet{http://mi.mathnet.ru/tmf976}
\crossref{https://doi.org/10.4213/tmf976}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1471186}
\zmath{https://zbmath.org/?q=an:0918.76030}
\transl
\jour Theoret. and Math. Phys.
\yr 1997
\vol 110
\issue 3
\pages 305--315
\crossref{https://doi.org/10.1007/BF02630456}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XU74600004}
Linking options:
https://www.mathnet.ru/eng/tmf976
https://doi.org/10.4213/tmf976
https://www.mathnet.ru/eng/tmf/v110/i3/p385
This publication is cited in the following 22 articles:
N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin, “Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment”, J Stat Phys, 192:2 (2025)
N. V. Antonov, M. M. Tumakova, “A General Vector Field Coupled to a Strongly Compressible Turbulent Flow”, J Math Sci, 275:3 (2023), 225
N. V. Antonov, M. M. Tumakova, “A general vector field coupled to a strongly compressible turbulent flow”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 5–24
Honkonen J., “Comment on “Turbulent Compressible Fluid: Renormalization Group Analysis, Scaling Regimes, and Anomalous Scaling of Advected Scalar Fields””, Phys. Rev. E, 104:2 (2021), 027101
Danco M., Hnatic M., Lucivjansky T., Mizisin L., “Renormalization Group Study of Superfluid Phase Transition: Effect of Compressibility”, Phys. Rev. E, 102:2 (2020), 022118
Menkyna M., “Influence of Compressibility on Scaling Regimes of Kraichnan Model With Finite Time Correlations: Two-Loop Rg Analysis”, Eur. Phys. J. B, 93:4 (2020), 71
Antonov N.V. Gulitskiy N.M. Kostenko M.M. Lucivjansky T., “Passive Advection of a Vector Field By Compressible Turbulent Flow: Renormalizations Group Analysis Near D = 4”, Universe, 5:1 (2019), 37
N. V. Antonov, N. M. Gulitskii, M. M. Kostenko, T. Lučivjanský, “Renormalization group analysis of models of advection of a vector admixture and a tracer field by a compressible turbulent flow”, Theoret. and Math. Phys., 200:3 (2019), 1294–1312
Michal Hnatič, Nikolay M. Gulitskiy, Tomáš Lučivjanský, Lukáš Mižišin, Viktor Škultéty, Springer Proceedings in Complexity, 11th Chaotic Modeling and Simulation International Conference, 2019, 175
Honkonen J. Lucivjansky T. Skultety V., “Influence of Turbulent Mixing on Critical Behavior of Directed Percolation Process: Effect of Compressibility”, Phys. Rev. E, 97:2 (2018), 022123
Antonov N.V. Gulitskiy N.M. Kostenko M.M. Lucivjansky T., “Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields”, Phys. Rev. E, 95:3 (2017), 033120
Antonov N.V. Hnatich M. Kapustin A.S. Lucivjansky T. Mizisin L., “Active-to-Absorbing Phase Transition Subjected to the Velocity Fluctuations in the Frozen Limit Case”, Phys. Part. Nuclei Lett., 14:6 (2017), 944–952
Antonov N.V. Gulitskiy N.M. Kostenko M.M. Lucivjansky T., “Stochastic Navier–Stokes Equation and Advection of a Tracer Field: One-Loop Renormalization Near D=4”, 5Th International Conference on New Frontiers in Physics, Epj Web of Conferences, 164, ed. Bravina L. Foka Y. Kabana S., E D P Sciences, 2017, 07044
Antonov N.V. Gulitskiy N.M. Kostenko M.M. Lucivjansky T., “Advection of a Passive Scalar Field By Turbulent Compressible Fluid: Renormalization Group Analysis Near D=4”, Xiith Quark Confinement and the Hadron Spectrum, Epj Web of Conferences, 137, ed. Foka Y. Brambilla N. Kovalenko V., E D P Sciences, 2017, UNSP 10003
Antonov N.V. Hnatic M. Kapustin A.S. Lucivjansky T. Mizisin L., “Directed Percolation Process in the Presence of Velocity Fluctuations: Effect of Compressibility and Finite Correlation Time”, Phys. Rev. E, 93:1 (2016), 012151
Danco M. Hnatic M. Komarova M.V. Lucivjansky T. Nalimov M.Yu., “Superfluid Phase Transition With Activated Velocity Fluctuations: Renormalization Group Approach”, Phys. Rev. E, 93:1 (2016), 012109
Pharasi H.K. Bhattacharjee J.K., “Dynamic Scaling and Large Scale Effects in Turbulence in Compressible Stratified Fluid”, Phys. Lett. A, 380:1-2 (2016), 222–226
A.V. Antonov, N.M. Gulitskiy, M.M. Kostenko, T. Lučivjanský, V.A. Andrianov, V.A. Matveev, V.A. Rubakov, V.T. Kim, A.A. Andrianov, M.D. Fitkevich, “Renormalization group analysis of a turbulent compressible fluid neard= 4: Crossover between local and non-local scaling regimes”, EPJ Web Conf., 125 (2016), 05006
Antonov N.V. Kostenko M.M., “Anomalous Scaling in Magnetohydrodynamic Turbulence: Effects of Anisotropy and Compressibility in the Kinematic Approximation”, Phys. Rev. E, 92:5 (2015), 053013
Antonov N.V. Kostenko M.M., “Anomalous Scaling of Passive Scalar Fields Advected By the Navier–Stokes Velocity Ensemble: Effects of Strong Compressibility and Large-Scale Anisotropy”, Phys. Rev. E, 90:6 (2014), 063016