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Renormalization Group in the Problem of Active Scalar Advection

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The field theoretic renormalization group (RG) is applied to a near-equilibrium fluid model associated with a scalar field (like temperature or density of an impurity) that is active, that is, affects the dynamics of the fluid itself. It is shown that the only possible nontrivial infrared asymptotic regimes are governed by “passive” fixed points of the RG equations, where the back reaction is irrelevant. This result resembles the result obtained by Nandy and Bhattacharjee (1998) in a model describing active convection by fully developed turbulence. Furthermore, the existence of “exotic” fixed points with negative and complex effective couplings and transport coefficients that may suggest possible directions for future studies is established.

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    N. V. Antonov

  2. L. D. Landau Institute for Theoretical Physics, Chernogolovka, Moscow Region, Russia

    M. M. Kostenko

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  1. N. V. Antonov
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Correspondence to N. V. Antonov.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 487, 2019, pp. 5–27.

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Antonov, N.V., Kostenko, M.M. Renormalization Group in the Problem of Active Scalar Advection. J Math Sci 257, 425–441 (2021). https://doi.org/10.1007/s10958-021-05492-2

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