DOI

The field theoretic renormalization group is applied to the strongly nonlinear stochastic advection-diffusion equation. The turbulent advection is modelled by the Kazantsev–Kraichnan “rapid-change” ensemble. As a requirement of the renormalizability, the model necessarily involves infinite number of coupling constants (“charges”). The one-loop counterterm is calculated explicitly. The corresponding renormalization group equation demonstrates existence of a pair of two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain infrared attractive regions, the problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant), the critical dimensions of the scalar field, the response field and the frequency are nonuniversal (through the dependence on the effective couplings) but satisfy certain exact identities. For the second surface (advection is relevant), the dimensions are universal and they are found exactly.

Original languageEnglish
Article number121
Number of pages16
JournalUniverse
Volume8
Issue number2
DOIs
StatePublished - 13 Feb 2022

    Research areas

  • Critical behaviour, Nonlinear diffusion, Renormalization group, Turbulence, nonlinear diffusion, RENORMALIZATION-GROUP ANALYSIS, MODEL, EROSION, renormalization group, turbulence, EQUATION, critical behaviour

    Scopus subject areas

  • Physics and Astronomy(all)

ID: 92566180