TY - JOUR

T1 - Strongly Nonlinear Diffusion in Turbulent Environment: A Problem with Infinitely Many Couplings

AU - Антонов, Николай Викторович

AU - Бабакин, Андрей Александрович

AU - Какинь, Полина Игоревна

PY - 2022/2/13

Y1 - 2022/2/13

N2 - 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.

AB - 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.

KW - Critical behaviour

KW - Nonlinear diffusion

KW - Renormalization group

KW - Turbulence

KW - nonlinear diffusion

KW - RENORMALIZATION-GROUP ANALYSIS

KW - MODEL

KW - EROSION

KW - renormalization group

KW - turbulence

KW - EQUATION

KW - critical behaviour

UR - http://www.scopus.com/inward/record.url?scp=85126727665&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e7d83c5c-e549-3651-b1c9-33b000b77d4a/

U2 - 10.3390/universe8020121

DO - 10.3390/universe8020121

M3 - Article

VL - 8

JO - Universe

JF - Universe

SN - 2218-1997

IS - 2

M1 - 121

ER -