TY - JOUR

T1 - Turbulent mixing of a critical fluid: The non-perturbative renormalization

AU - Налимов, Михаил Юрьевич

AU - Калагов, Георгий Алибекович

AU - Hnatič, M.

PY - 2018/1

Y1 - 2018/1

N2 - Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υ jυ i〉∼(P ji ⊥+αP ji ∥)/k d+ζ. Depending on the relations between the parameters ζ α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

AB - Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υ jυ i〉∼(P ji ⊥+αP ji ∥)/k d+ζ. Depending on the relations between the parameters ζ α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

UR - http://www.scopus.com/inward/record.url?scp=85033474816&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2017.10.024

DO - 10.1016/j.nuclphysb.2017.10.024

M3 - Article

VL - 926

SP - 1

EP - 10

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -