TY - JOUR

T1 - Effects of Turbulent Environment on Self-Organized Critical Behavior: Isotropy vs. Anisotropy

AU - Antonov , Nikolay V.

AU - Gulitskiy, Nikolay M.

AU - Kakin, Polina I.

AU - Kochnev , German E.

N1 - Publisher Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

PY - 2020/9/6

Y1 - 2020/9/6

N2 - We study a self-organized critical system under the influence of turbulent motion ofthe environment. The system is described by the anisotropic continuous stochastic equationproposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The motion of the environment ismodelled by the isotropic Kazantsev–Kraichnan “rapid-change” ensemble for an incompressiblefluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form∝ δ(t − t0)/kd+ξ, where k is the wave number and ξ is an arbitrary exponent with the most realisticvalues ξ = 4/3 (Kolmogorov turbulence) and ξ → 2 (Batchelor’s limit). Using the field-theoreticrenormalization group, we find infrared attractive fixed points of the renormalization group equationassociated with universality classes, i.e., with regimes of critical behavior. The most realistic valuesof the spatial dimension d = 2 and the exponent ξ = 4/3 correspond to the universality class ofpure turbulent advection where the nonlinearity of the Hwa–Kardar (HK) equation is irrelevant.Nevertheless, the universality class where both the (anisotropic) nonlinearity of the HK equationand the (isotropic) advecting velocity field are relevant also exists for some values of the parametersε = 4 − d and ξ. Depending on what terms (anisotropic, isotropic, or both) are relevant in specificuniversality class, different types of scaling behavior (ordinary one or generalized) are established.

AB - We study a self-organized critical system under the influence of turbulent motion ofthe environment. The system is described by the anisotropic continuous stochastic equationproposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The motion of the environment ismodelled by the isotropic Kazantsev–Kraichnan “rapid-change” ensemble for an incompressiblefluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form∝ δ(t − t0)/kd+ξ, where k is the wave number and ξ is an arbitrary exponent with the most realisticvalues ξ = 4/3 (Kolmogorov turbulence) and ξ → 2 (Batchelor’s limit). Using the field-theoreticrenormalization group, we find infrared attractive fixed points of the renormalization group equationassociated with universality classes, i.e., with regimes of critical behavior. The most realistic valuesof the spatial dimension d = 2 and the exponent ξ = 4/3 correspond to the universality class ofpure turbulent advection where the nonlinearity of the Hwa–Kardar (HK) equation is irrelevant.Nevertheless, the universality class where both the (anisotropic) nonlinearity of the HK equationand the (isotropic) advecting velocity field are relevant also exists for some values of the parametersε = 4 − d and ξ. Depending on what terms (anisotropic, isotropic, or both) are relevant in specificuniversality class, different types of scaling behavior (ordinary one or generalized) are established.

KW - self-organized criticality

KW - non-equilibrium critical behavior

KW - turbulent advection

KW - Renormalization group

KW - self-organized criticality

KW - non-equilibrium critical behavior

KW - turbulent advection

KW - renormalization group

KW - Non-equilibrium critical behavior

KW - Self-organized criticality

KW - Turbulent advection

KW - Renormalization group

UR - https://www.x-mol.com/paper/1302780518411243520

UR - http://www.scopus.com/inward/record.url?scp=85091943086&partnerID=8YFLogxK

U2 - 10.3390/UNIVERSE6090145

DO - 10.3390/UNIVERSE6090145

M3 - Article

VL - 6

JO - Universe

JF - Universe

SN - 2218-1997

IS - 9

M1 - 145

ER -