We study a self-organized critical system under the influence of turbulent motion of
the environment. The system is described by the anisotropic continuous stochastic equation
proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The motion of the environment is
modelled by the isotropic Kazantsev–Kraichnan “rapid-change” ensemble for an incompressible
fluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form
∝ δ(t − t
, where k is the wave number and ξ is an arbitrary exponent with the most realistic
values ξ = 4/3 (Kolmogorov turbulence) and ξ → 2 (Batchelor’s limit). Using the field-theoretic
renormalization group, we find infrared attractive fixed points of the renormalization group equation
associated with universality classes, i.e., with regimes of critical behavior. The most realistic values
of the spatial dimension d = 2 and the exponent ξ = 4/3 correspond to the universality class of
pure 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 equation
and the (isotropic) advecting velocity field are relevant also exists for some values of the parameters
ε = 4 − d and ξ. Depending on what terms (anisotropic, isotropic, or both) are relevant in specific
universality class, different types of scaling behavior (ordinary one or generalized) are established.
Original languageEnglish
Number of pages17
Issue number145
Publication statusPublished - 6 Sep 2020

Scopus subject areas

  • Statistical and Nonlinear Physics

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