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 $\propto \delta (t-t\prime )/k^{d+\xi }$, where k is the wave number and $\xi$ is an arbitrary exponent with the most realistic values $\xi =4/3$ (Kolmogorov turbulence) and $\xi \to 2$ (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 $\xi =4/3$ 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 $\epsilon =4-d$ and $\xi$. 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.

中文翻译：

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湍流环境对自组织临界行为的影响：各向同性与各向异性

我们研究了环境动荡影响下的自组织临界系统。该系统由Hwa和Kardar提出的各向异性连续随机方程描述。牧师 62：1813（1989）]。环境的运动是由各向同性的Kazantsev–Kraichnan对不可压缩流体的“快速变化”集合建模的：它是具有消失的相关时间和形式的对相关函数的高斯模型$\propto \delta （Ť-Ť\prime ）/{ķ}^{d+\xi }$，其中k是波数，$\xi$ 是具有最现实值的任意指数 $\xi =4/3$ （Kolmogorov湍流）和 $\xi \to 2$（Batchelor的限制）。使用场论重归一化组，我们找到了与普遍性类别（即临界行为体系）相关的重归一化组方程的红外吸引不动点。空间维度的最现实值$d=2$ 和指数 $\xi =4/3$对应于纯湍流对流的普遍性类别，其中Hwa–Kardar（HK）方程的非线性无关紧要。但是，对于某些参数值，也存在其中HK方程的（各向异性）非线性与（各向同性）对流速度场都相关的普适类。$\epsilon =4-d$ 和 $\xi$。根据在特定通用性类别中相关的术语（各向异性，各向同性或两者），建立了不同类型的缩放行为（普通的或广义的）。