论文标题
湍流环境对自组织的临界行为的影响：各向异性与各向异性
Effects of turbulent environment on self-organized critical behavior: Isotropy vs Anisotropy
论文作者
论文摘要
我们研究了环境动荡运动影响下的一个自组织的关键系统。该系统由HWA和Kardar提出的各向异性连续随机方程[{\ it phys。 Rev. Lett。} {\ bf 62}：1813（1989）]。环境的运动是由各向同性的kazantsev-kraichnan“快速变化”合奏的，用于不可压缩的液体：它是高斯随着相关时间而消失的相关时间和表格$ \proptoΔ（t-t-t'） / k^{d+ecut的$ k $ at $ k $ at $ at $ at $ at $ wave IS Wavel IS Wave IS $ wave IS Wavel IS的相关功能4/3 $（Kolmogorov湍流）和$ξ\至2 $（Batchelor的限制）。使用现场理论的重新归一化组，我们发现与通用类别相关的重新归一化组方程的红外固定点，即与关键行为的制度。空间维度的最现实值$ d = 2 $和指数$ $ $ $ $ξ= 4/3 $对应于纯湍流对流的通用类别，其中HWA-KARDAR（HK）方程的非线性是无关紧要的。然而，对于某些参数的某些值$ \ varepsilon = 4-d $和$ξ$，也存在HK方程（各向异性）非线性和（各向同性）上流速度字段的普遍性类别。根据特定的普遍性类别中的术语（各向异性，各向同性或两者兼有），建立了不同类型的缩放行为（普通的或普遍）。
We study a self-organized critical system under influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [{\it Phys. Rev. Lett.} {\bf 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 $\proptoδ(t-t') / k^{d+ξ}$, where $k$ is the wave number and $ξ$ is an arbitrary exponent with the most realistic values $ξ= 4/3$ (Kolmogorov turbulence) and $ξ\to 2$ (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 $ξ=4/3$ 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 $\varepsilon=4-d$ 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.
