Anomalous scaling in a model of passive scalar advection: Exact results.
Anomalous scaling in a model of passive scalar advection: Exact results.
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DOI：
10.1103/physreve.53.3518
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发表时间：
1995-04
期刊：
影响因子：
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通讯作者：
Adrienne L. Fairhall;Omri Gat;V. L’vov;I. Procaccia
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文献类型：
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作者：
Adrienne L. Fairhall;Omri Gat;V. L’vov;I. Procaccia
研究了Kraichnan的被动标量平流模型，其中驱动速度场具有快速的时间去相关，作为理解湍流系统中反常标量现象的个例模型。我们演示了重整化微扰理论的技术如何(在精确恢复之后)导致统计量的方程，也揭示了非微扰效应。结果表明，图解展开中的紫外发散转化为反常标度，内部长度作为重整化标度。在这篇文章中，我们解析地计算了由紫外线发散引起的无限反常指数集。尽管如此，非微扰效应提供了一种基于外部重整化尺度的反常标度的可能性。对这一复杂行为的机制进行了详细的研究和解释。我们用L、普罗卡西亚和费尔霍尔的语言证明了这一点。这个问题是“严重的”，即标量主场�=�c的反常指数。这正是条件
Kraichnan’s model of passive scalar advection in which the driving velocity field has fast temporal decorrelation is studied as a case model for understanding the appearance of anomalous scaling in turbulent systems. We demonstrate how the techniques of renormalized perturbation theory lead (after exact resummations) to equations for the statistical quantities that reveal also non perturbative effects. It is shown that ultraviolet divergences in the diagrammatic expansion translate into anomalous scaling with the inner length acting as the renormalization scale. In this paper we compute analytically the infinite set of anomalous exponents that stem from the ultraviolet divergences. Notwithstanding, non-perturbative effects furnish a possibility of anomalous scaling based on the outer renormalization scale. The mechanism for this intricate behavior is examined and explained in detail. We show that in the language of L’vov, Procaccia and Fairhall [Phys. Rev. E 50, 4684 (1994)] the problem is “critical” i.e. the anomalous exponent of the scalar primary field � = �c. This is precisely the condition