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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Computing the scaling exponents in fluid turbulence from first principles: the formal setup
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Computing the scaling exponents in fluid turbulence from first principles: the formal setup

机译：根据第一原理计算流体湍流中的标度指数：正式设置

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We propose a scheme for the calculation from the Navier-Stokes equations of the scaling exponents in of the nth order correlation functions in fully developed hydrodynamic turbulence. The scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the Euler equation. It constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents zeta(n). As a consequence the scaling exponents are determined by solvability conditions and not from power counting. It is argued that in order to achieve such a formulation one must recognize that the many-point spacetime correlation functions are not scale invariant in their time arguments, The assumption of full scale invariance leads unavoidably to Kolmogorov exponents. It is argued that the determination of all the scaling exponents in requires equations for infinitely many renormalized objects. One can however proceed in controlled successive approximations by successive truncations of the infinite hierarchy of equations. Clues as to how to truncate without reintroducing power counting can be obtained from renormalized perturbation theory. To this aim we show that the fully resummed perturbation theory is equivalent in its contents to the exact hierarchy of equations obeyed by the nth order correlation functions and Green's function. In light of this important result we can safely use finite resummations to construct successive closures of the infinite hierarchy of equations. This paper presents the conceptual and technical details of the scheme. The analysis of the high-order closure procedures which do not destroy the rescaling symmetry and the actual calculations for truncated models will be presented in a forthcoming paper in collaboration with V. Belinicher. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 24]
机译：我们提出了一个从Navier-Stokes方程中完全发展的水动力湍流中n阶相关函数的比例指数的计算方案。该方案是非扰动的，并且构造为尊重Euler方程的基本重新定标对称性。它构成了耦合方程式的无限层次结构，对于任何一组缩放指数zeta（n），在缩放方面均遵循相同的方程式。结果，缩放指数由可溶性条件确定，而不是由功率计数确定。有人认为，为了实现这一表述，必须认识到多点时空相关函数在其时间参数上不是标度不变的。全标度不变的假设不可避免地导致了Kolmogorov指数。有人认为，确定所有标度指数需要无穷多个重新规格化对象的方程。然而，可以通过无限次等式层级的连续截断以受控的逐次逼近进行。关于如何在不重新引入功率计数的情况下截断的线索可以从重新归一化的扰动理论中获得。为此，我们证明了完全恢复的扰动理论在内容上等同于n阶相关函数和格林函数所遵循的方程的精确层次。根据这一重要结果，我们可以安全地使用有限求和来构造无限级方程的连续闭合。本文介绍了该方案的概念和技术细节。将与V. Belinicher合作在即将发表的论文中介绍不会破坏重新缩放的对称性的高阶闭合过程的分析以及截断模型的实际计算。 （C）1998 Elsevier Science B.V.保留所有权利。 [参考：24]

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