Weak Solutions, Renormalized Solutions and Enstrophy Defects in 2D Turbulence
Weak Solutions, Renormalized Solutions and Enstrophy Defects in 2D Turbulence
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二维湍流中的弱解、重正化解和熵缺陷
DOI：
10.1007/s00205-005-0390-5
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发表时间：
2004
影响因子：
2.5
通讯作者：
H. J. Nussenzveig Lopes
中科院分区：
文献类型：
--
作者：
M. C. Lopes Filho;A. Mazzucato;H. J. Nussenzveig Lopes
涡度拟能是涡度平方积分的一半，在二维湍流理论中的作用类似于动能在三维湍流的柯尔莫哥洛夫理论中的作用。因此，获得在高雷诺数下涡度拟能耗散方式的描述是有趣的。在这篇文章中，我们探讨的概念，粘性和运输拟能亏损，这模型的空间结构的耗散拟能。这些概念是由G. Eyink试图调和Kraichnan-Batchelor理论的二维湍流与当前知识的性质弱解的方程的不可压缩和理想的流体运动。Eyink的理论产生了三个自然的问题：（i）存在的拟能缺陷，（ii）条件的平等运输和粘性拟能缺陷，（iii）条件的消失拟能缺陷。在[10]中，Eyink证明了一些与这些问题相关的结果，并提出了一个关于如何在物理意义上回答这些问题的猜想。本文改进和推广了Eyink的一些结果，并给出了他的猜想的一个反例。
Enstrophy, half the integral of the square of vorticity, plays a role in 2D turbulence theory analogous to the role of kinetic energy in the Kolmogorov theory of 3D turbulence. It is therefore interesting to obtain a description of the way enstrophy is dissipated at high Reynolds numbers. In this article we explore the notions of viscous and transport enstrophy defect, which model the spatial structure of the dissipation of enstrophy. These notions were introduced by G. Eyink in an attempt to reconcile the Kraichnan-Batchelor theory of 2D turbulence with current knowledge of the properties of weak solutions of the equations of incompressible and ideal fluid motion. Three natural questions arise from Eyink's theory: (i) existence of the enstrophy defects, (ii) conditions for the equality of transport and viscous enstrophy defects, (iii) conditions for the vanishing of the enstrophy defects. In [10], Eyink proved a number of results related to these questions and formulated a conjecture on how to answer these problems in a physically meaningful context. In the present article we improve and extend some of Eyink's results and present a counterexample to his conjecture.