Abstract

The title of this paper echoes the title of a paragraph in the famous book by Frisch on classical turbulence. In the relevant chapter, the author discusses the role of the statistical dynamics of vortex filaments in the fascinating problem of turbulence and the possibility of a breakthrough in constructing an advanced theory. This aspect arose due to the large amount of evidence, both experimental and numerical, that the vorticity field in turbulent flows has a pronounced filamentary structure. In fact, there is unquestionably a strong relationship between the dynamics of chaotic vortex filaments and turbulent phenomena. However, the question arises as to whether the basic properties of turbulence (cascade, scaling laws, etc.) are a consequence of the dynamics of the vortex filaments (the `dog' concept) or the latter have only a marginal significance (the `tail' concept). Based on well-established results regarding the dynamics of quantized vortex filaments in superfluids, we illustrate how these dynamics can lead to the main elements of the theory of turbulence. We cover key topics such as the exchange of energy between different scales, the possible origin of Kolmogorov-type spectra, and the free decay behavior.

中文翻译：

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古典湍流中涡旋丝的统计特征：狗还是尾巴？

摘要

本文的标题与弗里施着名的经典湍流一书中的一段标题相呼应。在相关的章节中，作者讨论了涡旋丝的统计动力学在引人入胜的湍流问题中的作用以及在构建高级理论方面取得突破的可能性。这一方面的出现是由于大量的实验和数值证据表明，湍流中的涡流场具有明显的丝状结构。实际上，毫无疑问，混沌涡旋丝的动力学与湍流现象之间存在很强的关系。然而，关于湍流的基本特性（级联，缩放定律等）是否是涡流丝（“狗”）动力学的结果，引起了一个问题。概念）或后者仅具有边际意义（“尾巴”概念）。基于关于超流体中量化涡流丝动力学的公认研究结果，我们说明了这些动力学如何导致湍流理论的主要内容。我们涵盖了关键主题，例如不同尺度之间的能量交换，Kolmogorov型谱的可能起源以及自由衰减行为。