One-dimensional wave turbulence
One-dimensional wave turbulence
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DOI：
10.1016/j.physrep.2004.04.002
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发表时间：
2004-08
期刊：
影响因子：
--
通讯作者：
V. Zakharova;eric Diasc;Andrei Pushkarevd
中科院分区：
文献类型：
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作者：
V. Zakharova;eric Diasc;Andrei Pushkarevd
湍流问题是理论物理学的中心问题之一。虽然充分发展的湍流理论已被广泛研究，但波动湍流理论的研究较少，部分原因是它发展较晚。波动湍流发生在非线性色散波的物理系统中。在大多数应用中，非线性很小，色散波相互作用很弱。弱湍流理论是一种统计描述弱非线性相互作用波随机相位的方法。弱波湍流理论的发展与等离子体物理学和风浪的某些问题有关，这并不奇怪。本审查仅限于一维波湍流，基本上是因为更精细的计算网格可以用于数值计算。大部分的审查是专门在各种波动方程的波动湍流，特别是在一个简单的一维模型波湍流介绍了Majda，McLaughlin和Tabak在1997年。所有考虑的方程都是模型方程，但也讨论了对物理系统（如海浪）的影响。主要结论是：纯弱湍流理论适用的范围较窄。一般说来，波浪湍流并不完全是弱的。与弱湍流分量一起，它可以包括相干结构，例如孤子、准孤子、塌缩或宽塌缩。结果，弱湍流和强湍流并存。在相干结构不能发展的情况下，弱湍流占主导地位。尽管这主要是一个综述文件，新的结果，以及提出，特别是自组织临界性和准孤子湍流。
The problem of turbulence is one of the central problems in theoretical physics. While the theory of fully developed turbulence has been widely studied, the theory of wave turbulence has been less studied, partly because it developed later. Wave turbulence takes place in physical systems of nonlinear dispersive waves. In most applications nonlinearity is small and dispersive wave interactions are weak. The weak turbulence theory is a method for a statistical description of weakly nonlinear interacting waves with random phases. It is not surprising that the theory of weak wave turbulence began to develop in connection with some problems of plasma physics as well as of wind waves. The present review is restricted to one-dimensional wave turbulence, essentially because finer computational grids can be used in numerical computations. Most of the review is devoted to wave turbulence in various wave equations, and in particular in a simple one-dimensional model of wave turbulence introduced by Majda, McLaughlin and Tabak in 1997. All the considered equations are model equations, but consequences on physical systems such as ocean waves are discussed as well. The main conclusion is that the range in which the theory of pure weak turbulence is valid is narrow. In general, wave turbulence is not completely weak. Together with the weak turbulence component, it can include coherent structures, such as solitons, quasisolitons, collapses or broad collapses. As a result, weak and strong turbulence coexist. In situations where coherent structures cannot develop, weak turbulence dominates. Even though this is primarily a review paper, new results are presented as well, especially on self-organized criticality and on quasisolitonic turbulence.