DETERMINING MODES AND FRACTAL DIMENSION OF TURBULENT FLOWS
DETERMINING MODES AND FRACTAL DIMENSION OF TURBULENT FLOWS
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DOI：
10.1017/s0022112085000209
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发表时间：
1985-01-01
影响因子：
3.7
通讯作者：
TEMAM, R
中科院分区：
文献类型：
--
作者：
CONSTANTIN, P;FOIAS, C;TEMAM, R
对三维Navier-Stokes方程的抽象性质的研究为该方程的时间渐近解提供了新的思路。这里，基于该研究的严格结果，使用启发式论证来说明描述流体流动的足够多的自由度与N-S吸引子的分维界之间的密切关系。特别是，它说明了如何从Navier-Stokes方程的性质中获得基于纯物理和量纲论证的自由度数目的传统估计。还阐明了函数空间中充分自由度数和吸引子的维度与雷诺数的关系。
Research on the abstract properties of the Navier–Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments, based on the rigorous results of that research, are used to show the intimate relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier–Stokes attractor. In particular it is demonstrated how the conventional estimate of the number of degrees of freedom, based on purely physical and dimensional arguments, can be obtained from the properties of the Navier–Stokes equation. Also the Reynolds-number dependence of the sufficient number of degrees of freedom and of the dimension of the attractor in function space is elucidated.