A continuous model for turbulent energy cascade
A continuous model for turbulent energy cascade
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DOI：
10.1017/cbo9781139235792.004
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
A. Cheskidov;S. Friedlander;R. Shvydkoy
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文献类型：
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作者：
A. Cheskidov;S. Friedlander;R. Shvydkoy
本文介绍了一种新的惯性能叶栅的频域偏微分方程组模型，该模型再现了Kolmogorov湍流理论的经典标度律。我们的观点是通过一个连续的标度范围来研究能量流，而不是离散的并矢标度集。所得到的模型是半直线上Burgers型方程的变体，带有一个边界条件，该边界条件表示积分尺度上的恒定能量输入。粘性耗散通过阻尼项来模拟。我们证明了在粘性和无粘性两种情况下都存在唯一的定常解，它在粘性消失的极限下复制了经典的耗散反常。对湍流定律的确定性方法，特别是对Onsager猜想的最新进展进行了综述。
In this paper we introduce a new PDE model in frequency space for the inertial energy cascade that reproduces the classical scaling laws of Kolmogorov's theory of turbulence. Our point of view is based upon studying the energy flux through a continuous range of scales rather than the discrete set of dyadic scales. The resulting model is a variant of Burgers equation on the half line with a boundary condition which represents a constant energy input at integral scales. The viscous dissipation is modeled via a damping term. We show existence of a unique stationary solution, both in the viscous and inviscid cases, which replicates the classical dissipation anomaly in the limit of vanishing viscosity. A survey of recent developments in the deterministic approach to the laws of turbulence, and in particular, to Onsager's conjecture is given.