Continuous representation for shell models of turbulence
Continuous representation for shell models of turbulence
复制标题
湍流壳模型的连续表示
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Mailybaev
中科院分区：
文献类型：
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作者：
A. Mailybaev
本文建立并分析了由湍流壳模型引起的一维连续水动力模型。这种连续模型经过傅里叶变换后，分裂成无数个不耦合的子系统，这些子系统都与同一个壳模型相同。考虑了允许这种结构的两种壳模型：壳间比λ = 23/2的并矢（Desnyansky-Novikov）模型和湍流的Sabra模型。连续模型允许理解壳模型解的各种属性，并在物理空间中提供它们的解释。我们证明了具有Kolmogorov标度的并矢模型的渐近解对应于物理空间中诱导连续解的激波（不连续），并且有限时间爆破及其粘性正则化遵循类似于Burgers方程的情形。对于Sabra模型，我们提供了爆破解和间歇湍流动力学的物理空间表示。
In this work we construct and analyze continuous hydrodynamic models in one space dimension, which are induced by shell models of turbulence. After Fourier transformation, such continuous models split into an infinite number of uncoupled subsystems, which are all identical to the same shell model. The two shell models, which allow such a construction, are considered: the dyadic (Desnyansky–Novikov) model with the intershell ratio λ = 23/2 and the Sabra model of turbulence with . The continuous models allow for understanding of various properties of shell model solutions and provide their interpretation in physical space. We show that the asymptotic solutions of the dyadic model with Kolmogorov scaling correspond to the shocks (discontinuities) for the induced continuous solutions in physical space, and the finite-time blowup together with its viscous regularization follow the scenario similar to the Burgers equation. For the Sabra model, we provide the physical space representation for blowup solutions and intermittent turbulent dynamics.