湍流中的相级联

Energy spectra and passive tracer cascades in turbulent flows

We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tracer forcing is in the inverse energy cascade range, and in 3D when the Schmidt number Sc is large). The extent of the tracer cascade range is then limited by the width of the range for the shallower of the two energy spectra. Nevertheless, we show that in dimension $d=2,3$ the tracer cascade range extends (up to a logarithm) to $κ_{d\text{D}}^{p}$,…

Turbulent cascades for a family of damped Szegö equations

In this paper, we study the transfer of energy from low to high frequencies for a family of damped Szegö equations. The cubic Szegö equation has been introduced as a toy model for a totally non-dispersive degenerate Hamiltonian equation. It is a completely integrable system which develops growth of high Sobolev norms, detecting transfer of energy and hence cascades phenomena. Here, we consider a two-parameter family of variants of the cubic Szegö equation and prove that adding a damping term unexpectedly promotes the existence of turbulent cascades. Furthermore, we give a panorama of the dynam…

湍流级联与分数场的一个线性随机模型

A Linear Stochastic Model of Turbulent Cascades and Fractional Fields

本文构造了一个由零阶微分算子控制的线性方程，在外力为统计均匀平稳随机过程时模拟湍流能量级联，并证明解在有限时刻光滑、在无穷时刻收敛到分数Gaussian场。

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

We establish Lagrangian formulae for energy conservation anomalies involving the discrepancy between short-time two-particle dispersion forward and backward in time. These results are facilitated by a rigorous version of the Ott-Mann-Gawȩdzki relation, sometimes described as a "Lagrangian analogue of the 4/5ths law". In particular, we prove that for any space-time $L^3$ weak solution of the Euler equations, the Lagrangian forward/backward dispersion measure matches on to the energy defect in the sense of distributions. For strong limits of $d\geq3$ dimensional Navier-Stokes solutions the defec…

湍流能量级联的连续模型

A continuous model for turbulent energy cascade

在本文中，我们介绍了一个新的PDE模型在频率空间的惯性能量级联再现经典的标度律Kolmogorov的湍流理论。我们的观点是基于研究的能量通量通过一个连续的尺度范围，而不是离散集的并矢尺度。由此产生的模型是一个变体的伯格斯方程的射线与边界条件，它代表了一个恒定的能量输入在积分尺度。粘性耗散通过阻尼项建模。我们表明存在一个独特的固定的解决方案，无论是在粘性和无粘的情况下，复制的经典耗散异常的极限消失粘度。最近的事态发展的调查确定性方法的法律动荡，特别是昂萨格的猜想。

泰勒-科特流中湍流的逆能量级联

Inverse Energy Cascade in Turbulent Taylor-Couette Flows

研究高雷诺数下泰勒-科特流中逆能量级联现象，揭示零剪切应力奇异点引发的湍流能量聚集与频谱峰值形成机制。