We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the probability distribution function (pdf) of the local power is well modelled by the pdf of the product of two joint normally distributed variables. In appropriate units, this distribution is parameterised only by the mean dissipation rate, $ε$. The large deviation function for this distribution is calculated exactly and shown to satisfy a Fluctuation Relation (FR) with a coefficient which depends on $ε$. This FR is entirely statistical in origin. The deviation from the model pdf are most pronounced for positive fluctuations of the power and can be traced to a slightly faster than Gaussian decay of the tails of the one-point velocity pdf. The resulting deviations from the FR are consistent with several recent experimental studies.
Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise
对于充分发展的湍流的壳模型和傅立叶空间中的不可压缩纳维-斯托克斯方程，当将高斯白噪声人为地添加到每个模式的方程中时，通过应用为非平衡Langevin系统开发的方法[Harada和Sasa，Phys. Rev. Lett. 95，130602（2005）]。我们数值验证壳模型的情况下，推导出的响应函数的表达式，作为噪声趋于零，收敛到无噪声的壳模型的响应函数。
Microscopic and Macroscopic Rayleigh-Benard Flows : Continuum and Particle Simulations, Turbulence, Fluctuations, Time Reversibility, and Lyapunov Instability
