AI 中文总结
该研究针对三维纳维-斯托克斯湍流，分析不确定性能量增长的关键影响因素，通过DNS模拟和$Q-R$平面分析，揭示应变率对极端不确定性产生事件的驱动作用。
AI 中文摘要
我们研究三维纳维-斯托克斯湍流中不确定性能量的指数增长，强调不确定性的间歇性和高度局域化放大/产生，这是理解湍流系统可预测性的关键因素。从纳维-斯托克斯方程中可识别出对不确定性产生项$P_{\triangle}$的增长/衰减有贡献的关键场：应变率、涡量和涡变形。在$Q-R$平面（其中$Q$和$R$是速度梯度张量的第二和第三不变量）中研究这些场的动力学，以理解它们在不确定性产生项$P_{\triangle}$演化中的作用。我们对不同雷诺数下周期性域中湍流直接数值模拟（DNS）的整个时空域上的应答概率函数进行估计。我们对局部不确定性产生项的罕见极端事件概率（作为不确定性能量、应变率、涡量和涡变形的函数）的估计，证实了应变率在驱动不确定性中的作用。当应变率和涡量过于接近它们的空间平均值时，仅基于此处考虑的场似乎无法进行稳定的概率预测。
英文摘要
We investigate the exponential growth of uncertainty energy in 3D Navier-Stokes turbulence, emphasising the intermittent and highly localized amplification/production of uncertainty, a critical factor in understanding the predictability of turbulent systems. From the Navier-Stokes equations one can identify some key fields contributing to the growth/decay of uncertainty-production term $P_Δ$: strain rate, vorticity, and vortex deformation. The dynamics of these fields are examined in the $Q-R$ plane, where $Q$ and $R$ are the second and third invariants of the velocity gradient tensor, to understand their role in the evolution of uncertainty-production term $P_Δ$. We proceed by estimating committor functions across the entire spatiotemporal domain of direct numerical simulations (DNS) of turbulence in a periodic domain at different Reynolds numbers. Our estimates of the probability of rare extreme events of local uncertainty-production term as a function of uncertainty energy, strain rate, vorticity, and vortex deformation confirm the role of strain rate in driving uncertainty. Where strain rate and vorticity are too close to their space-average values, stable probabilistic forecasts appear impossible solely on the basis of the fields considered here.
