三维Navier-Stokes方程turbulence中湍流度的估算
Estimating intermittency in three-dimensional Navier-Stokes turbulence
摘要：
解决了Navier-Stokes湍流计算分辨率难以实现的问题。结果表明，Navier-Stokes方程的解决方案可以潜在地表现出不同的时空$\mathbb{R}^{\pm}$在两个不同的区域，其中$\mathbb{R}^{-}$是由一个不相交的时空“异常”的工会。大的$|\nabla\bom|$值支配着$\mathbb{R}^{-}$，这与涡面或紧密盘绕的细丝的形成是一致的。解析$\mathbb{R}^{\pm}$中的区域所需的局部自由度$\mathcal{N}^{\pm}$满足$$\mathcal{N}^{\pm}(\bx, t)\lessgtr c_{\pm}\mathcal{R}_{u}^{3}$$，其中$\mathcal{R}_{u} = uL/ν$是取决于局部速度场$u(\bx, t)$的雷诺数。
英文摘要：
The issue of why computational resolution in Navier-Stokes turbulence is so hard to achieve is addressed. It is shown that Navier-Stokes solutions can potentially behave differently in two distinct regions of space-time $\mathbb{R}^{\pm}$ where $\mathbb{R}^{-}$ is comprised of a union of disjoint space-time `anomalies'. Large values of $|\nabla\bom|$ dominate $\mathbb{R}^{-}$, which is consistent with the formation of vortex sheets or tightly-coiled filaments. The local number of degrees of freedom $\mathcal{N}^{\pm}$ needed to resolve the regions in $\mathbb{R}^{\pm}$ satisfies $$\mathcal{N}^{\pm}(\bx, t)\lessgtr c_{\pm}\mathcal{R}_{u}^{3}$$ where $\mathcal{R}_{u} = uL/ν$ is a Reynolds number dependent on the local velocity field $u(\bx, t)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
