三维不可压缩流携带圆管的破坏

A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations

By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed that turbulence consists of a self-similar hierarchy of anti-parallel pairs of vortex tubes, in particular, stretching in larger-scale strain fields creates smaller-scale vortices. Inspired by their numerical result, we examine the Goto-Saito-Kawahara type of vortex-tubes behavior using the 3D incompressible Euler equations, and show that such behavior induces energy cascade in the absence of nonlinear scale-interaction. From this energy cascade, we prove a modified version of the zeroth-law. In the Appendix, we derive Kolmo…

Existence of knotted vortex tubes in steady Euler flows

We prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible Euler equation in R^3. More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in R^3, we show that they can be transformed with a C^m-small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity. The structure of the vortex lines in the tubes is extremely rich, presenting a positive-measure set of invariant tori and infinitely many periodic vortex lines. The problem of the existence of steady knotted vortex tubes…

绕小障碍物的不可压缩流动和粘性极限的消失

Incompressible flow around a small obstacle and the vanishing viscosity limit

在这篇文章中，我们考虑粘性流在外部的障碍物满足标准的无滑移边界条件的障碍物的表面。我们寻求的条件下，解决方案的Navier-Stokes系统在外部域收敛到解决方案的欧拉系统在全空间时，粘度和大小的障碍消失。我们证明了这种收敛是真的假设两个假设：第一，初始的外部域速度强烈收敛于$L^2$的全空间初始速度和第二，障碍物的直径是小于一个合适的常数倍粘度，或者，换句话说，障碍物是足够小的。只要已知极限问题的解存在并保持足够光滑，收敛性就成立。本文的工作是对文[1，2，3] [1] D. Iftimie和J. Kelliher，{ \it关于三维粘性不可压缩流体的消失障碍极限的评论。}可在http://math.univ-lyon1.fr/~iftimie/ARTICLES/viscoushrink3d.pdf上获得预印本。[2]D. Iftimie，M. C. Lopes Filho和H. J. Nussenzveig Lopes. { \it绕小障碍物的二维不可压缩理想流。}《偏微分方程通讯》{ \bf 28}（2003），第1-2期，第349- 379页。[3]D. Iftimie，M. C. Lopes Filho和H. J. Nussenzveig Lopes. { \it绕小障碍物的二维不可压缩粘性流。}《数学年鉴》{ \bf 336}（2006），第2期，第449- 489页。

Asymptotic Analysis of a Viscous Fluid in a Curved Pipe with Elastic Walls

This communication is devoted to the presentation of our recent results regarding the asymptotic analysis of a viscous flow in a tube with elastic walls. This study can be applied, for example, to the blood flow in an artery. With this aim, we consider the dynamic problem of the incompressible flow of a viscous fluid through a curved pipe with a smooth central curve. Our analysis leads to obtain an one dimensional model via singular perturbation of the Navier-Stokes system as $\varepsilon$, a non dimensional parameter related to the radius of cross-section of the tube, tends to zero. We allow …

面向三维不可压缩粘性流动的随机大涡模拟

Random large eddy simulation for 3-dimensional incompressible viscous flows

本研究结合随机涡方法与大涡模拟核心思想，提出基于滤波和抛物方程积分表示定理的Navier-Stokes方程闭合求解方案，规避三维积分核处理难题，经层流、湍流模拟验证有效。

湍流如何在一点处增长涡量

How turbulent flows grow vorticity at a point

本研究通过解析与数值方法构造涡量瞬子，揭示湍流中强涡量增长机制：经典拉伸放大仅限阈值内，超阈值需涡量波碰撞，与OpenAI的有限时间爆破解机制相似。