论文标题
间歇性，级联和薄套件在三维Navier-Stokes湍流中
Intermittency, cascades and thin sets in three-dimensional Navier-Stokes turbulence
论文作者
论文摘要
在三维Navier-Stokes流体湍流计算中间歇性的视觉表现似乎是低维或“薄”丝状集合，随着能量级联向下至小尺度，涡度和应变会在其上积聚。为了研究这种现象，本文的第一个任务是研究Navier-Stokes方程的弱解决方案如何与级联反应相关联，并因此与无限长度尺度的无限序列相关联。事实证明，该序列会收敛到有限的极限。第二个任务是显示这些结果如何用整数尺寸$ d = 1，\，2，\，3 $，并且鉴于薄套件的发生，以讨论流体如何找到最平稳，最消散的溶液类别而不是最单一的机制。
Visual manifestations of intermittency in computations of three dimensional Navier-Stokes fluid turbulence appear as the low-dimensional or `thin' filamentary sets on which vorticity and strain accumulate as energy cascades down to small scales. In order to study this phenomenon, the first task of this paper is to investigate how weak solutions of the Navier-Stokes equations can be associated with a cascade and, as a consequence, with an infinite sequence of inverse length scales. It turns out that this sequence converges to a finite limit. The second task is to show how these results scale with integer dimension $D=1,\,2,\,3$ and, in the light of the occurrence of thin sets, to discuss the mechanism of how the fluid might find the smoothest, most dissipative class of solutions rather than the most singular.
