论文标题
混合和扩散粗糙的剪切流
Mixing and diffusion for rough shear flows
论文作者
论文摘要
本文介绍了由粗糙（$ c^α$）剪切流动的被动标量的混合和扩散特性。我们表明，通常，人们不能期望粗糙的剪切流将无粘性混合的速率提高到没有临界点的光滑剪切速度。另一方面，扩散速度可能会更快地增强。这表明，在低规律性的情况下，无粘性混合特性和增强耗散之间的相互作用更加复杂，实际上与在平滑环境中有效的某些自然启发式方法相矛盾。
This article addresses mixing and diffusion properties of passive scalars advected by rough ($C^α$) shear flows. We show that in general, one cannot expect a rough shear flow to increase the rate of inviscid mixing to more than that of a smooth shear without critical points. On the other hand, diffusion may be enhanced at a much faster rate. This shows that in the setting of low regularity, the interplay between inviscid mixing properties and enhanced dissipation is more intricate, and in fact contradicts some of the natural heuristics that are valid in the smooth setting.
