Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence ✩
Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence ✩
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对熵、回文和二维湍流不变测度的估计 ✩
DOI：
10.1016/j.jde.2009.11.020
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发表时间：
2010
影响因子：
2.4
通讯作者：
M. Jolly
中科院分区：
文献类型：
--
作者：
R. Dascaliuc;C. Foias;M. Jolly
构造半积分曲线，限定了二维Navier-Stokes方程的全局吸引子在熵态和回态张成的平面上的投影。特别令人感兴趣的是平面上的某些区域，在这些区域中，回滞优于熵滞。先前的工作表明，如果全局吸引子的解在这样一个区域花费大量的时间，那么就会有一个更小长度尺度的熵级联，这是二维湍流理论的主要特征之一。半积分曲线将平面划分为流动方向范围有限的区域。这使我们能够估计间歇解决方案爆发到一个大的回显区域所需的平均时间。我们还推导了平均回传系数的一个明显的、普遍的上界，并表明它只适用于承认非线性项为零的统计稳态的力。
We construct semi-integral curves which bound the projection of the global attractor of the 2-D Navier–Stokes equations in the plane spanned by enstrophy and palinstrophy. Of particular interest are certain regions of the plane where palinstrophy dominates enstrophy. Previous work shows that if solutions on the global attractor spend a significant amount of time in such a region, then there is a cascade of enstrophy to smaller length scales, one of the main features of 2-D turbulence theory. The semi-integral curves divide the plane into regions having limited ranges for the direction of the flow. This allows us to estimate the average time it would take for an intermittent solution to burst into a region of large palinstrophy. We also derive a sharp, universal upper bound on the average palinstrophy and show that it is achieved only for forces that admit statistical steady states where the nonlinear term is zero.