Dissipation Length Scale Estimates for Turbulent Flows: A Wiener Algebra Approach
Dissipation Length Scale Estimates for Turbulent Flows: A Wiener Algebra Approach
复制标题
湍流的耗散长度尺度估计：维纳代数方法
作者：
A. Biswas;M. Jolly;V. Martinez;E. Titi
在本文中，建立了空间分析均匀半径的下界估计，用于 $$n$$n 环面上不可压缩的受迫纳维-斯托克斯系统的解。如果满足初始数据的某个界限，则该估计与先前已知的估计相匹配。特别是，有人认为，对于二维 (2D) 湍流，初始数据保证满足 2D 全局吸引子的很大一部分的假设界限，在这种情况下，半径的估计与 Kukavica (1998) 中发现的最著名的估计相匹配。这里采用的方法的一个关键特征是选择维纳代数作为相空间，即具有绝对收敛傅立叶级数的函数的巴纳赫代数，其结构适合使用所谓的格夫雷范数。我们注意到，该方法也可以应用于其他相空间，例如具有平方可和傅里叶级数的函数的相空间，在这种情况下，半径的估计与 Doering 和 Titi (1995) 的估计相匹配。然后可以类似地证明，对于三维 (3D) 湍流，该估计在 3D 弱吸引子的很大一部分上成立。
In this paper, a lower bound estimate on the uniform radius of spatial analyticity is established for solutions to the incompressible, forced Navier–Stokes system on an $$n$$n-torus. This estimate matches previously known estimates provided that a certain bound on the initial data is satisfied. In particular, it is argued that for two-dimensional (2D) turbulent flows, the initial data is guaranteed to satisfy this hypothesized bound on a significant portion of the 2D global attractor, in which case, the estimate on the radius matches the best known one found in Kukavica (1998). A key feature in the approach taken here is the choice of the Wiener algebra as the phase space, i.e., the Banach algebra of functions with absolutely convergent Fourier series, whose structure is suitable for the use of the so-called Gevrey norms. We note that the method can also be applied with other phase spaces such as that of the functions with square-summable Fourier series, in which case the estimate on the radius matches that of Doering and Titi (1995). It can then similarly be shown that for three-dimensional (3D) turbulent flows, this estimate holds on a significant portion of the 3D weak attractor.