Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus
Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus
复制标题
环面上随机受力纳维-斯托克斯方程中准稳态的选择
DOI：
10.1007/s00332-020-09621-0
复制
发表时间：
2020
影响因子：
3
通讯作者：
Spiliopoulos, K.
中科院分区：
文献类型：
--
作者：
Beck, M;Cooper, E.;Spiliopoulos, K.
考虑了二维不可压缩Navier-Stokes方程的随机强迫涡量方程、周期边界条件和粘度。已知确定性涡度方程的一类显式准平稳状态在有噪声和无噪声情况下解的长期演化中起重要作用。最近的结果表明，参数在选择哪个准平稳状态是最重要的方面起着核心作用。在本文中，我们的目标是开发一个有限维模型来捕捉随机涡度方程的这种选择机制。这是通过将傅里叶空间中的涡度方程投影到与最低的八个傅里叶模相对应的中心流形上来完成的。通过蒙特卡罗模拟，表明涡度方程和模型在长时间动力学的关键方面是一致的。在此比较之后，通过平均和均匀化技术对模型进行扰动分析，以确定感兴趣的统计量的阶动力学。
The stochastically forced vorticity equation associated with the two-dimensional incompressible Navier–Stokes equation onis considered for, periodic boundary conditions, and viscosity. An explicit family of quasi-stationary states of the deterministic vorticity equation is known to play an important role in the long-time evolution of solutions both in the presence of and without noise. Recent results show the parameterplays a central role in selecting which of the quasi-stationary states is most important. In this paper, we aim to develop a finite-dimensional model that captures this selection mechanism for the stochastic vorticity equation. This is done by projecting the vorticity equation in Fourier space onto a center manifold corresponding to the lowest eight Fourier modes. Through Monte Carlo simulation, the vorticity equation and the model are shown to be in agreement regarding key aspects of the long-time dynamics. Following this comparison, perturbation analysis is performed on the model via averaging and homogenization techniques to determine the leading order dynamics for statistics of interest for.