Gomé Sébastien, Tuckerman Laurette S, Barkley Dwight
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris, PSL Research University, Sorbonne Université, Université de Paris, Paris 75005, France.
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
Philos Trans A Math Phys Eng Sci. 2022 Jun 27;380(2226):20210036. doi: 10.1098/rsta.2021.0036. Epub 2022 May 9.
Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier-Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
已知剪切流中的过渡局部湍流要么衰减到吸收层流状态，要么通过分裂扩散。从一种状态到另一种状态的平均通过时间超指数地依赖于雷诺数，并导致一个交叉雷诺数，高于该雷诺数时扩散比衰减更有可能发生。在本文中，我们将一种罕见事件算法——自适应多级分裂算法应用于确定性纳维-斯托克斯方程，以研究过渡路径，并比直接模拟更有效地估计通道流中的大通过时间。我们建立了与极值分布的联系，并表明状态之间的过渡由一个与雷诺数自相似的区域介导。通过时间的超指数变化与极值分布参数对雷诺数的依赖性相关联。最后，受大偏差理论中的瞬子启发，我们表明衰减或分裂事件接近最可能的路径。本文是主题为“物理流体动力学中的数学问题（第二部分）”的一部分。
