Transition Threshold for the 3D Couette Flow in Sobolev Space
Transition Threshold for the 3D Couette Flow in Sobolev Space
复制标题
索伯列夫空间中三维库埃特流的转捩阈值
DOI：
10.1002/cpa.21948
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发表时间：
2018-03
影响因子：
3
通讯作者：
Dongyi Wei;Zhifei Zhang
中科院分区：
文献类型：
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作者：
Dongyi Wei;Zhifei Zhang
本文研究了高雷诺数Re下Sobolev空间三维Couette流的转捩阈值。证明了如果初始速度v0满足<$v0 −y，0，0 <$H2 ≤ c 0 Re −1，其中c 0> 0与Re无关，则三维Navier-Stokes方程的解在时间上是全局的，并且不会从Couette流过渡。这一结果证实了Trefethen等人在1993年提出的跃迁阈值猜想。此外，我们还证明了该解的长时间动力学表现为：对于t <$Re，由于三维提升效应，该解将经历从O（Re−1）到O（c 0）的瞬态增长;对于t <$Re 1/3，由于混合增强耗散效应，该解将迅速收敛到条纹解。© 2020威利期刊有限责任公司
In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number Re. It was proved that if the initial velocity v0 satisfies ∥v0−y,0,0∥H2≤c0Re−1 for some c0 > 0 independent of Re, then the solution of the 3D Navier‐Stokes equations is global in time and does not transition away from the Couette flow. This result confirms the transition threshold conjecture proposed by Trefethen et al. in 1993. Moreover, we prove that the long‐time dynamics of the solution behaves as: for t ≲ Re, the solution will experience a transient growth from O(Re−1) to O(c0) due to the 3D lift‐up effect; for t ≳ Re1/3, the solution will rapidly converge to a streak solution due to the mixing‐enhanced dissipation effect. © 2020 Wiley Periodicals LLC