Boundary layer models of the Hou-Luo scenario
Boundary layer models of the Hou-Luo scenario
复制标题
后洛情景边界层模型
DOI：
10.1016/j.jde.2021.07.007
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发表时间：
2021
影响因子：
2.4
通讯作者：
Kiselev, Alexander
中科院分区：
文献类型：
--
作者：
He, Siming;Kiselev, Alexander
流体力学三维欧拉方程的有限时间爆破与全局正则性问题是一个重大的开放性问题。几年前，Luo和Hou b[16]在大量数值模拟的基础上提出了一个新的有限时间爆炸情景。该场景是轴对称的，其特征是在位于包含流体的圆柱体边界的流动双曲点环附近涡度快速增长。在观察到强烈生长的地方，小边界层起着重要的作用。已经考虑了几种简化的情景模型，所有这些模型都导致有限时间内爆炸[3]，[2],[9],[13],[11],[15]。在本文中，我们提出了两个专门设计的模型，以深入了解位于边界的流动的双曲驻点附近的流体演化。其中一个模型着重分析了问题中存在的非线性效应的损耗。该模型的解被证明是全局规则的。与[3]、[2]等一维模型相比，第二个模型可以看作是在边界附近捕获精度上一个数量级的速度场的尝试。这个模型的解在有限时间内失效。
Finite time blow up vs global regularity question for 3D Euler equation of fluid mechanics is a major open problem. Several years ago, Luo and Hou [16] proposed a new finite time blow up scenario based on extensive numerical simulations. The scenario is axi-symmetric and features fast growth of vorticity near a ring of hyperbolic points of the flow located at the boundary of a cylinder containing the fluid. An important role is played by a small boundary layer where intense growth is observed. Several simplified models of the scenario have been considered, all leading to finite time blow up [3], [2], [9], [13], [11], [15]. In this paper, we propose two models that are designed specifically to gain insight in the evolution of fluid near the hyperbolic stagnation point of the flow located at the boundary. One model focuses on analysis of the depletion of nonlinearity effect present in the problem. Solutions to this model are shown to be globally regular. The second model can be seen as an attempt to capture the velocity field near the boundary to the next order of accuracy compared with the one-dimensional models such as [3], [2]. Solutions to this model blow up in finite time.
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影响因子：
1.2
作者：
T. Hou;Pengfei Liu
通讯作者：
T. Hou;Pengfei Liu
轴对称 3D 欧拉方程一维模型的爆破稳定性
影响因子：
3
作者：
Do, Tam;Kiselev, Alexander;Xu, Xiaoqian
通讯作者：
Xu, Xiaoqian
影响因子：
16.6
作者：
Saw, E. -W.;Kuzzay, D.;Faranda, D.;Guittonneau, A.;Daviaud, F.;Wiertel-Gasquet, C.;Padilla, V.;Dubrulle, B.
通讯作者：
Dubrulle, B.
影响因子：
2.8
作者：
Elgindi, Tarek M.;Jeong, In-Jee
通讯作者：
Jeong, In-Jee