Hopf-Bifurcation in a Navier-Stokes flow around a rotating body with respect to the angular velocity as bifurcation parameter

围绕旋转体的纳维-斯托克斯流中以角速度作为分岔参数的 Hopf 分岔

• 批准号: 427538878
• 负责人: Professor Dr. Mads Kyed
• 金额: --
• 依托单位: Department of Mechanical Engineering and Materials Science
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/427538878?language=en
• 关键词: Hopf; Bifurcation; Navier; Stokes; flow

We consider the Navier-Stokes equations governing the motion of a viscous fluid around a rotating body. If the angular velocity is small, it is easy the show that the solution is a steady-state. In experiments one can observe that the flow becomes time-periodic when the angular velocity exceeds a certain point. This observation indicates the occurence of a Hopf bifurcation. We want to give a mathematical proof that a Hopf bifurcation occurs with respect to the angular velocity as bifurcation parameter.

本文考虑粘性流体绕旋转物体运动的Navier-Stokes方程。如果角速度很小，很容易证明解是稳态的。在实验中可以观察到，当角速度超过某个点时，流动变得具有时间周期性。这一观测结果表明，一个霍普夫分岔的发生。给出了以角速度为分岔参数的Hopf分岔的数学证明。

项目成果

Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

执行时间周期运动的刚体周围的粘性流

• DOI: 10.1007/s00021-021-00556-4
• 期刊: Journal of Mathematical Fluid Mechanics
• 影响因子: 1.3
• 作者: T. Eiter;M. Kyed
• 通讯作者: M. Kyed