Elliptic Curves and Three-Dimensional Flow Patterns

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• 作者：Brian J. Cantwell
• 关键词：fluid mechanics ; turbulence ; transition ; elliptic curves ; critical points ; flow patterns ; velocity gradient ; round jet ; bifurcation
• 刊名：Nonlinear Dynamics
• 出版年：2000
• 出版时间：2000
• 年：2000
• 卷：22
• 期：1
• 页码：29-38
• 全文大小：63 KB
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

This paper is concerned with the geometry of flow patterns inthe classical problem of an impulsely-started, incompressible,axisymmetric, laminar jet generated by a point force. The second andthird invariants of the velocity gradient tensor, evaluated at criticalpoints in the jet, describe the fundamental dependence of the flow onthe jet Reynolds number. As the Reynolds number is increased from zeroto infinity, the critical points follow elliptic curves in the space ofinvariants and rational roots occur at bifurcation points in this space.The corresponding invariants of the acceleration gradient tensor traceout a trajectory with infinitely many, densely spaced rational roots.The results provide new insight into the viscous and pressure forceswhich act in the jet and the balance between strain and rotation whichleads to the onset of a starting vortex.