Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (9): 1191-1212.doi: https://doi.org/10.1007/s10483-017-2238-8

• 论文 •    下一篇

Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces

Qian SHI, Yu CHEN, Xilin XIE   

  1. Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
  • 收稿日期:2017-01-16 修回日期:2017-03-24 出版日期:2017-09-01 发布日期:2017-09-01
  • 通讯作者: Xilin XIE,E-mail:xiexilin@fudan.edu.cn E-mail:xiexilin@fudan.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Nos.11472082 and 11172069)

Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces

Qian SHI, Yu CHEN, Xilin XIE   

  1. Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, China
  • Received:2017-01-16 Revised:2017-03-24 Online:2017-09-01 Published:2017-09-01
  • Contact: Xilin XIE E-mail:xiexilin@fudan.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos.11472082 and 11172069)

摘要:

Incompressible viscous flows on curved surfaces are considered with respect to the interplay of surface geometry, curvature, and vorticity dynamics. Free flows and cylindrical wakes over a Gaussian bump are numerically solved using a surface vorticitystream function formulation. Numerical simulations show that the Gaussian curvature can generate vorticity, and non-uniformity of the Gaussian curvature is the main cause. In the cylindrical wake, the bump dominated by the positive Gaussian curvature can significantly affect the vortex street by forming velocity depression and changing vorticity transport. The results may provide possibilities for manipulating surface flows through local change in the surface geometry.

关键词: incompressible viscous, fillet welds, exact solution, theory of elasticity, curvature, vorticity dynamics, two-dimensional flow

Abstract:

Incompressible viscous flows on curved surfaces are considered with respect to the interplay of surface geometry, curvature, and vorticity dynamics. Free flows and cylindrical wakes over a Gaussian bump are numerically solved using a surface vorticitystream function formulation. Numerical simulations show that the Gaussian curvature can generate vorticity, and non-uniformity of the Gaussian curvature is the main cause. In the cylindrical wake, the bump dominated by the positive Gaussian curvature can significantly affect the vortex street by forming velocity depression and changing vorticity transport. The results may provide possibilities for manipulating surface flows through local change in the surface geometry.

Key words: fillet welds, exact solution, theory of elasticity, two-dimensional flow, incompressible viscous, vorticity dynamics, curvature

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