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On the origins of vortex shedding in two-dimensional incompressible flows

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Abstract

An exegesis of a novel mechanism leading to vortex splitting and subsequent shedding that is valid for two-dimensional incompressible, inviscid or viscous, and external or internal or wall-bounded flows, is detailed in this research. The mechanism, termed the vortex shedding mechanism (VSM) is simple and intuitive, requiring only two coincident conditions in the flow: (1) the existence of a location with zero momentum and (2) the presence of a net force having a positive divergence. Numerical solutions of several model problems illustrate causality of the VSM. Moreover, the VSM criteria is proved to be a necessary and sufficient condition for a vortex splitting event in any two-dimensional, incompressible flow. The VSM is shown to exist in several canonical problems including the external flow past a circular cylinder. Suppression of the von Kármán vortex street is demonstrated for Reynolds numbers of 100 and 400 by mitigating the VSM.

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References

  1. Theofilis, V., Hein, S., Dallmann, U.: On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Philos. Trans. R. Soc. A 358, 3229–3246 (2000)

    Article  MATH  Google Scholar 

  2. Obabko, A., Cassel, K.: Navier–Stokes solutions of unsteady separation induced by a vortex. J. Fluid Mech. 465, 99–130 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Marquillie, M., Ehrenstein, U.: On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 490, 169–188 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ehrenstein, U., Gallaire, F.: Two-dimensional global low-frequency oscillations in a separating boundary-layer flow. J. Fluid Mech. 614, 315–327 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Griffith, M., Leweke, T., Thompson, M., Hourigan, K.: Steady inlet flow in stenotic geometries: convective and absolute instabilities. J. Fluid Mech. 616, 111–133 (2008)

    Article  MATH  Google Scholar 

  6. Gharib, M., Rambod, E., Shariff, K.: A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Boghosian, M.E.: Flow in partially constricted planar channels-origins of vortex shedding and global stability of Navier–Stokes solutions. Ph.D. thesis, Illinois Institute of Technology, Chicago, Illinois (2011)

  8. Boghosian, M., Cassel, K.: A pressure-gradient mechanism for vortex shedding in constricted channels. Phys. Fluids 25, 477–492 (2013). doi:10.1063/1.4841576

    Article  Google Scholar 

  9. Hunt, J., Wray, A., Moin, P.: Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88, pp. 193–208 (1988)

  10. Kolar, V.: Vortex identification: new requirements and limitations. Int. J. Heat Fluid Flow 28, 638–652 (2007)

    Article  Google Scholar 

  11. Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Batchelor, G.: Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1967)

    MATH  Google Scholar 

  13. Fischer, P.: An overlapping Schwarz method for spectral element solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 133, 84–101 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kaiktsis, L., Karniadakis, G., Orszag, S.: Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step. J. Fluid Mech. 321, 157–187 (1996)

    Article  MATH  Google Scholar 

  15. Alam, M., Sandham, N.: Direct numerical simulation of short laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28 (2000)

    Article  MATH  Google Scholar 

  16. Obabko, A., Cassel, K.: On the ejection-induced instability in Navier–Stokes solutions of unsteady separation. Philos. Trans. R. Soc. A 363, 1189–1198 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Koumoutsakos, P., Leonard, A.: High-resolution simulations of the flow around an impulsively started cylinder using vortex methods. J. Fluid Mech. 296, 1–38 (1995)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

Research reported in this publication was supported by the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) of the National Institutes of Health under Award Number R01DK090769. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. In addition, the authors want to thank Dr. Aleksandr V. Obabko and Professor Sudhakar E. Nair for insightful discussions that improved this work.

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Authors and Affiliations

  1. Mechanical, Materials and Aerospace Engineering Department, Illinois Institute of Technology, Chicago, IL, USA

    M. E. Boghosian & K. W. Cassel

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  1. M. E. Boghosian
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  2. K. W. Cassel
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Correspondence to M. E. Boghosian.

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Communicated by Dr. Jeff D. Eldredge.

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Boghosian, M.E., Cassel, K.W. On the origins of vortex shedding in two-dimensional incompressible flows. Theor. Comput. Fluid Dyn. 30, 511–527 (2016). https://doi.org/10.1007/s00162-016-0395-8

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  • DOI: https://doi.org/10.1007/s00162-016-0395-8

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