Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 746752, 18 pages
http://dx.doi.org/10.1155/2012/746752
Research Article

Application of the Poor Man's Navier-Stokes Equations to Real-Time Control of Fluid Flow

1Department of Civil Engineering, City College of the City University of New York, New York, NY 10031, USA
2Departments of Mechanical Engineering and Mathematics, University of Kentucky, Lexington, KY 40506, USA

Received 3 May 2012; Revised 17 July 2012; Accepted 17 July 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 James B. Polly and J. M. McDonough. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Gad-El-Hak and H. Tsai, Transition and Turbulence Control, World Scientific Books, Hackensack, NJ, USA, 2005.
  2. N. Kasagi, Y. Suzuki, and K. Fukagata, “Microelectromechanical systems-based feedback control of turbulence for skin friction reduction,” Annual Review of Fluid Mechanics, vol. 41, pp. 231–251, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. K. Fukagata and N. Kasagi, “Drag reduction in turbulent pipe flow with feedback control applied partially to wall,” International Journal of Heat and Fluid Flow, vol. 24, no. 4, pp. 480–490, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. S. F. Tardu, “Active control of near-wall turbulence by local oscillating blowing,” Journal of Fluid Mechanics, vol. 439, pp. 217–253, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. K. Angele, N. Kurimoto, Y. Suzuki, and N. Kasagi, “Evolution of the streamwise vortices in a coaxial jet controlled with micro flap actuators,” Journal of Turbulence, vol. 7, no. 73, pp. 1–19, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. P. Moin and T. Bewley, “Application of control theory to turbulence,” in 20th Australian Fluid Mechanics Conference, pp. 109–117, Springer, New York, NY, USA, 1995. View at Google Scholar
  7. A. H. Techet, F. S. Hover, and M. S. Triantafyllou, “Separation and turbulence control in biomimetic flows,” Flow, Turbulence and Combustion, vol. 71, no. 1–4, pp. 105–118, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. P. Moin and T. Bewley, “Feedback control of turbulence,” Applied Mechanics Reviews, vol. 47, no. 6, pp. S3–S12, 1994. View at Google Scholar
  9. F. Abergel and R. Temam, “On some control problems in fluid mechanics,” Theoretical and Computational Fluid Dynamics, vol. 1, no. 6, pp. 303–325, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. R. M. May, “Simple mathematical models with very complicated dynamics,” Nature, vol. 261, no. 5560, pp. 459–467, 1976. View at Publisher · View at Google Scholar · View at Scopus
  11. J. M. McDonough and M. T. Huang, “A “poor man's Navier-Stokes equation”: derivation and numerical experiments—the 2-D case,” International Journal for Numerical Methods in Fluids, vol. 44, no. 5, pp. 545–578, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. B. Polly, Numerical experiments of the 3-D poor man's Navier-Stokes equations [M.S. thesis], University of Kentucky, Lexington, Ky, USA, 2012.
  13. T. Yang, J. M. McDonough, and J. D. Jacob, “Two-dimensional “poor man's Navier-Stokes equation” model of turbulent flows,” AIAA Journal, vol. 41, no. 9, pp. 1690–1696, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. E. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, 1963. View at Publisher · View at Google Scholar
  15. D. Ruelle and F. Takens, “On the nature of turbulence,” Communications in Mathematical Physics, vol. 20, pp. 167–192, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge, UK, 2001. View at Zentralblatt MATH
  17. P. Constantin and C. Foias, Navier-Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill, USA, 1988. View at Zentralblatt MATH
  18. C. Foias, O. Manley, R. Rosa, and R. Temam, Navier-Stokes Equations and Turbulence, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. M. Hénon, “A two-dimensional mapping with a strange attractor,” Communications in Mathematical Physics, vol. 50, no. 1, pp. 69–77, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems, Textbooks in Mathematical Sciences, Springer, New York, NY, USA, 1996. View at Publisher · View at Google Scholar
  21. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. D. Y. Chen, L. Shi, H. T. Chen, and X. Y. Ma, “Analysis and control of a hyperchaotic system with only one nonlinear term,” Nonlinear Dynamics, vol. 67, no. 3, pp. 1745–1752, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. M. P. Aghababa and H. P. Aghababa, “A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs,” Nonlinear Dynamics, vol. 69, no. 4, pp. 1903–1914, 2012. View at Publisher · View at Google Scholar