Controlling flow turbulence

Chaos

Volumn 13, Issue 1, 2003, Pages 64-70

  Guan, Shuguang ^a   Zhou, Y C ^a   Wei, G W ^a,b   Lai, C H ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037354951     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1539017     Document Type: Article

References (32)

1. A concise and authoritative review with a good number of cross references on fluid turbulence: K. R. Sreenivasan, Rev. Mod. Phys. 71, S383 (1999).
2. The engineering aspects of controlling turbulence are described by M. Gad-el-Hak, in Flow Control: Fundamentals and Practices, edited by M. Gad-el-Hak, A. Pollard, and J.-P. Bonnet (Springer-Verlag, New York, 1998).
3. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
4. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
5. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
6. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
7. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
8. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
9. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
10. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
11. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
12. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
13. B. A. Huberman and E. Lumer, IEEE Trans. Circuits Syst. 37, 547 (1990); E. A. Jackson and A. Hubler, Physica D 44, 407 (1990); R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990); Y. Braiman and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991); V. Petrov, V. Gaspar, J. Masere, and K. Show-alter, Nature (London) 361, 240 (1993); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); D. Auerbach, ibid. 72, 1184 (1994); I. Aranson, H. Levine, and L. Tsimring, ibid. 72, 2561 (1994); G. A. Johnson, M. Löcher, and E. R. Hunt, Phys. Rev. E 51, R1625 (1995); L. Kocarev, U. Parlitz, T. Stojanovski, and P. Janjic, ibid. 56, 1238 (1997); a review on theory and experiments of controlling chaos: S. Boccaletti, C. Grebogi, Y.-C. Lai. H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
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23. In 2D turbulence, the pseudoscalar vorticity ω = (0,0,ω) is perpendicular to the velocity gradients. Therefore the vorticity is Lagrangian invariant of the flow in the limit of small, viscosities and the mechanism of vortex stretching is forbidden.
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26. In 3D turbulence, the energy transfer from large scales to small scales through vortex stretching. Contrarily, in the 2D case, the nonlinear interaction leads to an inverse energy cascade and a direct enstrophy cascade due to the dual conservation of energy and enstrophy. Experiments on quasi-2D turbulence were reported by J. Sommeria, J. Fluid Mech. 170, 139 (1986); P. Tabeling, S. Burkhart, O. Cardoso, and H. Willaime, Phys. Rev. Lett. 67, 3772 (1991).
27. In 3D turbulence, the energy transfer from large scales to small scales through vortex stretching. Contrarily, in the 2D case, the nonlinear interaction leads to an inverse energy cascade and a direct enstrophy cascade due to the dual conservation of energy and enstrophy. Experiments on quasi-2D turbulence were reported by J. Sommeria, J. Fluid Mech. 170, 139 (1986); P. Tabeling, S. Burkhart, O. Cardoso, and H. Willaime, Phys. Rev. Lett. 67, 3772 (1991).
28. S. Y. Yang, Y C. Zhou, and G. W. Wei, Comput. Phys. Commun. 143, 113 (2002).
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