Toward a Structural Understanding of Turbulent Drag Reduction: Nonlinear Coherent States in Viscoelastic Shear Flows

Physical Review Letters

Volumn 89, Issue 20, 2002, Pages

  Stone, Philip A ^a   Waleffe, Fabian ^b   Graham, Michael D ^a  

^a University of Wisconsin–Madison ^*  (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; SHEAR FLOW; STEADY FLOW; TURBULENCE; VISCOELASTICITY;

VISCOELASTIC SHEAR FLOWS;

DRAG;

EID: 4243426377     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.89.208301     Document Type: Article

References (35)

1. P. Virk, AIChE J. 21, 625 (1975).
2. J. Lumley, Annu. Rev. Fluid Mech.ARVFA3 1, 367 (1969).
3. W. McComb, The Physics of Fluid Turbulence (Oxford University Press, New York, 1990).
4. D. Walker and W. Tiederman, J. Fluid Mech.JFLSA7 218, 377 (1990).
5. G. Donohue, W. Tiederman, and M. Reischman, J. Fluid Mech.JFLSA7 56, 559 (1972).
6. J. den Toonder, M. Hulsen, G. Kuiken, and F. Nieuwstadt, J. Fluid Mech.JFLSA710.1017/S0022112097004850 337, 193 (1997).
7. A. Draad, G. Kuiken, and F. Nieuwstadt, J. Fluid Mech.JFLSA710.1017/S0022112098003139 377, 267 (1998).
8. M. Escudier, F. Presti, and S. Smith, J. Non-Newton. Fluid Mech.10.1016/S0377-0257(98)00098-6 81, 197 (1999).
9. R. Sureshkumar, A. Beris, and R. Handler, Phys. FluidsPHFLE610.1063/1.869229 9, 743 (1997).
10. C. Dimitropoulos, R. Sureshkumar, A. Beris, and R. Handler, Phys. FluidsPHFLE610.1063/1.1345882 13, 1016 (2001).
11. S. Robinson, Annu. Rev. Fluid Mech.ARVFA310.1146/annurev.fluid.23.1.601 23, 601 (1991).
12. M. Nagata, J. Fluid Mech.JFLSA7 217, 519 (1990).
13. R. Clever and F. Busse, J. Fluid Mech.JFLSA710.1017/S0022112097005818 344, 137 (1997).
14. F. Waleffe, Phys. Rev. Lett.10.1103/PhysRevLett.81.4140 81, 4140 (1998).
15. B. Eckhardt, K. Marzinzik, and A. Schmiegel, in A Perspective Look at Nonlinear Media, Lecture Notes in Physics (Springer, New York, 1998).
16. F. Waleffe, J. Fluid Mech.JFLSA710.1017/S0022112001004189 435, 93 (2001).
17. A saddle-node bifurcation, also known as a turning point, limit point, or fold, arises when two steady states appear spontaneously as a parameter increases
18. S.H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Addison-Wesley, Reading, MA, 1994).
19. F. Daviaud, J. Hegseth, and P. Bergé, Phys. Rev. Lett.10.1103/PhysRevLett.69.2511 69, 2511 (1992).
20. S. Bottin, O. Dauchot, F. Daviaud, and P. Mannveille, Phys. FluidsPHFLE610.1063/1.869773 10, 2597 (1998).
21. J. Jimenez and M. Simens, J. Fluid Mech.JFLSA710.1017/S0022112001004050 435, 81 (2001).
22. G. Kawahara and S. Kida, J. Fluid Mech.JFLSA7 449, 291 (2001).
23. F. Waleffe, Phys. FluidsPHFLE610.1063/1.869185 9, 883 (1997).
24. S. Girimaji and S. Pope, J. Fluid Mech.JFLSA7 220, 427 (1990).
25. J. Lumley, Symp. Math.SYPMA3 9, 315 (1972).
26. G. Ryskin, Phys. Rev. Lett.10.1103/PhysRevLett.59.2059 59, 2059 (1987).
27. L. Leal, in Structure of Turbulence and Drag Reduction (Springer-Verlag, Berlin, 1990).
28. M. Chertkov, Phys. Rev. Lett.10.1103/PhysRevLett.84.4761 84, 4761 (2000).
29. E. Balkovsky, A. Fouxon, and V. Lebedev, Phys. Rev. Lett.10.1103/PhysRevLett.84.4765 84, 4765 (2000).
30. R. Bird, C. Curtiss, R. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1987), Vol.�2, 2nd ed.
31. M. Tabor and P. de Gennes, Europhys. Lett. 2, 519 (1986).
32. P. de Gennes, Introduction to Polymer Dynamics (Cambridge University Press, New York, 1990).
33. K. Sreenivasan and C. White, J. Fluid Mech.JFLSA710.1017/S0022112099007818 409, 149 (2000).
34. S. Sibilla and A. Baron, Phys. FluidsPHFLE610.1063/1.1448497 14, 1123 (2002).
35. E. de Angelis, C.M. Casciola, and R. Piva, Comput. Fluids10.1016/S0045-7930(01)00069-X 31, 495 (2002).