Variational bound on energy dissipation in turbulent shear flow

Physical Review Letters

Volumn 79, Issue 21, 1997, Pages 4170-4173

  Nicodemus, Rolf ^a   Grossmann, Siegfried ^a   Holthaus, Martin ^a  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); EQUATIONS OF MOTION; OPTIMIZATION; REYNOLDS NUMBER; SHEAR FLOW; TURBULENT FLOW; VARIATIONAL TECHNIQUES;

BUSSE BOUND; COUETTE FLOW; DOERING-CONSTANTIN VARIATIONAL PRINCIPLE; WAVE NUMBERS;

ENERGY DISSIPATION;

EID: 0031272173     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.79.4170     Document Type: Article

References (17)

1. C. R. Doering and P. Constantin, Phys. Rev. E 49, 4087 (1994).
2. P. Constantin and C. R. Doering, Phys. Rev. E 51, 3192 (1995).
3. C. R. Doering and P. Constantin, Phys. Rev. E 53, 5957 (1996).
4. L. N. Howard, Annu. Rev. Fluid Mech. 4, 473 (1972).
5. F. H. Busse, J. Fluid Mech. 41, 219 (1970).
6. F. H. Busse, Adv. Appl. Mech. 18, 77 (1978).
7. R. Nicodemus, S. Grossmann, and M. Holthaus, Physica (Amsterdam) 101D, 178 (1997).
8. D. D. Joseph, Stability of Fluid Motions I and II (Springer-Verlag, Berlin, 1976).
9. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
10. R. Nicodemus, S. Grossmann, and M. Holthaus, “Variational Bound on Energy Dissipation in Plane Couette Flow,” Phys. Rev. E(to be published).
11. R. Nicodemus, S. Grossmann, and M. Holthaus, “The Background Flow Method. Part 1: Constructive Approach to Bounds on Energy Dissipation” (to be published);
12. R. Nicodemus, S. Grossmann, and M. Holthaus “The Background Flow Method. Part 2: Asymptotic Theory of Dissipation Bounds” (to be published).
13. R. R. Kerswell, Physica (Amsterdam) 100D, 355 (1997).
14. C. R. Doering and P. Constantin, Phys. Rev. Lett. 69, 1648 (1992).
15. H. Reichardt, Gesetzmäßigkeiten der geradlinigen turbulenten Couetteströmung (Mitteilungen aus dem Max-Planck-Institut für Strömungsforschung, No. 22, Göttingen, 1959).
16. D. P. Lathrop, J. Fineberg, and H. L. Swinney, Phys. Rev. Lett. 68, 1515 (1992).
17. S. Grossmann, Phys. Rev. E 51, 6275 (1995).