Structure and dynamics of low Reynolds number turbulent pipe flow

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1888, 2009, Pages 473-488

  Duggleby, Andrew ^a   Ball, Kenneth S ^b   Schwaenen, Markus ^a  

^a Department of Electrical and Computer Engineering   (United States)

^b Virginia Polytechnic Institute and State University   (United States)

Author keywords

Channel flow; Dynamics; Pipe flow; Proper orthogonal decomposition; Structures; Turbulence

Indexed keywords

CHANNEL FLOW; DYNAMICAL SYSTEMS; DYNAMICS; FLOW FIELDS; JOINTS (STRUCTURAL COMPONENTS); NUMERICAL ANALYSIS; PIPE; PIPE FLOW; REYNOLDS NUMBER; WALL FLOW;

BASIS SETS; BURSTING EVENTS; CHAOTIC ATTRACTORS; CONSTANT PHASE; FOURIER; FOURIER METHODS; NUMERICAL CALCULATIONS; PROPER ORTHOGONAL DECOMPOSITION; REYNOLDS STRESSES; SIMULATED FLOWS; SIMULATION TIMES; STRUCTURE AND DYNAMICS; STRUCTURES; TRANSFER ENERGIES; TURBULENT CHANNEL FLOWS; TURBULENT PIPE FLOWS; WAVE NUMBERS;

TURBULENCE;

EID: 58149107813     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2008.0241     Document Type: Article

References (26)

1. Ball, K. S., Sirovich, L. & Keefe, L. R. 1991 Dynamical eigenfunction decomposition of turbulent channel flow. Int. J. Numer. Methods Fluids 12, 587. (doi:10.1002/fld.1650120606)
2. Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577-594. (doi:10.1017/S0022112079001191)
3. Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765-777. (doi: 10.1063/1.857730)
4. Duggleby, A. & Paul. M. R. 2008 Exploring extensive chaos in Rayleigh-Bénard convection using fractal and Karhunen-Loève dimensions. In XXII Int. Conf. Theoretical and Applied Mechanics.
5. Duggleby. A., Ball, K. S. & Paul. M. R. 2007a The effect of spanwise wall oscillation on turbulent pipe flow structures resulting in drag reduction. Phys. Fluids 19, 125-127. (doi:10.1063/1.2825428)
6. Duggleby, A., Ball, K. S., Paul, M. R. & Fischer, P. F. 2007b Dynamical eigenfunction decomposition of turbulent pipe flow. J. Turbulence 8, 1-28. (doi: 10.1080/14685240701376316)
7. Fischer, P. F., Ho, L. W., Karniadakis, G. E., Ronouist, E. M. & Patera, A. T. 1988 Recent advances in parallel spectral element simulation of unsteady incompressible flows. Com/put. Struct. 30, 217-231. (doi:10.1016/0045-7949(88)90228-3)
8. Green, M. A., Rowley, C. W. & Hallcr, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111-120. (doi:10.1017/S0022112006003648)
9. Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, coherent structures, dynamical systems, and symmetry. Cambridge, UK: Cambridge University Press.
10. Keller, L. V. & Friedmann, A. A. 1925 Differentialgleichung für die turbulente bewegung einer kompressiblen flüssigkeit. In Proc. 1st Int. Congress Applied Mechanics, Delft, pp. 395-405.
11. Kim, J., Moin, P. & Moser, R. 1987 Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133. (doi:10.1017/S0022112087000892)
12. Kline, S. J., Reynolds, W. C, Schraub, F. A. & Rundstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741-773. (doi:10.1017/S0022112067001740)
13. Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 29-303.
14. Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. Moscow, Russia: Nauka.
15. Prandtl, L. 1925 Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech. 5, 136-139.
16. Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels. Phil. Trans. R. Soc. 174, 935-982. (doi:10.1098/rstl.1883.0029)
17. Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601-639. (doi:10.1146/annurev.fl.23. 010191.003125)
18. Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I: coherent structures. Q. Appl. Math. XLV, 561-571.
19. Sirovich, L., Ball, K. S. & Keefe, L. R. 1990 Plane waves and structures in turbulent channel flow. Phys. Fluids A 12, 2217-2226. (doi:10.1063/1.857808)
20. Sirovich; L., Ball, K. S. & Handler, R. A. 1991 Propagating structures in wall-bounded turbulent flows. Theor. Comput. Fluid Dyn. 2, 307. (doi:10.1007/BF00271470)
21. Taylor. G. I. 1921 Diffusion by continuous movements. Proc. Land. Math. Soc. 20. 196-211. (doi:10.1112/plms/s2-20.1.196)
22. Taylor, G. I. 1935 Statistical theory of turbulence, I III. Proc. R. Soc. A 151, 465-478. (doi:10. 1098/rspa. 1935.0161)
23. Townsend. A. A. 1956 The structure of turbulent shear flows. Cambridge, UK: Cambridge University Press.
24. Tufo, H. M. & Fischer, P. F. 1999 Terascale spectral element algorithms and implementations. In Proc. of the ACM/IEEE SC99 Conf. on High Performance Networking and Computing. Gordon Bell Prize paper, IEEE Computer Society,
25. von Kármán, T. 1930 Mechanische Ähnlichkeit und Turbulenz. In Nachr. Ges. Wiss. Göttingen, Math.-Phys. KL., pp. 58-76.
26. Webber, G. A., Handler, R. A. & Sirovich, L. 2002 Energy dynamics in a turbulent channel flow using the Karhunen-Loève approach. Int. J. Numer. Methods Fluids 40, 1381-1400. (doi:10. 1002/fld.414)