Nonlinear analysis of near-wall turbulence time series

Applied Scientific Research (The Hague)

Volumn 57, Issue 3-4, 1996, Pages 235-261

  Porporato, A ^a   Ridolfi, L ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Attractor reconstruction; Bursting; Near wall turbulence; Nonlinear analysis; Nonlinear prediction

Indexed keywords

ANEMOMETERS; LASER DOPPLER VELOCIMETERS; NUMERICAL ANALYSIS; VELOCITY MEASUREMENT; WALL FLOW;

COHERENT STRUCTURES; LASER DOPPLER ANEMOMETER; NEAR WALL FLOW; SCALAR TIME SERIES;

TURBULENCE;

EID: 65749321444     PISSN: 00036994     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02506062     Document Type: Article

References (70)

1. Abarbanel, H.D.J, Brown, R., Sidorovich, J.J. and Tsimring, L.S., The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65(4) (1993) 1331-1392.
2. Aranson, I.S., Gaponov-Grekhov, A.V. and Rabinovich, M.I., The onset and spatial development of turbulence in flow systems. Physica D 33 (1988) 1-20.
3. Atten, P., Caputo, J.G., Malraison, B. and Gagne, Y., Détermination de dimension d'attracteurs pour différents écoulements. J. Méc. théor. appl. Numéro spécial (1984) 133-156.
4. Aubry, N., Holmes, P., Lumley, J.L. and Stone, E., The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192 (1988) 115-173.
5. Badii, R., Broggi, B., Derighetti, B., Ravani, M., Ciliberto, S., Politi, A. and Rubio, M.A., Dimension increase in filtered chaotic signals. Phys Rev. Lett. 60(11) (1988) 979-982.
6. Bergé, P., Pomean, Y. and Vidal, Ch., Order within Chaos. Wiley, Chichester (1987).
7. Berkooz, G., Holmes, P., Lumley, J.L., Aubry, N. and Stone, E., Observations regarding "Coherence and chaos in a model of turbulent boundary layer" by X. Zhou and L. Sirovich. (Phys. Fluids A, 4 (1992) 2855). Phys. Fluids 6(4) (1994) 1574-1578.
8. Bonetti, M., Meynart, R., Boon, J.P. and Olivari, D., Chaotic dynamics in a periodically excited air jet. Phys. Rev. Lett. 55 (1985) 492-495.
9. Brandstater, A. and Swinney, H.L., Strange attractors in weakly turbulent Couette-Taylor flow. Phys. Rev. A. 35(5) (1987) 2207-2220.
10. Brandstater, A., Swinney, H.L. and Chapman, G.T., Characterizing turbulent channel flow. In: Mayer-Kress, G. (ed.), Dimension and Entropies in Chaotic Systems: Qualification of Complex Behavior. Springer-Verlag, Berlin (1986) pp. 150-157.
11. Butera, L., Porporato, A., Ridolfi, L. and Sordo, S., Autocorrelation and related quantities of the longitudinal turbulence velocity component. An experimental investigation in a water flow in a smooth pipe. In: Proceedings 2nd Int. Conference on Exp. Fluid Mech., Turin, Italy (1994), pp. 339-348.
12. Butera, L., Ridolfi, L. and Sordo, S., On the hypothesis of self-similarity for velocity distribution in turbulent flows. Excerpta 8 (1994) 63-94.
13. Buzug, Th. and Pfister, P., Optimal delay time and embedding dimension for delay time coordinates by analysis of the global static and local dynamical behavior of strange attractors. Phys. Rev. A 45(10) (1992) 7073-7084.
14. Buzug, Th. and Pfister, P., Comparison of algorithms calculating optimal embedding parameters for delay time co-ordinates. Physica D 58 (1992) 127-132.
15. Buzug, Th., Reimers, T. and Pfister, P., Optimal reconstruction of strange attractors from purely geometrical arguments. Europhys. Lett. 13 (1990) 605-610.
16. Casdagli, M., Nonlinear prediction of chaotic time series. Physica D 35 (1989) 335-356.
17. Casdagli, M., Eubank, S., Farmer, J.D. and Gibson, J., State space reconstruction in the presence of noise. Physica D 51 (1991) 52-98.
18. Constantin, P., Foias, C., Manley, O.P. and Temam, R., Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150 (1985) 427-440.
19. Cross, M.C. and Hohenberg, P.C., Pattern formation outside of equilibrium. Rev. Mod. Phys. 65(3) (1993) 851-1112.
20. Durst, F., Jovanovic, J. and Sender, J., LDA measurements in the near-wall region of a turbulent pipe flow. J. Fluid Mech. 295 (1995) 305-335.
21. Eckmann, J.-P. and Ruelle, D., Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D 56 (1992) 185-187.
22. Eden, A., Foias, C., Nikolaenko, B. and Temam, R., Exponential Attractors for Dissipative Evolution Equations. Wiley, Chichester (1994).
23. Farmer, J.D. and Sidorovich, J.J., Predicting chaotic time series. Phys. Rev. Lett. 59(8) (1987) 845-848.
24. Farmer, J.D. and Sidorovich, J.J., Exploiting chaos to predict the future and reduce noise. In: Lee, Y.C. (ed.), Evolution, Learning and Cognition. World Science, River Edge, NJ (1988) pp. 277-330.
25. Gad-el-Hak, M., Interactive control of turbulent boundary layers: A futuristic overview. AIAA Journal 32(9) (1994) 1753-1765.
26. Gaster, M., The nonlinear phase of wave growth leading to chaos and breakdown to turbulence in a boundary layer as an example of an open system. Proc. R. Soc. Lond. A 430 (1990) 3-24.
27. Grappin, R. and Léorat, J., Lyapunov exponents and the dimension of periodic incompressible Navier-Stokes flows: Numerical measurements. J. Fluid Mech. 222 (1991) 61-94.
28. Grassberger, P., An optimized box-assisted algorithm for fractal dimensions. Phys. Lett. A 148 (1991) 63-68.
29. Grassberger, P. and Procaccia, I., Characterization of strange attractors. Phys. Rev. Lett. 50 (1983) 346-349.
30. Grassberger, P., Schreiber, Th. and Schaffrath, C., Nonlinear time sequence analysis. Internat. J. Bifurcation and Chaos 1(3) (1991) 521-547.
31. Grassberger, P., Hegger, R., Kantz, H., Schaffrath, C. and Schreiber, T., On noise reduction methods for chaotic data. Chaos 3(2) (1993) 127-141.
32. Hamilton, J.M., Kim, J. and Waleffe, F., Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287 (1995) 317-348.
33. Healey, J.J., A dynamical systems approach to the early stages of boundary-layer transition. J. Fluid Mech. 255 (1993) 667-681.
34. Healey, J.J., Time series analysis of physical systems possessing homoclinicity. Physica D 80 (1995) 48-60.
35. Holmes, P., Can dynamical systems approach turbulence? In: Lumley, J.L. (ed.), Proc. Whither Turbulence? Turbulence at the Crossroads. Lecture Notes in Applied Physics, Vol. 357. Springer-Verlag, New York (1990) pp. 197-249 and 306-309.
36. Huang, Y. and Huang, H., On the transition to turbulence in pipe flow. Physica D 37 (1989) 153-159.
37. Jimènez, J and Moin, P., The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225 (1991) 213-240.
38. Keefe, L., Moin, P. and Kim, J., The dimension of attractors underlying periodic turbulent Poiseuille flow. J. Fluid Mech. 242 (1992) 1-29.
39. Lichaber, A. and Maurer, J., A Rayleigh-Bérnard experiment: Helium in a small box. In: Riste, T. (ed.), Nonlinear Phenomena at Phase Transitions and Instabilities. Plenum, New York (1981) pp. 259-267.
40. Luchik, T.S. and Tiederman, W.G., Timescale and structure of ejections and bursts in turbulent channel flows. J. Fluid Mech. 174 (1987) 529-552.
41. Manneville, P., From chaos to turbulence in fluid dynamics. In: Szemplinska-Stupnicka, W. and Troger, H. (eds), Engineering Applications of Dynamics of Chaos. Springer-Verlag, Vienna, New York (1991) pp. 67-135.
42. Mullin, T. and Price, T. J., An experimental observation of chaos arising from the interaction of steady and time-dependent flows. Nature 340 (1989) 294-296.
43. Neremberg, M.A.H. and Essex, C., Correlation dimension and systematic geometric effects. Phys. Rev. A 42(12) (1990) 7065-7075.
44. Newell, C., Rand, A. and Russell, D., Turbulent transport and the random occurrence of coherent events. Physica D 33 (1988) 281-303.
45. Packard, N.H., Crutchfield, J.P., Farmer, J.D. and Shaw, R.S., Geometry from a time series. Phys. Rev. Lett. 45 (1980) 712-716.
46. Pfister, G., Schmidt, H., Cliffe, K.A. and Mullin, T., Bifurcation phenomena in Taylor-Couette flow in a very short anulus. J. Fluid Mech. 191 (1988) 1-18.
47. Porporato, A., Searching for low-dimension elements in near-wall turbulence. Ph.D. Thesis, Department of Hydraulics, Transport and Civil Infrastructure, Polytechnic of Turin (1996) [in Italian].
48. Porporato, A. and Ridolfi, L., Analysis of randomly sampled data using fuzzy and nonlinear techniques. In: Proceedings 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon (1996) pp. 36.3.1-6.
49. Porporato, A. and Ridolfi, L., Nonlinear analysis of river flow time sequences. Water Resources Res. 33(6) (1996) 1353-1367.
50. Rapp, P.E., Albano, A.M., Schmah, T.I. and Farwell, L.A., Filtered noise can mimic low-dimensional chaotic attractor. Phys. Rev. E 47(4) (1993) 2289-2297.
51. Robinson, S.K., Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 23 (1991) 601-624.
52. Sanghi, S. and Aubry, N., Mode interaction models for near-wall turbulence. J. Fluid Mech. 247 (1993) 455-488.
53. Sauer, T., Time series prediction using delay co-ordinate embedding. In: Weigend, A.S. and Gershenfeld, N.A. (eds), Time Series Prediction, SFI Studies in the Sciences of Complexity, Proc., Vol. XV. Addison-Wesley, Reading, MA (1993) pp. 175-194.
54. Schreiber, Th. and Grassberger, P., A simple noise-reduction method for real data. Phys. Lett. A 160 (1991) 411-418.
55. Schuster, H.G., Deterministic Chaos, 3rd ed. Physik Verlag, Weinheim (1995).
56. Sieber, M., Experiments on the attractor-dimension for turbulent pipe flow. Phys. Lett. A 122(9) (1987) 467-470.
57. Sirovich, L. and Rodriguez, J.D., Coherent structures and chaos: A model problem. Phys. Lett. A 120 (1987) 211-214.
58. Sirovich, L. and Zhou, X., Dynamical model of wall-bounded turbulence. Phys. Rev. Letters 72(3) (1994) 340-343.
59. Sirovich, L. and Zhou, X., Reply to "Observations regarding "Coherence and chaos in a model of turbulent boundary layer" by X. Zhou and L. Sirovich (Phys. Fluids A, 4 (1992) 2855)". Phys. Fluids 6(4) (1994) 1579-1582.
60. Sreenivasan, K.R. and Ramshankar, R., Transition intermittency in open flows, and intermittency routes to chaos. Physica D 23 (1986) 246-258.
61. Sugihara, G. and May, R.M., Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344 (1990) 734-741.
62. Takens, F., Detecting Strange Attractors in Turbulence. Lectures Notes in Mathematics, Vol. 898. Springer-Verlag, Berlin (1981).
63. Temam, R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, Berlin (1988).
64. Tennekes, H. and Lumley, J.L., A First Course in Turbulence. The MIT Press, Cambridge, MA (1972).
65. Theiler, J., Spurious dimension from correlation algorithms applied to limited time-series data. Phys. Rev. A 34(3) (1986) 2427-2432.
66. Tsonis, A.A., Chaos. From Theory to Applications. Plenum Press, New York (1992).
67. Tsonis, A.A., Triantafyllou, G.N. and Elsner, J.B., Searching for determinism in observed data: A review of the issue involved. Nonlinear Processes in Geophysics 1 (1994) 12-25.
68. Williams-Stuber, K. and Gharib, M., Transition from order to chaos in the wake of an airfoil. J. Fluid Mech. 213 (1990) 29-57.
69. Zhou, X. and Sirovich, L., Coherence and chaos in a model of turbulent boundary layer. Phys. Fluids A 4(12) (1992) 2855-2874.
70. Zhou, J., Adrian, R.J. and Balachandar, S., Autogeneration of near-wall vortical structures in channel flow. Phys. Fluids 8(1) (1996) 288-300.