Investigation of the Dynamics of Near-Wall Turbulence Using Nonlinear Time Sequence Analysis

  • Amilcare Porporato
  • Luca Ridolfi
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 36)

Abstract

It is widely accepted that the wall turbulent flows are globally high dimensional (e.g. Keefe, Kim & Moin 1992). Therefore the system is not globally treatable either theoretically or in experiments and, at best, we can only focus our study on the main features of the dynamics. Fortunately this approach is not in actual fact restrictive, since it is also naturally suggested by the presence of coherent structures which, in a certain sense, constitute the skeleton of the near-wall turbulence. Because of their coherency and simplicity in relation to the rest of the dynamics, it is likely that in phase space such organized flow structures correspond to distinct and fairly simple orbits that, at random intervals, leave and suddenly reconnect to the large dimensional part of the attractor (Newell et al., 1988). In particular, in the low dimensional model of Aubry et al. (1988), the bursting phenomenon is shown to correspond in phase space to heteroclinic excursions (see also Sanghi & Aubry, 1993, and references therein). These theoretical studies, as well as certain ad hoc simplified numerical simulations (Hamilton et al. 1995), can capture the main features of the near-wall dynamics and are very important for highlighting the physical origin of the bursting process. However, they still have too little contact with the real turbulence. From the experimental and numerical point of view, the bursting process is quantitatively studied by means of conditional sampling techniques (e.g. Luchik & Tiederman, 1987), that unfortunately suffer from a certain subjectivity in the choice of the threshold values.

Keywords

Coherent Structure Chaotic Time Series Nonlinear Prediction Local Linear Approximation Turbulent Signal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aubry, N., Holmes, P., Lumley, J. L. & Stone, E. (1988)The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115.MathSciNetADSMATHCrossRefGoogle Scholar
  2. Buzug, Th. & Pfister, P. (1992) Comparison of algorithms calculating optimal embedding parameters for delay time coordinates. Physica D 58, 128.ADSCrossRefGoogle Scholar
  3. Farmer, D. J. & Sidorovich, J. J. (1987) Predicting chaotic time series. Phys Rev. Lett. 59 (8), 845.MathSciNetADSCrossRefGoogle Scholar
  4. Grassberger, P. Schreiber, Th. & Schaffrath, C. (1991) Nonlinear time sequence analysis. Int. J. Bif. & Chaos. 1(3), 521.MathSciNetMATHCrossRefGoogle Scholar
  5. Hamilton, J. M., Kim, J. & Waleffe, F. (1995) Regeneration mechanism of near-wall turbulent structures. J. Fluid Mech. 287, 317.ADSMATHCrossRefGoogle Scholar
  6. Keefe, L, Moin, P. & Kim, J. (1992) The dymension of attractors underlying periodic turbulent Poiseuille flow. J. Fluid Mech. 242, 1.MathSciNetADSMATHCrossRefGoogle Scholar
  7. Luchik, T. S. & Tiederman, W. G. (1987) Timescale and structure of ejections and burst in turbulent channel flow. J. Fluid Mech. 174, 529.ADSCrossRefGoogle Scholar
  8. Newell, A. C., Rand, D. A. & Rüssel, D. (1988) Turbulent transport and the random occurrence of coherent events. Phisica D 33, 281.ADSMATHCrossRefGoogle Scholar
  9. Porporato, A (1996) Ricerca di elementi di bassa dimensione nella turbolenza di parete. Ph.D. Thesis, Dept of Hydraulics-Polytechnic of Turin, (in Italian)Google Scholar
  10. Sanghi, S. & Aubry, N. (1993) Mode interaction models for near-wall turbulence. J. Fluid Mech. 247, 455.MathSciNetADSMATHCrossRefGoogle Scholar
  11. Takens, F. (1980) Detecting strange attractors in turbulence. In Lectures Notes in Math. vol. 898. Springer.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Amilcare Porporato
    • 1
  • Luca Ridolfi
    • 1
  1. 1.Department of Hydraulics, Transports and Civil InfrastructuresPolytechnic of TurinItaly

Personalised recommendations