Advertisement

Stochastic Estimation of the Structure of Turbulent Fields

  • R. J. Adrian
Part of the International Centre for Mechanical Sciences book series (CISM, volume 353)

Abstract

The stochastic estimation method educes structure by approximating an average field in terms of event data that are given. The estimated fields satisfy the continuity equation, and they possess the correct scales of length and/or time. The fundamental concepts of general stochastic estimation and the specific application of this technique to the estimation of conditional averages are discussed. Linear stochastic estimation of random fields and of their conditional averages is developed as the principal tool, and its accuracy is demonstrated. The linear stochastic estimate is expressible in terms of second order correlation functions between the given event data and the quantity being estimated. This establishes a simple link between conditional averages, the coherent structure that they represent and correlation functions. The related problems of selecting events and interpreting the estimates that result from a given set of events are explored by considering events of increasing complexity: single-point vectors, two-point vectors, local deformation tensors, multi-point vectors, space-time vectors, and space-wave-number events. General kinematic and statistical properties are derived, and stochastically estimated structures from various types of turbulent flows are described and related to the underlying coherent structures.

Keywords

Wall Shear Stress Shear Layer Coherent Structure Vortex Ring Proper Orthogonal Decomposition 
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. Adrian, R. J. (1977) On the role of conditional averages in turbulence theory. In J. Zakin and G. Patterson, Eds. Turbulence in Liquids. Princeton, NJ: Science Press, 323–332.Google Scholar
  2. Adrian, R. J. (1979) Conditional eddies in isotropic turbulence. Phys. Fluids 22, 2065–2070.CrossRefMATHADSGoogle Scholar
  3. Adrian, R. J., Moin, P., Moser, R. D. (1987) Stochastic estimation of conditional eddies in turbulent channel flow, in: Moin, P., Reynolds, W. R., Eds. Proc. of the 1987 Summer Program of the Center for Turbulence Research, CTR-S87. NASA Ames Research Center, Moffett Field, CA, 7–20..Google Scholar
  4. Adrian, R. J., Moin, P. (1988) Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531–559.CrossRefMATHADSGoogle Scholar
  5. Adrian, R. J., Jones, B. G., Chung, M. K., Hassan, Y., Nithianandan, C. K., Tung, A. T.-C. (1989) Approximation of turbulent conditional averages by stochastic estimation. Phys. Fluids A. 1, 992–998.CrossRefADSGoogle Scholar
  6. Adrian, R. J. (1990) Linking correlations and structure: stochastic estimation and conditional averaging. in: Kline, S. J., Afgan, N. H., Eds. Near Wall Turbulence, Proc. Zaric Memorial Intl. Symp., Washington D.C.: Hemisphere, 430–436.Google Scholar
  7. Adrian, R. J. (1990) Stochastic estimation of sub-grid scale motions. Appl. Mech. Rev. 43, 5214–5218.Google Scholar
  8. Bagwell, T. G., Adrian, R. J., Moser, R. D., Kim, J. (1993) Improved approximation of wall shear stress boundary conditions for large eddy simulations. In: So, R., Launder, B., Eds. Near Wall Turbulent Flows. Amsterdam: Elsevier Science, 265–275.Google Scholar
  9. Bagwell, T. G. (1994) Stochastic Estimation of Near Wall Closure in Turbulence Models. Ph. D. thesis, Univ. Illinois, Urbana, Illinois.Google Scholar
  10. Balachandar, S., Adrian, R. J. (1993) Structure extraction by stochastic estimation with adaptive events. J. Theoret. Comput. Fluid Dyn. 5, 243–257.CrossRefMATHADSGoogle Scholar
  11. Batchelor, G. K. (1986) The Theory of Homogeneous Turbulence, Cambridge Univ. Press, Cambridge.Google Scholar
  12. Berkooz, G., Elezgaray, J., Holmes, P. Lumley, J. and Poje, A. (1993) The proper orthogonal decomposition, wavelets and modal approaches to the dynamics of coherent structures, In: Bonnet, J. P., Glauser, M. N., Eds. Eddy Structure Identification in Free Turbulent Shear Flows. Dordrecht: Kluwer. 325–336.Google Scholar
  13. Brereton, G. J. (1992) Stochastic estimation as a statistical tool for approximating turbulent conditional averages. Phys. Fluids A 4, 2046–2054.CrossRefADSGoogle Scholar
  14. Bonnet, J. P., Cole, D. R., Delville, J., Glauser, M. N., Ukeiley, L. S. (1994) Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure. Exp. Fluids 17, 307–314.CrossRefGoogle Scholar
  15. Chang, P. J. (1985) Fluctuating Pressure and Velocity Fields in the Near Field of a Round Jet. Ph.D. thesis, Univ. Illinois, Urbana, Illinois.Google Scholar
  16. Chang, P. J., Adrian, R. J., Jones, B. G. (1985) Fluctuating pressure and velocity fields in the near field of a round jet. Univ. Illinois, Urbana, Illinois, Theo. & Appl. Mech. Report No. 475, UILU-ENG 85–6006.Google Scholar
  17. Cole, D. R., Glauser, M. N., Guezennec, Y. G. (1992) An application of the stochastic estimation to the jet mixing layer. Phys. Fluids A 4, 192–194.CrossRefADSGoogle Scholar
  18. Ditter, J. L. (1987) Stochastic Estimation of Eddies Conditioned on Local Kinematics: Isotropic Turbulence. M.S. thesis, Univ. Illinois, Urbana, IL.Google Scholar
  19. Ditter, J.L. and Adrian, R.J. (1988). “Local flow structures around kinematic events in isotropic turbulence,” presented at 11th Symp. on Turbulence, October 17–19, 1988, Univ. of Missouri-Rolla.Google Scholar
  20. Deutsch, R. (1965) Estimation Theory. New York: Prentice-Hall, 1965.MATHGoogle Scholar
  21. Elam, K. S. (1987) Conditional Reynolds Stresses in the Near Field of a Round Jet. M.S. Thesis, Univ. Illinois, Urbana, Illinois.Google Scholar
  22. Gieseke, T. J., Guezennec, Y. G. (1993) Stochastic estimation of multipoint conditional averages and their spatio-temporal evolution. in: Bonnet, J. P., Glauser, M. N., Eds. Eddy Structure Identification in Free Turbulent Shear Flows. Dordrecht: Kluwer, 281–292. ISBN: 0–7923-2449–8.CrossRefGoogle Scholar
  23. Guezennec, Y., Piomelli, U., and Kim, J. (1987) in Proc. 1987 Summer Program of Center for Turbulence Research, NASA Ames/Stanford Univ., Stanford, CA 263.Google Scholar
  24. Guezennec, Y. (1989) Stochastic estimation of coherent structure in turbulent boundary layers. Phys. Fluids A 1, 1054.MathSciNetCrossRefADSGoogle Scholar
  25. Hassan, Y. A. (1980) Experimental and Modeling Studies of Two-Point Stochastic Structure in Turbulent Pipe Flow. Ph.D. thesis, Urbana, IL: Univ. Illinois.Google Scholar
  26. Johnsen, H., Pecseli, H. L., Trulsen, J. C. (1985) Conditional eddies, or clumps, in ionbeam-generated turbulence. Phys. Rev. Lett. 55, 2297–2300.CrossRefADSGoogle Scholar
  27. Johnsen, H., Pecseli, H. L., Trulsen, J. C. (1986) Conditional eddies in plasma turbulence. Plasma Physics and Controlled Fusion 28, 1519–1523.CrossRefADSGoogle Scholar
  28. Kendall, T. M. (1992) Dynamics of Conditional Vortices in Turbulent Channel Flow: A Direct Numerical Simulation. M.S. thesis, Univ. Illinois, Urbana, Illinois.Google Scholar
  29. LeBoeuf R. L., Mehta, R. Improved methods for linear estimation of velocity records. Exp. Fluids 17, 32–38.Google Scholar
  30. Lundgren, T.S. (1967) Distribution functions in the statistical theory of turbulence. Phys. Fluids 10, 969.CrossRefADSGoogle Scholar
  31. Moin, P., Adrian, R. J., Kim, J. (1987) Stochastic estimation of organized structures in turbulent channel flow, in: Proc. 6th Turbulent Shear Flow Symp., Toulouse, 1987, 16.9.116. 9. 8.Google Scholar
  32. Monin, A. S. (1967a) Equation for finite-dimensional probability distributions of turbulent field. Dokl. Akad. Nauk SSSR 177, 1036–1038.Google Scholar
  33. Nithianandan, C. K. (1980) Fluctuating velocity pressure field structure in a round jet turbulent mixing region. Ph.D. thesis, University of Illinois, Urbana, Illinois.Google Scholar
  34. Novikov, E. A. (1967) Kinetic equations for vorticity field. Dokl. Akad. Nauk. SSSR 177, 299–301.Google Scholar
  35. Novikov, E. A. (1993) A new approach to the problem of turbulence, based on the conditionally averaged Navier-Stokes equations. Fluid Dynamics Res. 12, 107–126.CrossRefADSGoogle Scholar
  36. Papoulis, A. (1984) Probability, Random Variables and Stochastic Theory. New York: McGraw-Hill.Google Scholar
  37. Perry, A. E., and Chong, M. A. (1987) A description of eddying motions in flow patterns using critical-point concepts. Ann. Rev. Fluid Mech. 19, 125–155.CrossRefADSGoogle Scholar
  38. Piomelli, U. (1987) Models for Large Eddy Simulations of Turbulent Channel Flows Including Transpiration. Ph.D. thesis, Stanford Univ., Stanford, California.Google Scholar
  39. Robinson, S. K. (1991) Coherent motions in the turbulent boundary layer, Ann. Rev. Fluid Mech. 23, 601–640.CrossRefADSGoogle Scholar
  40. Rogers, M. M., Moin, P. (1987) The structure of the vorticity field in homogeneous turbulent flows, J. Fluid Mech. 176, 33.CrossRefADSGoogle Scholar
  41. Schumann, U. (1975) Subgrid scale model for finite difference simulations of turbulent flows in plant channels and annuli. J. Comput. Phys. 18, 376–404.MathSciNetCrossRefMATHADSGoogle Scholar
  42. Townsend, A. A. (1976) The Structure of Turbulent Shear Flow, 2nd Ed. Cambridge University Press, Cambridge.MATHGoogle Scholar
  43. Tung, A.T.C. and Adrian, R. J. (1980) Higher-order estimates of conditional eddies in isotropic turbulence. Phys. Fluids 23, 1469–1470.CrossRefADSGoogle Scholar
  44. Tung, A. T. C. (1982) Properties of Conditional Eddies in Free Shear Flows. Ph.D. thesis, Univ. Illinois, Urbana, Illinois.Google Scholar
  45. Ukeiley, L., Cole, D. R., Glauser, M. (1993) An examination of the axisymmetric jet mixing layer using coherent structure detection techniques. In: Bonnet, J. P., Glauser, M. N., Eds. Eddy Structure Identification in Free Turbulent Shear Flows. Dordrecht: Kluwer. 325–336.CrossRefGoogle Scholar
  46. Van Atta, C. W. and Chen, W. Y. (1968) Correlation measurements in grid turbulence using digital harmonic analysis. J. Fluid Mech. 34, 497–515.CrossRefADSGoogle Scholar
  47. Willmarth, W. W., and Wooldridge, C. E. (1963) Measurements of the correlation between the fluctuating velocities and the fluctuating wall pressure in a thick turbulent boundary layer. AGARD Rep. 456.Google Scholar
  48. Zhou, Z., Adrian, R. J., and Balachandar, S. (1995) Autogeneration of near-wall vortical structures in channel flow. Submitted to Phys. Fluids.Google Scholar

Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • R. J. Adrian
    • 1
  1. 1.University of IllinoisUrbanaUSA

Personalised recommendations