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Stochastic Estimation of the Structure of Turbulent Fields

  • Chapter
Eddy Structure Identification

Part of the book series: International Centre for Mechanical Sciences ((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.

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References

  • 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 

  • Adrian, R. J. (1979) Conditional eddies in isotropic turbulence. Phys. Fluids 22, 2065–2070.

    Article  MATH  ADS  Google Scholar 

  • 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 

  • Adrian, R. J., Moin, P. (1988) Stochastic estimation of organized turbulent structure: homogeneous shear flow. J. Fluid Mech. 190, 531–559.

    Article  MATH  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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 

  • Adrian, R. J. (1990) Stochastic estimation of sub-grid scale motions. Appl. Mech. Rev. 43, 5214–5218.

    Google Scholar 

  • 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 

  • Bagwell, T. G. (1994) Stochastic Estimation of Near Wall Closure in Turbulence Models. Ph. D. thesis, Univ. Illinois, Urbana, Illinois.

    Google Scholar 

  • Balachandar, S., Adrian, R. J. (1993) Structure extraction by stochastic estimation with adaptive events. J. Theoret. Comput. Fluid Dyn. 5, 243–257.

    Article  MATH  ADS  Google Scholar 

  • Batchelor, G. K. (1986) The Theory of Homogeneous Turbulence, Cambridge Univ. Press, Cambridge.

    Google Scholar 

  • 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 

  • Brereton, G. J. (1992) Stochastic estimation as a statistical tool for approximating turbulent conditional averages. Phys. Fluids A 4, 2046–2054.

    Article  ADS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  ADS  Google Scholar 

  • Ditter, J. L. (1987) Stochastic Estimation of Eddies Conditioned on Local Kinematics: Isotropic Turbulence. M.S. thesis, Univ. Illinois, Urbana, IL.

    Google Scholar 

  • 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 

  • Deutsch, R. (1965) Estimation Theory. New York: Prentice-Hall, 1965.

    MATH  Google Scholar 

  • Elam, K. S. (1987) Conditional Reynolds Stresses in the Near Field of a Round Jet. M.S. Thesis, Univ. Illinois, Urbana, Illinois.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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 

  • Guezennec, Y. (1989) Stochastic estimation of coherent structure in turbulent boundary layers. Phys. Fluids A 1, 1054.

    Article  MathSciNet  ADS  Google Scholar 

  • 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 

  • Johnsen, H., Pecseli, H. L., Trulsen, J. C. (1985) Conditional eddies, or clumps, in ionbeam-generated turbulence. Phys. Rev. Lett. 55, 2297–2300.

    Article  ADS  Google Scholar 

  • Johnsen, H., Pecseli, H. L., Trulsen, J. C. (1986) Conditional eddies in plasma turbulence. Plasma Physics and Controlled Fusion 28, 1519–1523.

    Article  ADS  Google Scholar 

  • 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 

  • LeBoeuf R. L., Mehta, R. Improved methods for linear estimation of velocity records. Exp. Fluids 17, 32–38.

    Google Scholar 

  • Lundgren, T.S. (1967) Distribution functions in the statistical theory of turbulence. Phys. Fluids 10, 969.

    Article  ADS  Google Scholar 

  • 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 

  • Monin, A. S. (1967a) Equation for finite-dimensional probability distributions of turbulent field. Dokl. Akad. Nauk SSSR 177, 1036–1038.

    Google Scholar 

  • 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 

  • Novikov, E. A. (1967) Kinetic equations for vorticity field. Dokl. Akad. Nauk. SSSR 177, 299–301.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Papoulis, A. (1984) Probability, Random Variables and Stochastic Theory. New York: McGraw-Hill.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Piomelli, U. (1987) Models for Large Eddy Simulations of Turbulent Channel Flows Including Transpiration. Ph.D. thesis, Stanford Univ., Stanford, California.

    Google Scholar 

  • Robinson, S. K. (1991) Coherent motions in the turbulent boundary layer, Ann. Rev. Fluid Mech. 23, 601–640.

    Article  ADS  Google Scholar 

  • Rogers, M. M., Moin, P. (1987) The structure of the vorticity field in homogeneous turbulent flows, J. Fluid Mech. 176, 33.

    Article  ADS  Google Scholar 

  • Schumann, U. (1975) Subgrid scale model for finite difference simulations of turbulent flows in plant channels and annuli. J. Comput. Phys. 18, 376–404.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Townsend, A. A. (1976) The Structure of Turbulent Shear Flow, 2nd Ed. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Tung, A.T.C. and Adrian, R. J. (1980) Higher-order estimates of conditional eddies in isotropic turbulence. Phys. Fluids 23, 1469–1470.

    Article  ADS  Google Scholar 

  • Tung, A. T. C. (1982) Properties of Conditional Eddies in Free Shear Flows. Ph.D. thesis, Univ. Illinois, Urbana, Illinois.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Van Atta, C. W. and Chen, W. Y. (1968) Correlation measurements in grid turbulence using digital harmonic analysis. J. Fluid Mech. 34, 497–515.

    Article  ADS  Google Scholar 

  • 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 

  • Zhou, Z., Adrian, R. J., and Balachandar, S. (1995) Autogeneration of near-wall vortical structures in channel flow. Submitted to Phys. Fluids.

    Google Scholar 

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Authors and Affiliations

  1. University of Illinois, Urbana, IL, USA

    R. J. Adrian

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  1. R. J. Adrian
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Editors and Affiliations

  1. University of Poitiers, France

    J. P. Bonnet

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© 1996 Springer-Verlag Wien

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Adrian, R.J. (1996). Stochastic Estimation of the Structure of Turbulent Fields. In: Bonnet, J.P. (eds) Eddy Structure Identification. International Centre for Mechanical Sciences, vol 353. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2676-9_3

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  • DOI: https://doi.org/10.1007/978-3-7091-2676-9_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82802-1

  • Online ISBN: 978-3-7091-2676-9

  • eBook Packages: Springer Book Archive

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