Advertisement

A Stochastic Analysis of the Displacements of Fluid Elements in Inhomogeneous Turbulence Using Kraichnan’s Method of Random Modes

  • C. Turfus
  • J. C. R. Hunt

Abstract

At an instant in time a homogeneous turbulent flow field can be represented as a summation of random Fourier components; this can be extended to describe turbulence near an interface or a boundary in shear-free flow, by adding an irrotational velocity field. The time evolution of the flow can be simulated by assuming that the modes are oscillatory functions of time with random frequencies and random amplitudes: i) our model simulates the energy containing eddies and the inertial subrange eddies with a (5/3) energy spectrum; ii) the time scale for the decorre lation of each eddy is made proportional to its length-scale corresponding to an Eulerian power spectrum proportional to ω −5/3.

Keywords

Velocity Field Large Eddy Simulation Internal Wave Random Mode Lagrangian Statistic 
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. [1]
    Durbin, P.A. (1983) Stochastic differential equations and turbulent dispersion. NASA Reference Publication 1103.Google Scholar
  2. [2]
    van Dop, H., Nieuwstadt. F.T.M & Hunt, J.C.R. (1985) Random walk models for particle displacements in inhomogeneous unsteady turbulent flows. Phys. Fluids. 28, 1639–1653.CrossRefMATHADSGoogle Scholar
  3. [3]
    Sawford, B. & Hunt, J.C.R. (1986) Effects of turbulence structure, molecular diffusion and source size on fluctuations of concentration in homogeneous turbulence. J. Fluid Mech. 165, 373–400. J. Fluid Mech.CrossRefMATHADSGoogle Scholar
  4. [4]
    Corrsin, S. (1963) J. Atmos. Sci. 20, 115–119.CrossRefADSGoogle Scholar
  5. [5]
    Snyder, W.H. & Lumley, J.L. (1981) Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41–71.CrossRefADSGoogle Scholar
  6. [6]
    Kraichnan, H. (1970) Diffusion by a random velocity field. Phys. Fluids. 13, 22–31.CrossRefMATHADSGoogle Scholar
  7. [7]
    Drummond, I.T. Duane, S. & Horgan, R.R. (1984) Scalar diffusion in simulated helical turbulence with molecular diffusivity. J. Fluid Mech. 138, 75–91.CrossRefMATHADSGoogle Scholar
  8. [8]
    Hunt, J.C.R. (1984) Turbulent structure in thermalconvection and shear-free boundary layers. J. Fluid Mech. 138, 161–184.CrossRefMATHADSGoogle Scholar
  9. [9]
    Carruthers, D.J., Hunt, J.C.R. & Turfus, C. (1986) Turbulent flow near density inversion layers. Proc. of Euromech. 199, ‘Direct and Large Eddy Simulation of Turbulent Flows’. Ed. U. Schumann.Google Scholar
  10. [10]
    Batchelor, G.K. (1953) Theory of Homogeneous Turbulence. C.U.P.Google Scholar
  11. [11]
    Tennekes, H. (1975) Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561–567.CrossRefMATHADSGoogle Scholar
  12. [12]
    Townsend, A.A. (1966). Internal waves produced by a convective layer. J. Fluid Mech. 24, 307–319.CrossRefADSMathSciNetGoogle Scholar
  13. [13]
    Carruthers, D.J. & Hunt, J.C.R. (1986) Velocity fluctuations near an interface between a turbulent region and a stably stratified layer. J. Fluid Mech. 165, 475–501.CrossRefMATHADSGoogle Scholar
  14. [14]
    Hunt, J.C.R. & Graham, J.M.R. (1978) Free-stream turbulence near plane bounaries. J. Fluid Mech. 84, 209–235.CrossRefMATHADSMathSciNetGoogle Scholar
  15. [15]
    Turfus, C. (1985) Stochastic Modelling of Turbulent Dispersion near Surfaces. Ph.D. Dissertation, University of Cambridge.Google Scholar
  16. [16]
    Rao, N.J., Borwankar, J.D., Ramkrishna, D. (1974) Numerical solution of Ito integral equations. SIAM J. Control 12, 124–139.CrossRefMATHGoogle Scholar
  17. [17]
    Wyngaard, J.C. & Brost, R.A. (1984) Top-down and bottom-up diffusion in the convective boundary layer. J. Atmos. Sci. 41, 102–112.CrossRefADSGoogle Scholar
  18. [18]
    Thomson, D.J. (1984) Random walk modelling of diffusion in inhomogeneous turbulence. Quart. J. Roy. Met. Soc. 110, 1107–1120.CrossRefADSGoogle Scholar
  19. [19]
    Hunt, J.C.R. (1985) Turbulent diffusion from sources in complex flows. Ann. Rev. Fluid Mech. 17 447–485.CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • C. Turfus
    • 1
  • J. C. R. Hunt
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

Personalised recommendations