Generalized Langevin equation for relative turbulent dispersion

Journal of Fluid Mechanics

Volumn 357, Issue , 1998, Pages 167-198

  Heppe, Burkhard M O ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PARTICLES (PARTICULATE MATTER); PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; REYNOLDS NUMBER; TWO PHASE FLOW; VISCOUS FLOW; WHITE NOISE;

EULERIAN PROBABILITY DENSITY; LANGEVIN EQUATION; MORI-ZWANZIG PROJECTOR METHOD; RICHARDSON LAW;

TURBULENT FLOW;

EID: 0032000939     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112097008069     Document Type: Article

References (49)

1. ADRIAN, R. J. 1996 Stochastic estimation of the structure of turbulent fields. In Eddy Structure Identification (ed. J. P. Bonnet), pp. 145-196. Springer.
2. BATCHELOR, G. K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345-362.
3. BATCHELOR, G. K. 1959 Small scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113-134.
4. BORGAS, M. S. & SAWFORD, B. L. 1994 A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence. J. Fluid Mech. 279, 69-99.
5. BORGAS, M. S. & SAWFORD, B. L. 1996 Molecular diffusion and viscous effects on concentration statistics in grid turbulence. J. Fluid Mech. 324, 25-54.
6. CHING, E. S. C., L'VOV, V. S., PODIVILOV, E. & PROCACCIA, I. 1996 Conditional statistics in scalar turbulence: Theory versus experiment. Phys. Rev. E 54, 6364-6371.
7. 0) for the Lagrangian structure function, using a second-order Lagrangian model of grid turbulence. Phys. Fluids 7, 3083-3090.
8. DU, S., WILSON, J. D. & YEE, E. 1994 On the moments approximation method for constructing a Lagrangian stochastic model. Boundary-Layer Met. 70, 273-292.
9. DURBIN, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuation in homogeneous turbulence. J. Fluid Mech. 100, 279-302.
10. ELLIOTT, F. W. & MAJDA, A. J. 1996 Pair dispersion over an inertial range spanning many decades. Phys. Fluids 8, 1052-1060.
11. FRISCH, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
12. FUNG, J. C. H., HUNT, J. C. R., MALIK, N. A. & PERKINS, R. J. 1992 Kinematic simulation of homogeneous turbulence by using random Fourier modes. J. Fluid Mech. 236, 281-318.
13. FUNG, J. C. H. & VASSILICOS, J. C. 1997 Two-particle dispersion in turbulent-like flow. Phys. Rev. E (submitted).
14. GRABERT, H. 1982 Projection Operator Techniques in Non-equilibrium Statistical Mechanics. Springer.
15. GRABERT, H., HANGGI, P. & TALKNER, P. 1980 Microdynamics and nonlinear stochastic processes of gross variables. J. Statist. Phys. 22, 537-552.
16. GROSSMANN, S. & PROCACCIA, I. 1984 Unified theory of relative turbulent diffusion. Phys. Rev. A 29, 1358-1365.
17. GROSSMANN, S. & THOMAE, S. 1982 Correlation decay of Lagrangian velocity differences in locally isotropic turbulence. Z. Phys. B - Condensed Matter 49, 253-261 (referred to herein as GT82).
18. HEINZ, S. 1997 Nonlinear Lagrangian equations for turbulent motion and buoyancy in inhomogenous flows. Phys. Fluids 9, 703-716.
19. HEPPE, B. M. O. 1997 Stochastic Lagrangian models of dispersion and mixing in homogeneous turbulence. PhD dissertation, University of Cambridge.
20. KAPLAN, H. & DINAR, N. 1988 A three-dimensional stochastic model for concentration fluctuation statistics in isotropic homogeneous turbulence. J. Comput. Phys. 79, 317-335.
21. KAPLAN, H. & DINAR, N. 1993 A three-dimensional model for calculating the concentration distribution in inhomogeneous turbulence. Boundary Layer Met. 62, 217-245.
22. KRAICHNAN, R. H. 1970 Convergence to turbulent functions. J. Fluid Mech. 41, 189-217.
23. KRAICHNAN, R. H. 1994 Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72, 1016-1019.
24. KRAICHNAN, R. H., YAKHOT, V. & CHEN, S. 1995 Scaling relations for a randomly advected passive scalar field. Phys. Rev. Lett. 75, 240-243.
25. LINDENBERG, K. & WEST, B. 1990 The Non-equilibrium Statistical Mechanics of Open and Closed Systems. VCH Publisher.
26. LOHSE, D. 1995 Crossover from high to low Reynolds number turbulence. Phys. Rev. Lett. 73, 3223-3226.
27. LUMLEY, J. L. 1970 Stochastic Tools in Turbulence. Academic Press.
28. MALIK, N. A. 1991 Studies in turbulent dispersion using kinematic simulation. PhD dissertation, University of Cambridge.
29. MONIN, A. S. & YAGLOM, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.
30. NOVIKOV, E. A. 1969 Relation between the Lagrangian and Eulerian description of turbulence. Appl. Math. Mech. 33, 862-864.
31. NOVIKOV, E. A. 1989 Two-particle dispersion of turbulence. Markov property, and intermittency. Phys. Fluids A 1, 326-330.
32. PEDRIZZETTI, G. & NOVIKOV, E A. 1994 On Markov modelling of turbulence. J. Fluid Mech. 280, 69-93.
33. POPE, S. B. 1985 P.D.F. methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119-192.
34. POPE, S. B. 1994 Lagrangian p.d.f. methods for turbulent flows. Ann. Rev. Fluid Mech. 26, 23-63.
35. POPE, S. B. & CHING, E. S. C. 1993 Stationary probability function: An exact result. Phys. Fluids A 5, 1529-1531.
36. SAWFORD, B. L. 1991 Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids A 3, 1577-1586.
37. SAWFORD, B. L. & HUNT, J. C. R. 1986 Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence. J. Fluid Mech. 165, 373-400.
38. SREENIVASAN, K. R. 1984 On the scaling of the turbulent energy-dissipation rate. Phys. Fluids 27, 1048-1051.
39. TATARSKI, V. I. 1960 Radiophysical methods of investigating atmospheric turbulence. Izv. Vyssh. Uchebn. Zaved. 3 Radiofizika 4, 551-583.
40. TAYLOR, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196-212.
41. THOMSON, D. J. 1987 Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180, 529-556.
42. THOMSON, D. J. 1990 A stochastic model for the motion of particle pair in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance. J. Fluid Mech. 210, 113-153.
43. THOMSON, D. J. 1996 The second-order moment structure of dispersing plumes and puffs. J. Fluid Mech. 320, 305-329.
44. TOWNSEND, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
45. YEUNG, P. K. 1994 Direct numerical simulation of two-particle relative diffusion in isotropic turbulence. Phys. Fluids 6, 3416-3428.
46. YEUNG, P. K. 1997 One- and two-particle Lagrangian acceleration correlations in numerically simulated homogeneous turbulence. Phys. Fluids 9, 2981-2990.
47. YEUNG, P. K. & POPE, S. B. 1989 Lagrangian statistics from direct numerical simulation of isotropic turbulence. J. Fluid Mech. 207, 531-586.
48. ZWANZIG, R. 1961 Memory effects in irreversible thermodynamics. Phys. Rev. 124, 983-992.
49. ZWANZIG, R. 1980 Problems in nonlinear transport theory. In Systems Far from Equilibrium (ed. L. Garrido), pp. 198-225. Springer.