Scalar turbulence

Nature

Volumn 405, Issue 6787, 2000, Pages 639-646

  Shralman, Boris I ^a   Siggia, Eric D ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b ROCKEFELLER UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLUORESCENT DYE;

ADVECTION; TURBULENT FLOW;

COMBUSTION; FORCE; MAGNETIC FIELD; PRIORITY JOURNAL; REVIEW; TURBULENT FLOW; VELOCITY;

EID: 0034621898     PISSN: 00280836     EISSN: None     Source Type: Journal    
DOI: 10.1038/35015000     Document Type: Review

References (56)

1. Pasquill, F. & Smith, F. B. Atmospheric Diffusion (Ellis Norwood, Chichester, 1983).
2. Dibble, R. W., Warnatz, J. & Maas, U. Combustion: Physical and Chemical Fundamentals, Modelling and Simulations, Experiments, Pollutant Formation (Springer, New York, 1996).
3. Proctor, M. R. E. & Gilbert, A. D. (eds) Lectures on Solar and Planetary Dynamos 117 (Cambridge Univ. Press, Cambridge, 1994).
4. Berg, H C. Bacterial microprocessing. Cold Spring Harbor Symp. Quant. Biol. 55, 539-545 (1990).
5. Atema, J. Chemical signals in the marine environment: dispersal, detection, and temporal signal analysis. Proc. Natl Acad. Sci. 92, 62-66 (1995).
6. Mafraneto, A. & Carde, R. T. Fine-scale structure of pheromone plumes modulates upwind orientation fo flying moths. Nature 369, 142-144 (1994).
7. Sreenivasan, K. R. On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165-182 (1991).
8. Warhaft, Z. Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203-240 (2000).
9. Sreenivasan, K. & Antonia, R. A. The phenomenology of small scale turbulence. Annu. Rev. Fluid Mech. 21, 435-472 (1997).
10. Frisch, U. Turbulence: The legacy of AN Kolmogorov (Cambridge Univ. Press, Cambridge, 1995).
11. Monin, A. S. & Yaglom, A. M. Statistical Fluid Mechanics (MIT Press, Cambridge, 1975).
12. Tennekes, H. & Lumley, J. A. First Course in Turbulence (MIT Press, Cambridge, 1972).
13. Edouard, S. et al. The effect of small-scale inhomogeneities on ozone depletion in the Arctic. Nature 384, 444-447 (1996).
14. Kraichnan, R. H. Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945 (1968); Convection of a passive scalar by a quasi-uniform random straining field. J. Fluid Mech. 64, 737-762 (1974).
15. Kraichnan, R. H. Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945 (1968); Convection of a passive scalar by a quasi-uniform random straining field. J. Fluid Mech. 64, 737-762 (1974).
16. Kraichnan, R. H. Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72, 1016-1019 (1994).
17. Holzer, M. & Siggia, E. D. Turbulent mixing of a passive scalar. Phys. Fluids 6, 1820-1837 (1994).
18. Pumir, A. A numerical study of the mixing of a passive scalar in 3 dimensions in the presence of a mean gradient. Phys. Fluids 6, 2118-2132 (1994).
19. Gawcedzki, K. & Kupiainen, A. Anomalous scaling of the passive scalar. Phys. Rev. Lett. 75, 3834-3837 (1995).
20. Chertkov, M., Falkovich, G., Kolokolov, I. & Lebedev, V. Normal and anomalous scaling of the fourth-order correlation function of randomly advected passive scalar. Phys. Rev. E 52, 4929-4941 (1995).
21. Shraiman, B. I. & Siggia, H. D. Anomalous scaling of a passive scalar in a turbulent flow. C.R. Acad. Sci. 321, 279-284 (1995).
22. Antonia, R. A. & van Atta, C. W. Structure functions of temperature fluctuations in turbulent shear flows. J. Fluid Mech. 84, 561-580 (1978).
23. Gibson, C., Freihe, C. & McConnell, S. Structure of sheared turbulent fields. Phys. Fluids 20, S156-S167 (1977).
24. Mestayer, P. G. Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 125, 475-503 (1982).
25. Jayesh & Warhaft, Z. Probability distributions of a passive scalar in grid generated turbulence. Phys. Rev. Lett. 67, 3503-3506 (1991).
26. Mydlarsky, L., Pumir, A., Shraiman, B. I., Siggia, E. D. & Warhaft, Z. Structure and multi-point correlators for turbulent advection. Phys. Rev. Lett. 81, 4373-4376 (1998).
27. Gollub, J. P., Clarke, J., Gharib, M., Lane, B. & Mesquita, O. N. Fluctuations and transport in a stirred fluid with a mean gradient. Phys. Rev. Lett. 67, 3507-3511 (1991).
28. Ottino, J. M. The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge Univ. Press, New York, 1989).
29. Ott, E. Chaos in Dynamical Systems (Cambridge Univ Press, New York, 1994).
30. Williams, B. S., Marteau, D. & Gollub, J. P. Mixing of a passive scalar in magnetically forced two-dimensional turbulence. Phys. Fluids 9, 2061-2080 (1997).
31. Miller, P. L. & Dimotakis, P. E. Measurements of scalar power spectra in high Schmidt number turbulent jets. J. Fluid Mech. 308, 129-146 (1996).
32. Chen, S. & Kraichnan, R. H. Simulations of a randomly advected passive scalar field. Phys. Fluids 68, 2867-2884 (1998).
33. Feynman, R. & Hibbs, A. Quantum Mechanics and Path Integrals (McGraw Hill, New York, 1965).
34. Drummond, I. T. Path-integral for turbulent diffusion. J. Fluid Mech. 123, 59-68 (1982).
35. Molchanov, S., Ruzmaikin, A. & Sokolov, A. Kinematic dynamo. Sov. Phys. Usp. 28, 307-327 (1985).
36. Shraiman, B. I. & Siggia, E. D. Lagrangian path integrals and fluctuations in random flow. Phys. Rev. E 49, 2912-2927 (1994).
37. Bernard, D., Gawedzki, K. & Kupiainen, A. Slow modes in passive advection. J. Stat. Phys. 90, 519-569 (1997).
38. Chertkov, M., Falkovich, G. & Kolokolov, I. Intermittent dissipation in PS turbulence. Phys. Rev. Lett. 80, 2121-2124 (1998).
39. Buck, K. A. & Dahm, W. I. A. Experimental study of the fine scale structure of conserved scalar mixing inturbulent shear flows. Part I. Sc » 1. J. Fluid Mech. 317, 21-71 (1996).
40. Fairhall, A., Gat, O., L'vov, V. & Procaccia, I. Anomalous scaling in a model of passive scalar advection. Phys. Rev. E 53, 3518-3535 (1996).
41. Shraiman, B. I. & Siggia, E. D. Symmetry and scaling of turbulent mixing. Phys. Lett. 77, 2463-2466 (1996); Anomalous scaling of passive scalar near Batchelor limit. Phys. Rev. E 57, 2965-2977 (1998).
42. Shraiman, B. I. & Siggia, E. D. Symmetry and scaling of turbulent mixing. Phys. Lett. 77, 2463-2466 (1996); Anomalous scaling of passive scalar near Batchelor limit. Phys. Rev. E 57, 2965-2977 (1998).
43. Pumir, A., Shraiman, B. I. & Siggia, E. D. Perturbation theory for the δ-correlated model of passive scalar advection near the Batchelor limit. Phys. Rev. E 55, R1263-R1266 (1997).
44. Balkovsky, E., Chertkov, M., Kolokolov, I. & Lebedev, V. 4-th order correlation fucntion of a randomly advected passive scalar. JETP Lett. 61, 1049-1054 (1995).
45. Pumir, A. Anomalous scaling behaviour of a passive scalar in the presence of a mean gradient. Europhys. Lett. 34, 25-29 (1996).
46. Pumir, A. Structure of the three-point correlation function of a passive scalar in the presence of a mean gradient. Phys. Rev. E 57, 2914-2929 (1998).
47. Frisch, U., Mazzino, A., Noullez, A. & Vergassola, M. Lagrangian method for multiple correlations in passive scalar advection. Phys. Fluids. 11, 2178-2186 (1999).
48. Celani, A., Lanotte, A., Mazzino, A. & Vergassola, M. Universality and saturation of intermittency in passive scalar turbulence. Phys. Rev. Lett. 84, 2385-2388 (2000).
49. Chertkov, M. Instanton for random advection. Phys. Rev. E 55, 2722-2735 (1997).
50. Balkovsky, E. & Lebedev, V. Instanton for the Kraichnan random advection model. Phys. Rev. E 58, 5776-5795 (1998).
51. Chertkov, M., Falkovich, G., Kolokolov, V. & Vergassola, M. Small scale magnetic dynamo. Phys. Rev. Lett. 83, 4065-4068 (1999).
52. Chertkov, M., Kolokolov, L., Vergassola, M. Inverse versus direct cascades in turbulent advection. Phys. Rev. Lett. 80, 512-515 (1998).
53. Fournier, J.-D., Frisch, U. & Rose, H. Infinite-dimensional turbulence. J. Phys. A 11, 187-198 (1978).
54. Wilson, K. G. The renormalization group and critical phenomena. Rev. Mod. Phys. 55, 583-600 (1983).
55. Pumir, A. & Shraiman, B. I. Persistent small scale anisotropy in homogeneous shear flows. Phys. Rev. Lett. 75, 3114-3117 (1995).
56. Warhaft, Z. & Garg, S. On the small scale structure of simple shear flow. Phys. Fluids 10, 662-673 (1998).