Stochastic suspensions of heavy particles

Physica D: Nonlinear Phenomena

Volumn 237, Issue 14-17, 2008, Pages 2037-2050

  Bec, Jérémie ^a   Cencini, Massimo ^b,c   Hillerbrand, Rafaela ^d   Turitsyn, Konstantin ^e,f  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c ISC CNR   (Italy)

^d UNIVERSITY OF OXFORD   (United Kingdom)

^e UNIVERSITY OF CHICAGO   (United States)

^f LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

Inertial particles; Kraichnan model; Lyapunov exponent; Stochastic flows

Indexed keywords

LYAPUNOV METHODS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

CORRELATION DIMENSIONS; DISSIPATIVE DYNAMICS; INERTIAL PARTICLES; KRAICHNAN MODEL; LYAPUNOV EXPONENT; SPATIALLY SELF-SIMILAR; STATISTICAL PROPERTIES; STOCHASTIC FLOWS;

SUSPENSIONS (FLUIDS);

EID: 47249084637     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.02.022     Document Type: Article

References (53)

1. Kraichnan R.H. Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11 (1968) 945-953
2. Falkovich G., Gawȩdzki K., and Vergassola M. Particles and fields in fluid turbulence. Rev. Modern Phys. 73 (2001) 913-975
3. Pruppacher H., and Klett J. Microphysics of Clouds and Precipitation (1996), Kluwer Academic Publishers, Dordrecht
4. Pinsky M.B., and Khain A.P. Turbulence effects on droplet growth and size distribution in clouds- a review. J. Aerosol. Sci. 28 (1997) 1177-1214
5. Falkovich G., Fouxon A., and Stepanov M.G. Acceleration of rain initiation by cloud turbulence. Nature 419 (2002) 151-154
6. Rothschild B.J., and Osborn T.R. Small-scale turbulence and plankton contact rates. J. Plankton Res. 10 (1988) 465-474
7. Sundby S., and Fossum P. Feeding conditions of Arcto-Norwegian cod larvae compared with the Rothschild-Osborn theory on small-scale turbulence and plankton contact rates. J. Plankton Res. 12 (1990) 1153-1162
8. Mann J., Ott S., Pécseli H.L., and Trulsen J. Predator-prey encounters in turbulent waters. Phys. Rev. E 65 (2002) 026304
9. Eaton J.K., and Fessler J.R. Preferential concentration of particles by turbulence. Int. J. Multiphase Flow 20 (1994) 169-209
10. Hogan R.C., and Cuzzi J.N. Stokes and Reynolds number dependence of preferential particle concentration in simulated three-dimensional turbulence. Phys. Fluids 13 (2001) 2938-2945
11. Bec J. Fractal clustering of inertial particles in random flows. Phys. Fluids 15 (2003) L81-L84
12. Falkovich G., Fouxon A., and Stepanov M. In: Gyr A., and Kinzelbach W. (Eds). Sedimentation and Sediment Transport (2003), Kluwer Academic Publishers, Dordrecht 155-158
13. Bec J., Cencini M., and Hillerbrand R. Clustering of heavy particles in random self-similar flow. Phys. Rev. E 75 (2007) 025301
14. Piterbarg L.I. The top Lyapunov exponent for stochastic flow modeling the upper ocean turbulence. SIAM J. Appl. Math. 62 (2002) 777-800
15. Duncan K., Mehlig B., Östlund S., and Wilkinson M. Clustering by mixing flows. Phys. Rev. Lett. 95 (2005) 240602
16. Bec J., Cencini M., and Hillerbrand R. Heavy particles in incompressible flows: The large Stokes number asymptotics. Physica D 226 (2007) 11-22
17. Reade W.C., and Collins L.R. Effect of preferential concentration on turbulent collision rates. Phys. Fluids 12 (2000) 2530-2540
18. Bec J., Celani A., Cencini M., and Musacchio S. Clustering and collisions of heavy particles in random smooth flows. Phys. Fluids 17 (2005) 073301
19. Eckmann J.-P., and Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Modern Phys. 57 (1985) 617-656
20. Paladin G., and Vulpiani A. Anomalous scaling laws in multifractal objects. Phys. Rep. 156 (1987) 147-225
21. L. Arnold, Random Dynamical Systems, Springer Monographs in Mathematics, Berlin, New York, 2003
22. Sauer T.D., and Yorke J.A. Are the dimensions of a set and its image equal under typical smooth functions?. Ergodic Theory Dynam. Syst. 17 (1997) 941-956
23. Wang L.-P., Wexler A.S., and Zhou Y. On the collision rate of small particles in isotropic turbulence. Part I. Zero-inertia case. Phys. Fluids 10 (1998) 266-276
24. Zhou Y., Wang L.-P., and Wexler A.S. On the collision rate of small particles in isotropic turbulence. Part II. Finite-inertia case. Phys. Fluids 10 (1998) 1206-1216
25. Mehlig B., and Wilkinson M. Coagulation by random velocity fields as a Kramers problem. Phys. Rev. Lett. 92 (2004) 250602
26. Mehlig B., Wilkinson M., Duncan K., Weber T., and Ljunggren M. Aggregation of inertial particles in random flows. Phys. Rev. E 72 (2005) 051104
27. Wilkinson M., and Mehlig B. Caustics in turbulent aerosols. Europhys. Lett. 71 (2005) 186-192
28. Bec J., Biferale L., Boffetta G., Cencini M., Musacchio S., and Toschi F. Lyapunov exponents of heavy particles in turbulence. Phys. Fluids 18 (2006) 091702
29. Gawȩdzki K., and Vergassola M. Phase transition in the passive scaler advection. Physica D 138 (2000) 63-90
30. Deutsch J.M. Aggregation-disorder transition induced by random forces. J. Phys. A 18 (1985) 1449-1456
31. Wilkinson M., and Mehlig B. Path coalescence transition and its applications. Phys. Rev. E 68 (2003) 040101
32. Derevyanko S., Falkovich G., Turitsyn K., and Turitsyn S. Lagrangian and Eulerian descriptions of inertial particles in random flows. J. Turbul. 8 1 (2007) 1-18
33. Liboff R. Introductory Quantum Mechanics (2003), Addison-Wesley
34. M. Wilkinson, B. Mehlig, S. Östlund, K.P. Duncan, Unmixing in random flows. Preprint nlin.CD/0612061, 2006
35. Majda A., Timofeyev I., and Vanden Eijnden E. A mathematical framework for stochastic climate models. Comm. Pure Appl. Math. 54 (2001) 891-974
36. Nakajima S. On quantum theory of transport phenomena: Steady diffusion. Progr. Theoret. Phys. 20 (1958) 948-959
37. Zwanzig R. Ensemble method in the theory of universality. J. Chem. Phys. 33 (1960) 1338-1341
38. Risken H. The Fokker-Planck Equation (1989), Springer-Verlag, Berlin
39. Chaturvedi S., and Shibata F. Time-convolutionless operator formalism for elimination of fast variables. Applications to Brownian motion. Zeit. Phys. B 35 (1979) 297-308
40. Zaichik L.I., and Alipchenkov V. Pair dispersion and preferential concentration of particles in isotropic turbulence. Phys. Fluids 15 (2003) 1776-1787
41. Falkovich G., and Pumir A. Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids 16 (2004) L47-L50
42. Sigurgeirsson H., and Stuart A.M. A model for preferential concentration. Phys. Fluids 14 (2002) 4352-4361
43. Hunt B., and Kaloshin V. How projections affect the dimension spectrum of fractal measures. Nonlinearity 10 (1997) 1031-1046
44. Balkovsky E., Falkovich G., and Fouxon A. Intermittent distribution of inertial particles in turbulent flows. Phys. Rev. Lett. 86 (2001) 2790-2793
45. Biferale L., Cencini M., Lanotte A., Sbragaglia M., and Toschi F. Anomalous scaling and universality in hydrodynamic systems with power-law forcing. New J. Phys. 6 (2004) 37
46. P. Horvai, Lyapunov exponent for inertial particles in the 2D Kraichnan model as a problem of Anderson localization with complex valued potential, Preprint nlin.CD/0511023, 2005
47. Frisch U. Turbulence: The Legacy of A.N. Kolmogorov (1995), Cambridge University Press, Cambridge UK
48. I. Fouxon, P. Horvai, Single and two-particle motion of heavy particles in turbulence, Preprint arXiv:0704.3893, 2007
49. Boffetta G., De Lillo F., and Gamba A. Large scale inhomogeneity of inertial particles in turbulent flow. Phys. Fluids 16 (2004) L20-L23
50. Chen L., Goto S., and Vassilicos J.C. Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553 (2006) 143-154
51. Bec J., Biferale L., Cencini M., Lanotte A., Musacchio S., and Toschi F. Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98 (2007) 084502
52. Yoshimoto H., and Goto S. Self-similar clustering of inertial particles in homogeneous turbulence. J. Fluid Mech. 577 (2007) 275-286
53. Falkovich G., Musacchio S., Piterbarg L., and Vucelja M. Inertial particles driven by a telegraph noise. Phys. Rev. E 76 (2007) 026313