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Point-source dispersion of quasi-neutrally-buoyant inertial particles

  • Marco Martins AfonsoEmail author
  • Sílvio M. A. Gama
Regular Article
  • 23 Downloads
Part of the following topical collections:
  1. Flowing Matter, Problems and Applications

Abstract.

We analyze the evolution of the distribution, both in the phase space and in the physical space, of inertial particles released by a spatially-localized (punctual) source and advected by an incompressible flow. The difference in mass density between fluid and particles is assumed to be small, and represents the basic parameter for a regular perturbative expansion. By means of analytical techniques such as Hermitianization, we derive a chain of equations of the advection-diffusion-reaction type, easily solvable at least numerically. Our procedure provides results also for finite particle inertia, away from the over-damped limit of quasi-tracer dynamics.

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Keywords

Topical issue: Flowing Matter, Problems and Applications 

References

  1. 1.
    G. Falkovich, K. Gawedzki, M. Vergassola, Rev. Mod. Phys. 73, 913 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    E. Balkovsky, G. Falkovich, A. Fouxon, Phys. Rev. Lett. 86, 2790 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    M. Wilkinson, B. Mehlig, Phys. Rev. E 68, 040101(R) (2003)ADSCrossRefGoogle Scholar
  4. 4.
    J. Bec, J. Fluid Mech. 528, 255 (2005)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    M. Cencini, J. Bec, L. Biferale, G. Boffetta, A. Celani, A.S. Lanotte, S. Musacchio, F. Toschi, J. Turbul. 7, 36 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    J. Bec, M. Cencini, R. Hillerbrand, Phys. Rev. E 75, 025301 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    G. Falkovich, S. Musacchio, L. Piterbarg, M. Vucelja, Phys. Rev. E 76, 026313 (2007)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Volk, E. Calzavarini, G. Verhille, D. Lohse, N. Mordant, J.F. Pinton, F. Toschi, Physica D 237, 2084 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    F. Toschi, E. Bodenschatz, Annu. Rev. Fluid Mech. 41, 375 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    J.P.L.C. Salazar, L.R. Collins, Annu. Rev. Fluid Mech. 41, 405 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    M. Bourgoin, H. Xu, New J. Phys. 16, 085010 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    G. Mussetti, J.O. Pralits, A. Mazzino, Meccanica 49, 2543 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    M.C. Bove, P. Brotto, F. Cassola, E. Cuccia, D. Massabò, A. Mazzino, A. Piazzalunga, P. Prati, Atmos. Environ. 94, 274 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    G.I. Taylor, Proc. Lond. Math. Soc. s2-20, 196 (1922)CrossRefGoogle Scholar
  15. 15.
    L.F. Richardson, Proc. R. Soc. Lond. A 110, 709 (1926)ADSCrossRefGoogle Scholar
  16. 16.
    A. Celani, M. Martins Afonso, A. Mazzino, Punctual emission of a passive scalar in turbulent flows, in Proceedings of the Conference Mathematical Modeling and Computational Physics 2006, Tatranská Štrba (Slovakia), August 28--September 1, 2006, to be published in Phys. Part. Nuclei LettGoogle Scholar
  17. 17.
    A. Celani, M. Martins Afonso, A. Mazzino, Mixing of a passive scalar emitted from a random-in-time point source, in Advances in Turbulence XI, Proceedings of the 11th EUROMECH European Turbulence Conference 2007, Porto (Portugal), June 25--28, edited by J.M.L.M. Palma, A. Silva Lopes, Springer Proc. Phys., Vol. 117 (Springer, Heidelberg, 2007) pp. 206--208Google Scholar
  18. 18.
    A. Celani, M. Martins Afonso, A. Mazzino, J. Fluid Mech. 583, 189 (2007)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    S. Thalabard, J. Stat. Mech. 2018, 033210 (2018)MathSciNetCrossRefGoogle Scholar
  20. 20.
    M. Martins Afonso, A. Mazzino, Geophys. Astrophys. Fluid Dyn. 105, 553 (2011)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    M. Martins Afonso, S.M.A. Gama, C. R. Méc. 346, 121 (2017)CrossRefGoogle Scholar
  22. 22.
    M. Martins Afonso, P. Muratore-Ginanneschi, S.M.A. Gama, A. Mazzino, Phys. Rev. Fluids 3, 044501 (2018)ADSCrossRefGoogle Scholar
  23. 23.
    M. Linkes, M. Martins Afonso, P. Fede, J. Morchain, P. Schmitz, Chem. Eng. Sci. 81, 8 (2012)CrossRefGoogle Scholar
  24. 24.
    O. Simonin, P. Février, J. Laviéville, J. Turbul. 3, 040 (2002)ADSCrossRefGoogle Scholar
  25. 25.
    P. Février, O. Simonin, K.D. Squires, J. Fluid Mech. 533, 1 (2005)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    M.W. Reeks, Phys. Fluids A 3, 446 (1991)ADSCrossRefGoogle Scholar
  27. 27.
    M.W. Reeks, Phys. Fluids A 4, 1290 (1992)ADSCrossRefGoogle Scholar
  28. 28.
    M.W. Reeks, J. Fluid Mech. 522, 263 (2005)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    D.C. Swailes, Y. Ammar, M.W. Reeks, Y. Drossinos, Phys. Rev. E 79, 036305 (2009)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    R. Smith, J. Fluid Mech. 195, 587 (1988)ADSCrossRefGoogle Scholar
  31. 31.
    R. Smith, J. Fluid Mech. 215, 195 (1990)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    R. Smith, J. Fluid Mech. 152, 217 (1985)ADSCrossRefGoogle Scholar
  33. 33.
    R. Gatignol, J. Méc. Théor. Appl. 1, 143 (1983)Google Scholar
  34. 34.
    M.R. Maxey, J.J. Riley, Phys. Fluids 26, 883 (1983)ADSCrossRefGoogle Scholar
  35. 35.
    R. Zwanzig, J. Stat. Phys. 9, 215 (1973)ADSCrossRefGoogle Scholar
  36. 36.
    M.W. Reeks, Phys. Fluids 31, 1314 (1988)ADSCrossRefGoogle Scholar
  37. 37.
    O. Cépas, J. Kurchan, Eur. Phys. J. B 2, 221 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)ADSCrossRefGoogle Scholar
  39. 39.
    C.W. Gardiner, Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences (Springer, 1985)Google Scholar
  40. 40.
    H. Risken, The Fokker-Planck Equation: Methods of Solutions and Applications (Springer, 1989). Google Scholar
  41. 41.
    N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, 2007)Google Scholar
  42. 42.
    E. Krasnoff, R.L. Peskin, Geophys. Astrophys. Fluid Dyn. 2, 123 (1971)ADSCrossRefGoogle Scholar
  43. 43.
    D.J. Thomson, J. Fluid Mech. 180, 529 (1987)ADSCrossRefGoogle Scholar
  44. 44.
    S.B. Pope, Annu. Rev. Fluid Mech. 26, 23 (1994)ADSCrossRefGoogle Scholar
  45. 45.
    B. Sawford, Annu. Rev. Fluid Mech. 33, 289 (2001)ADSCrossRefGoogle Scholar
  46. 46.
    J.P. Minier, J. Pozorski, Phys. Fluids 9, 1748 (1997)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    J. Pozorski, J.P. Minier, Int. J. Multiphase Flow 24, 913 (1998)CrossRefGoogle Scholar
  48. 48.
    J.P. Minier, E. Peirano, Phys. Rep. 352, 1 (2001)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    E. Peirano, J.P. Minier, Phys. Rev. E 65, 046301 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    J.P. Minier, E. Peirano, S. Chibbaro, Phys. Fluids 16, 2419 (2004)ADSCrossRefGoogle Scholar
  51. 51.
    A. Babiano, J.H.E. Cartwright, O. Piro, A. Provenzale, Phys. Rev. Lett. 84, 5764 (2000)ADSCrossRefGoogle Scholar
  52. 52.
    C. Marchioli, M. Fantoni, A. Soldati, Phys. Fluids 19, 098101 (2007)ADSCrossRefGoogle Scholar
  53. 53.
    T. Sapsis, G. Haller, Phys. Fluids 20, 017102 (2008)ADSCrossRefGoogle Scholar
  54. 54.
    M. Martins Afonso, A. Celani, A. Mazzino, P. Olla, Renormalized transport of inertial particles, in Advances in Turbulence XII, Proceedings of the 12th EUROMECH European Turbulence Conference 2009, Marburg (Germany), September 7--10, edited by B. Eckhardt, Springer Proc. Phys., Vol. 132 (Springer, Heidelberg, 2009) pp. 505--508Google Scholar
  55. 55.
    M. Martins Afonso, A. Mazzino, P. Muratore-Ginanneschi, Inertial-particle dispersion and diffusion, in Advances in Turbulence XIII, Proceedings of the 13th EUROMECH European Turbulence Conference 2011, Warsaw (Poland), September 12--15, 2011, edited by K. Bajer, J. Phys.: Conf. Ser., Vol. 318 (IOP Publishing Ltd, 2011) p. 052014Google Scholar
  56. 56.
    M. Martins Afonso, J. Phys. A 41, 385501 (2008)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    M. Martins Afonso, A. Mazzino, P. Muratore-Ginanneschi, J. Fluid Mech. 694, 426 (2012)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    H. Grad, Commun. Pure Appl. Math. 2, 325 (1949)CrossRefGoogle Scholar
  59. 59.
    P.K. Suetin, Classical Orthogonal Polynomials (Nauka, 1979)Google Scholar
  60. 60.
    P.K. Suetin, Orthogonal Polynomials in Two Variables, Vol. 3 (CRC Press, 1999)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Centro de Matemática da Universidade do PortoPortoPortugal

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