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Electrohydrodynamic generation of atmospheric turbulence

Yuan Yao* and Jesse Capecelatro

  • Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48105, USA

  • *yyaoaa@umich.edu
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Phys. Rev. Fluids 4, 123701 – Published 18 December, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.123701

Abstract

Ionization produced by cosmic rays and atmospheric radioactivity creates charged short life-time aerosol droplets in the upper troposphere. Inhomogeneities in the spatial distribution of aerosol droplets lead to time-varying electric fields and space charge, which can often be amplified by more than three orders of magnitude in extreme conditions, such as thunderstorms. The nonlinear coupling between ionized air, charged aerosol droplets, and the background electric field can result in electrohydrodynamic body forces that augment atmospheric turbulence. In this paper, a theoretical and numerical study on the electrohydrodynamic generation of atmospheric turbulence under fair weather and thunderstorm conditions is presented. Linear stability shows that coupling between ionized air and a background electric field acts to increase turbulent kinetic energy (TKE) in the upper troposphere, albeit over long time durations. Direct simulations of charged droplets in homogeneous shear flow demonstrate a nonlinear feedback mechanism capable of accelerating the growth rate. Streamwise velocity gradients induce fluctuations in droplet concentration and electric potential, resulting in a body force that generates vertical velocity fluctuations. Pressure strain then transfers this energy to turbulent fluctuations in the streamwise direction and the process repeats. This feedback mechanism was found to augment TKE at late stages of the shear layer growth.

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References (62)

  1. B. A. Tinsley, R. P. Rohrbaugh, M. Hei, and K. V. Beard, Effects of image charges on the scavenging of aerosol particles by cloud droplets and on droplet charging and possible ice nucleation processes, J. Atmos. Sci. 57, 2118 (2000).
  2. F. Yu and R. P. Turco, From molecular clusters to nanoparticles: Role of ambient ionization in tropospheric aerosol formation, J. Geophys. Res.: Atmospheres 106, 4797 (2001).
  3. S. N. Tripathi and R. G. Harrison, Enhancement of contact nucleation by scavenging of charged aerosol particles, Atmos. Res. 62, 57 (2002).
  4. B. A. Tinsley, Scavenging of condensation nuclei in clouds: Dependence of sign of electroscavenging effect on droplet and CCN sizes, in Extended Abstracts, 14th Conference on Cloud Physics and Precipitation (ICCP, Bologna, Italy, 2004), pp. 248–252.
  5. M. J. Rycroft, S. Israelsson, and C. Price, The global atmospheric electric circuit, solar activity and climate change, J. Atmos. Sol. Terr. Phys. 62, 1563 (2000).
  6. D. Siingh, V. Gopalakrishnan, R. P. Singh, A. K. Kamra, S. Singh, V. Pant, R. Singh, and A. K. Singh, The atmospheric global electric circuit: An overview, Atmos. Res. 84, 91 (2007).
  7. W. A. Hoppel and S. G. Gathman, Charge transport through an aerosol cloud, J. Appl. Phys. 41, 1971 (1970).
  8. R. Bruinsma and S. Alexander, Theory of electrohydrodynamic instabilities in electrolytic cells, J. Chem. Phys. 92, 3074 (1990).
  9. G. Tomar, V. Shankar, A. Sharma, and G. Biswas, Electrohydrodynamic instability of a confined viscoelastic liquid film, J. Non-Newtonian Fluid Mech. 143, 120 (2007).
  10. P. Atten, F. M. J. McCluskey, and A. C. Lahjomri, The electrohydrodynamic origin of turbulence in electrostatic precipitators, IEEE Trans. Ind. Appl. IA-23, 705 (1987).
  11. E. M. Lifshitz and L. P. Pitaevskii, Physical kinetics (Pergamon Press, Oxford, 1981).
  12. A. V. Timofeev and B. N. Shvilkin, Drift-dissipative instability of an inhomogeneous plasma in a magnetic field, Soviet Phys. Usp. 19, 149 (1976).
  13. A. A. Galeev, S. S. Moiseev, and R. Z. Sagdeev, The theory of the stability of non-uniform plasma and anomalous diffusion, J. Nucl. Energy C 6, 645 (1964).
  14. M. Di Renzo and J. Urzay, Aerodynamic generation of electric fields in turbulence laden with charged inertial particles, Nat. Commun. 9, 1676 (2018).
  15. Y. Yao and J. Capecelatro, Competition between drag and Coulomb interactions in turbulent particle-laden flows using a coupled-fluid–Ewald-summation based approach, Phys. Rev. Fluids 3, 034301 (2018).
  16. A. U. Karnik and J. S. Shrimpton, Mitigation of preferential concentration of small inertial particles in stationary isotropic turbulence using electrical and gravitational body forces, Phys. Fluids 24, 073301 (2012).
  17. J. Lu, H. Nordsiek, E. W. Saw, and R. A. Shaw, Clustering of Charged Inertial Particles in Turbulence, Phys. Rev. Lett. 104, 184505 (2010).
  18. J. K. Eaton and J. R. Fessler, Preferential concentration of particles by turbulence, Int. J. Multiphase Flow 20, 169 (1994).
  19. S. Elghobashi and G. C. Truesdell, Direct simulation of particle dispersion in a decaying isotropic turbulence, J. Fluid Mech. 242, 655 (1992).
  20. P. J. Ireland, A. D. Bragg, and L. R. Collins, The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects, J. Fluid Mech. 796, 617 (2016).
  21. J. P. L. C. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, Experimental and numerical investigation of inertial particle clustering in isotropic turbulence, J. Fluid Mech. 600, 245 (2008).
  22. J. Chun, D. L. Koch, S. L. Rani, A. Ahluwalia, and L. R. Collins, Clustering of aerosol particles in isotropic turbulence, J. Fluid Mech. 536, 219 (2005).
  23. M. R. Maxey, The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields, J. Fluid Mech. 174, 441 (1987).
  24. L. P. Wang and M. R. Maxey, Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence, J. Fluid Mech. 256, 27 (1993).
  25. A. Aliseda, A. Cartellier, F. Hainaux, and J. C. Lasheras, Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence, J. Fluid Mech. 468, 77 (2002).
  26. P. J. Ireland, A. D. Bragg, and L. R. Collins, The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects, J. Fluid Mech. 796, 659 (2016).
  27. K. A. Browning, T. W. Harrold, and J. R. Starr, Richardson number limited shear zones in the free atmosphere, Q. J. R. Meteorol. Soc. 96, 40 (1970).
  28. A. A. Townsend, Excitation of internal waves in a stably-stratified atmosphere with considerable wind-shear, J. Fluid Mech. 32, 145 (1968).
  29. K. H. Lloyd, C. H. Low, and R. A. Vincent, Turbulence, billows and gravity waves in a high shear region of the upper atmosphere, Planet. Space Sci. 21, 653 (1973).
  30. P. Gualtieri, F. Picano, and C. M. Casciola, Anisotropic clustering of inertial particles in homogeneous shear flow, J. Fluid Mech. 629, 25 (2009).
  31. C. Nicolai, B. Jacob, and R. Piva, On the spatial distribution of small heavy particles in homogeneous shear turbulence, Phys. Fluids 25, 083301 (2013).
  32. M. H. Kasbaoui, D. L. Koch, G. Subramanian, and O. Desjardins, Preferential concentration driven instability of sheared gas–solid suspensions, J. Fluid Mech. 770, 85 (2015).
  33. R. G. Harrison and M. H. P. Ambaum, Enhancement of cloud formation by droplet charging, Proc. R. Soc. London A 464, 2561 (2008).
  34. L. Zhou and B. A. Tinsley, Production of space charge at the boundaries of layer clouds, J. Geophys. Res.: Atmospheres 112, D11203 (2007).
  35. J. M. Rosen, D. J. Hofmann, and W. Gringel, Measurements of ion mobility to 30 km, J. Geophys. Res.: Atmospheres 90, 5876 (1985).
  36. E. W. McDaniel and E. A. Mason, The Mobility and Diffusion of Ions in Gases (Wiley, New York, 1973).
  37. H. Volland, Atmospheric Electrodynamics (Springer-Verlag, New York, 1984).
  38. J. M. Schneider and P. K. Watson, Electrohydrodynamic stability of space-charge-limited currents in dielectric liquids. I. Theoretical study, Phys. Fluids 13, 1948 (1970).
  39. J. Wang, W. B. Rossow, and Y. Zhang, Cloud vertical structure and its variations from a 20-yr global rawinsonde dataset, J. Climate 13, 3041 (2000).
  40. J. C. Wyngaard and O. R. Coté, The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer, J. Atmos. Sci. 28, 190 (1971).
  41. L. Kelvin, Stability of fluid motion: Rectilinear motion of viscous fluid between two parallel plates, Philos. Mag. 24, 188 (1887).
  42. M. H. Kasbaoui, R. G. Patel, D. L. Koch, and O. Desjardins, An algorithm for solving the Navier–Stokes equations with shear-periodic boundary conditions and its application to homogeneously sheared turbulence, J. Fluid Mech. 833, 687 (2017).
  43. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Hydrodynamic stability without eigenvalues, Science 261, 578 (1993).
  44. E. R. Mansell and C. L. Ziegler, Aerosol effects on simulated storm electrification and precipitation in a two-moment bulk microphysics model, J. Atmos. Sci. 70, 2032 (2013).
  45. O. Desjardins, G. Blanquart, G. Balarac, and H. Pitsch, High order conservative finite difference scheme for variable density low Mach number turbulent flows, J. Comput. Phys. 227, 7125 (2008).
  46. J. Capecelatro and O. Desjardins, An Euler–Lagrange strategy for simulating particle-laden flows, J. Comput. Phys. 238, 1 (2013).
  47. L. Schiller and A. Naumann, A drag coefficient correlation, Ver. Deutsch. Ing. Zeitung 77, 318 (1935).
  48. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
  49. J. Lowell and A. C. Rose-Innes, Contact electrification, Adv. Phys. 29, 947 (1980).
  50. S. Matsusaka, H. Maruyama, T. Matsuyama, and M. Ghadiri, Triboelectric charging of powders: A review, Chem. Eng. Sci. 65, 5781 (2010).
  51. H. Grosshans and M. V. Papalexandris, Direct numerical simulation of triboelectric charging in particle-laden turbulent channel flows, J. Fluid Mech. 818, 465 (2017).
  52. X. Jin and J. S. Marshall, The role of fluid turbulence on contact electrification of suspended particles, J. Electrostatics 87, 217 (2017).
  53. T. Gebhardt and S. Grossmann, Chaos transition despite linear stability, Phys. Rev. E 50, 3705 (1994).
  54. A. Schmiegel and B. Eckhardt, Fractal Stability Border in Plane Couette Flow, Phys. Rev. Lett. 79, 5250 (1997).
  55. B. Gayen and M. Alam, Algebraic and exponential instabilities in a sheared micropolar granular fluid, J. Fluid Mech. 567, 195 (2006).
  56. P. Sagaut and C. Cambon, Homogeneous Turbulence Dynamics (Cambridge University Press, Cambridge, 2008).
  57. M. Malik, J. Dey, and M. Alam, Linear stability, transient energy growth, and the role of viscosity stratification in compressible plane Couette flow, Phys. Rev. E 77, 036322 (2008).
  58. K. M. Butler and B. F. Farrell, Three-dimensional optimal perturbations in viscous shear flow, Phys. Fluids 4, 1637 (1992).
  59. P. J. Schmid, Nonmodal stability theory, Annu. Rev. Fluid Mech. 39, 129 (2007).
  60. E. J. Hinch, Perturbation Methods (Cambridge University Press, Cambridge, 1991).
  61. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
  62. M. Malik, M. Alam, and J. Dey, Nonmodal energy growth and optimal perturbations in compressible plane Couette flow, Phys. Fluids 18, 034103 (2006).

Outline

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Phys. Rev. Fluids 4, 123701– Published 18 December, 2019
  • Received 5 February 2019
Article part of CHORUS
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