Abstract
Evolution of droplets and turbulence in a small box which is ascending inside the maritime cumulus cloud has seamlessly been simulated for about 10 min from the view point of the microscopic dynamics. It is found that the kinetic energy spectrum obeys the Kolmogorov spectrum \(k^{-5/3}\) at low to moderate wavenumbers, while the spectra of the temperature and the water vapor mixing ratio are modified, close to \(k^{-1/3}\) at low wavenumbers and roll off more slowly than the exponential in the diffusive range. This modification of the spectra arises from the condensation-evaporation and the liquid water mass loading to the flow. It is also found that the spectra related to the cloud droplets consist of two contributions, one is from the spatially correlated part and the other is from the uncorrelated part which originates from the discreteness of droplets. The former dominates the spectrum at low to moderate wavenumbers and the latter at high wavenumbers. We argue the effects of the two contributions on the turbulence spectra.
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References
Ayala, O., Rosa, B., Wang, L.-P., Grabowski, W.W.: Effects of turbulence on the geometric collision rate of sedimenting droplets: Part 1. Results from direct numerical simulation. New J. Phys. 10, 075015 (2008)
Devenish, B.J., Bartello, P., Brenguier, J.-L., Collins, L.R., Grabowski, W.W., IJzermans, R.H.A., Malinowski, S.P., Reeks, M.W., Vassilicos, J.C., Wang, L.-P., Warhaft. Z.: Droplet growth in warm turbulent clouds. Q. J. R. Meteorol. Soc. 138, 1401–1429 (2012)
Falkovich, G., Fouxon, A., Stepanov, M.G.: Acceleration of rain initiation by cloud turbulence. Nature 419, 151–154 (2004)
Gotoh, T., Suehiro, T., Saito, I.: Continuous growth of cloud droplets in cumulus cloud. New J. Phys. 18, 043042 (2016)
Grabowski, W.W., Wang, L.-P.: Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293–324 (2013)
Hall, W.D.: A detailed microphysical model within a two-dimensional dynamic framework: model description and preliminary results. J. Atmos. Sci 37, 2486–2507 (1980)
Landau, L.D., Lifshitz, E.M.: Statistical Physics. Third edition, Part 1, volume 5. Pergamon, Oxford, 1980
Onishi, R., Matsuda, K., Takahashi, K.: Lagrangian tracking simulation of droplet growth in turbulence? Turbulence enhancement of autoconversion rate. J. Atmos. Sci. 72, 2591–2607 (2015)
Rosa, B., Parishani, H., Ayala, O., Grabowski, W.W., Wang, L.-P.: Kinematic and dynamic collision statistics of cloud droplets from high-resolution simulations. New J. Phys. 15, 045032 (2013)
Saito, I., Gotoh, T.: Turbulence and cloud droplets in cumulus clouds. New J. Phys. 20, 023001 (2018)
Sardina, G., Picano, F., Brandt, L., Caballero, R.: Continuous growth of droplet size variance due to condensation in turbulent clouds. Phys. Rev. Lett. 115, 1–5 (2015)
Shaw, R.A.: Particle-turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183–227 (2003)
Sundaram, S., Collins, L.R.: Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109 (1997)
Sundaram, S., Collins, L.R.: A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379, 105–143 (1999)
Takahashi, T.: Warm rain development in a three-dimensional cloud model. J. Atmos. Sci. 71, 1991–2013 (1981)
Vaillancourt, P.A., Yau, M.K., Grabowski, W.W.: Microscopic approach to cloud droplet growth by condensation. Part 1: model description and results without turbulence. J. Atmos. Sci. 58, 1945–1964 (2001)
Vaillancourt, P.A., Yau, M.K., Bartello, P., Grabowski, W.W.: Microscopic approach to cloud droplet growth by condensation. Part II: turbulence, clustering, and condensational growth. J. Atmos. Sci. 59, 3421–3435 (2002)
Wang, P.K.: Physics and Dynamics of Clouds and Precipitation. Cambridge University Press, Cambridge (2013)
Acknowledgements
This research used the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science, through the High Performance Computing Infrastructure (HPCI) System Research Project (hp160085, hp170189). The computational supports provided by Japan High Performance Computing and Networking, Large-scale Data Analyzing and Information Systems (JHPCN) (jh160012, jh170013), by High Performance Computing (HPC 2016) at Nagoya University and by “Plasma Simulator” under the auspices of the NIFS Collaboration Research program (NIFS16KNSS076) are also gratefully acknowledged. Development of some numerical codes used in this work was supported in part by the “Code development support program” of Numerical Simulation Reactor research Project (NSRP), NIFS. I. S. and T. G. and T. W. are supported by Grants-in-Aid for Scientific Research Nos. 15H02218, 26420106, respectively, from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan.
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Saito, I., Gotoh, T., Watanabe, T. (2019). Cloud Turbulence and Droplets. In: Gorokhovski, M., Godeferd, F. (eds) Turbulent Cascades II. ERCOFTAC Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-12547-9_19
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DOI: https://doi.org/10.1007/978-3-030-12547-9_19
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