How To Calculate Turbulent Collision

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1 Impact of turbulent collisions on cloud development Ryo Onishi and Keiko Takahashi Earth Simulator Center (ESC), Japan Agency of Marine-Earth Science and Technology (JAMSTEC)

2 Turbulent collision kernel model

3 turbulent collision kernel model K c ( ) 2 r, r, l, u',re 2 π R w g( ) 1 2 η λ = r R R : collision radius (=r 1 +r 2 ) w r : radial relative velocity at contact g(r) : radial distribution function at contact St=0 St=0.2 St=1 St=4

4 DNS of particle suspended steady isotropic turbulence 2πL particles L 0 [m] Grid points Air turbulence : Re λ =36~83 ω + ( U ) ω = ( w ) U + ν 2 ω+ F t periodic BC (quasi-spectral method) forcing Water droplets : St=0.1~200 dv p U ( x p ) v p = dt τ p (Lagrangian tracking method)

01 96 3 Air turbulence : Re λ =36~83 ω + ( U ) ω = ( w ) U + ν 2 ω+ F t

5 construction of g(r) model

6 Model for g(r) in monodisperse system y 1 y 2 DNS y 1, y 2, y 3 with smoothing functions g(r) y St

7 g(r)-1 (=R g ) model results

8 Collision kernel model for monodisperse particles K c 2 = 2π R w g( R) (< Wr > is from Wang. et al. 2000) r DNS (Re λ =54) Wang et al. (Re λ =54) present model (Re λ =54) K c / λr St

2000) r 150 100 DNS (Re λ =54) Wang et al.

9 Collision kernel model for bi-disperse particles Turbulent contribution kernel g(r) for bi-disperse system g(r) for mono-disperse system in Zhou et al. (2001) Total kernel (turbulent & gravitational contributions)

system g(r) for mono-disperse system in Zhou et al.

10 Collision kernels for bi-disperse particles K c,total (r 1,r 2 ) / λ R Re λ =44.3 DNS present model hydrodynamic model DNS results present model Hydrodynamic kerne r 2 [μm] ( r 1 =30 [μm] )

11 Turbulent collision impact on cloud development

12 Multi-Scale Simulator for the Geoenvironment (MSSG) Applicable to global, regional and local scales seamlessly Ying-Yang grid for globe Consists of 3 modes; atmos. / ocean / coupled Highly optimized for the Earth Simulator (ES) global scale 1~10 km mesoscale 100m~5km urban scale 1m~100m

13 MSSG-Bin method (Hybrid-Bin method) Bulk method spectral Bin method for liquid water, and conventional Bulk method for solid water AP MSSG-Bin method 雲 water droplet 雨 Reisner et al. (1998) n p (r) mr [ kg/(m 3 unit ln r)] size distributions r [μm] mass doubling, 33 bins

14 Collision kernel models Hydrodynamic (Gravitational) Collision Kernel Model (No turbulent collisions) K c 2 ( r1, r2 ) = πr V ( r1 ) V ( r1 ) ( R : collision radius (=r 1 +r 2 ), V :settling velocity ) our Turbulent Collision Kernel Model (with turbulent collisions) K c 2 ( r1, r2, lη, u',reλ ) = 2πR wr g( R) w r : radial relative velocity at contact (Wang et al. 2000) g(r) : radial distribution function at contact (Onishi p.h.d thesis 2005)

Collision Kernel Model (with turbulent collisions) K c 2 ( r1, r2, lη, u',reλ ) = 2πR wr g( R) w r : radial

15 Algorithm for Explicit turbulent collision calculation MSSG Dynamics compressive N-S eq. (static Smagorinsky model) etc Flow turbulent statistics ε ε = SGS ( Cs Δ) 2 S 3 u' Δ S / 2 l η = ( ν 3 / ε ) 1/ 4 15 l = ν λ u' ε u'lλ Re λ = ν Microphysics(Bin method) collision growth condensation growth etc K c ( r, r2, l η, u',re 1 λ )

(static Smagorinsky model) etc Flow turbulent statistics ε ε = SGS ( Cs Δ) 2 S 3

16 RICO model intercomparison Initial data from Rain In Cumulus over the Ocean field campaign by GCSS Practical for investigating cloud microphysical processes white:q c >1e-5, blue:q r >3e-6 24-hour-simulation with MSSG-Bulk method km domain, Δ H =100m, Δ z =40m, Periodic B.C., 24 hours integration

processes white:q c >1e-5, blue:q r >3e-6 24-hour-simulation with MSSG-Bulk

17 extra 1-hour simulation for visualization (MSSG-Bulk) 1-hour-simulation with MSSG-Bulk method

18 RICO intercomparison participants model microphysics timestep [s] duration for 24h integration [h] MESO-NH 1st moment, Kessler SAM 1st moment 2 JAMSTEC 1st moment 1 Utah 1st moment? EULAG 1st moment? 2DSAM 1st moment? DALES 2nd moment, Nc fixed 1 UCLA 2nd moment, Nc fixed ~1.5 WVU 2nd moment, Nc fixed ~1.65 COAMPS 2nd moment? ??? 190 UKMO 2nd moment, Nc fixed ~ RAMS 2nd moment+ccn 2 weeks 2DHARMA bin model (33) ,000 RAMS@NOAA bin model (33) 2 5,400 SAMEX bin model?? MSSG-Bulk 1 st moment (2 nd for ice), Nc fixed ~ MSSG-Bin bin model (33) ~2.2 1, ? *yellow: Bulk models * blue: Bin models 3 bin models & 12 bulk models Ref: Margreet van Zanten, GCSS-GPCI/BLCI-RICO Workshop, NY, 2006

?? 190 UKMO 2nd moment, Nc fixed ~0.7 500 RAMS 2nd moment+ccn 2 weeks 2DHARMA bin model (33) 3.5 10,000 RAMS@NOAA bin model (33) 2 5,400 SAMEX bin model?

19 Mixing Ratios of Liquid Water (q l ) and Rain Water (q r ) (fresh AP on ground surface. CCN recycling and break-up are not included.) MSSG-Bin with Turb. Kc graphs from GCSS-BLC wg, RICO< Significant impact hydr&turb_case1-4.x33 of turbulent collisions is shown.

) MSSG-Bin with Turb. Kc graphs from GCSS-BLC wg, RICO<http://www.knmi.

20 surface precipitation in time Surface Precipitation [W/m hour averaging MSSG-Bin with KcHydr MSSG-Bin with KcTurb Time [hour]

10 0 4hour averaging MSSG-Bin with KcHydr

21 Concluding Remarks MSSG-Bin model with turbulent collision model reveals the importance of turbulent droplet collisions in cloud development. In RICO (shallow Cu) case, turbulent collisions significantly weaken the updraft, consequently decrease turbulence intensity due to quick removal of water lower the cloud height shorten the rain initiation time

Towards Multiscale Simulations of Cloud Turbulence

Towards Multiscale Simulations of Cloud Turbulence Ryo Onishi *1,2 and Keiko Takahashi *1 *1 Earth Simulator Center/JAMSTEC *2 visiting scientist at Imperial College, London (Prof. Christos Vassilicos)