Towards Multiscale Simulations of Cloud Turbulence

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1 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) International MetStorm Conference 9 June, 2011 ***Some figures and slides are removed from original talk***

2 MSSG (Multi-Scale Simulator for the Geoenvironment) High-resolution cloud simulations (LES) with MSSG-Bin microphysical scheme Turbulent collisions of droplets RICO DNS for colliding droplets in high-re flows Our numerical schemes validation of turbulent collision models

Turbulent collisions of droplets RICO DNS for colliding droplets in

3 Earth Simulator Mar Sept Processors : 5,120 (640 nodes) Peak performance 40 TFLOPS Main memory 10 TB Earth Simulator 2 Mar Processors : 1,280 (160 nodes) Peak performance 131 TFLOPS Main memory 20 TB 3

4 global scale 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) mesoscale urban scale 4

6 Observation (CMAP, JJA) MSSG-A (Δ H =40 km, 32 levels, 5yrs ave-jja) **skip** precipitation at JJA

7 NICAM-7km (Miura et al., 2008) observation (TRMM 3B42) 5[m/s] 5[m/s] MSSG-10km 30 days from Dec 15, [m/s] 7

8 Δ H =2.7 km, 72 layers MSSG result is operationally provided to

9 turbulence (large-eddy) resolving mesoscale simulation

10 Yin-Yang system for global simulations lat-long system for regional simulations Ref. Kageyama & Sato (2004)GGG Baba et al. (2010)MWR

11 MSSG-Bulk model (Reisner et al. (1998) with modification by Thompson (2004))

12 purely spectral-bin scheme for warm clouds MSSG-Bin model (Onishi & Takahashi, submitted) 12

13 Stochastic Collision Equation (SCE) n p (r ) 1 r = K ( r ' ', r ' ) n ( r ' ' ) n ( r ' ) dr ' K c (r, r ' )n p (r )n p (r ' )dr ' c p p 0 0 t 2 col Collision kernel Gravitational (Hydrodynamic) Collision Kernel (No turbulent collisions) K c (r1, r2 ) = πr 2 V (r1 ) V (r1 ) ( R : collision radius (=r1+r2), V :settling velocity ) Turbulent Collision Kernel wr : radial relative velocity at contact (Wang et al. 2000) g(r) : radial distribution function at contact (Onishi 2005, Onishi et al etc )

) = πr 2 V (r1 ) V (r1 ) ( R : collision radius (=r1+r2), V :settling velocity ) Turbulent Collision Kernel wr : radial

14 MSSG Dynamics compressive N-S eq. (static Smagorinsky model) etc Flow turbulent statistics ε ε = SGS ( Cs ) 2 3 S u' S / 2 local isotropy 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

15 Field campaign for shallow cumulus developing over the ocean near the Barbuda islands (18.0N;61.5W). projects/rico/

16 init. vert. prof. 24h simulation withδx=δy=100m, Δz=40m 4 U 4km 3 V z [km] periodic B.C km km U, V[m/s] Heat flux: wθl=-ch* U *(θl-sst*(p0/p)(rd/cp)) Water vapor flux: wqt=-cq* U *(qt-qsat(tsfc)) Momentum flux: uw=-u*cm* U vw=-v*cm* U where Cm= Ch = Cq = z [km] z [km] 3 surface fluxes qv[g/kg] θ[k] 320

8km -10-5 U, V[m/s] 4 4 3 Heat flux: wθl=-ch* U *(θl-sst*(p0/p)(rd/cp)) Water vapor flux:

17 Δx=100m 1-hour-simulation with MSSG-Bulk method (for visualization)

18 Δx=100m Bulk scheme Bin scheme (r>40μm droplets are recognized as rain drops) Clouds distribute uniformly in Bulk simulation (w/o CCN), while rather patchily in Bin simulation (with CCN).

19 projects/rico/

20 Earth Simulator Center 20

21 Cloud simulation using MSSG-Bin scheme Earth Simulator Center Δ H =25m, Δ V =20m 512x512x200 grids 33 bins 3D Mie scattering

22 Earth Simulator Center

23 MSSG-Bin with Turb. Kc Significant hydr&turb_case1-4.x33 impact of turbulent collisions

24 Applicability of the turbulent collision model has not been confirmed. Re λ =10 3~4 in cumulus clouds, while available DNS data is for Re λ <10 2. We need DNS data for high Re λ.

25 >Our numerical schemes >Validation of turbulent collision models

26 St R : collision radius (=r1+r2) wr : radial relative velocity at contact g(r) : radial distribution function at contact preferential distribution St=0 St=0.2 St=1 St=4

27 Paper name Wang et al.(2000)jfm fluid cell- paralle calculat index liza- Reλ,max ion method tion PSM w 75.4 Reade&Collins(2000)PF PSM Zhou et al.(2001)jfm PSM w - 58 Ayala et al.(2007)jcp PSM w shared 72.4 Ayala et al.(2008)njp PSM w shared 72.4 Wang et al.(2008)njp PSM w shared 72.4 Woittiez et al.(2009)jas FDM Onishi et al.(2009)pf PSM w/o shared 68.4 Flow: Euler Particle: Lagrange Table 1 Review of recent studies on collision frequencies of inertia particles in stationary isotropic turbulence. Pseudo-Spectral Model (PSM) has been used for flow! 27

28 Steady isotropic air turbulence: Finite-Difference Model (FDM) 4 th -order conservative scheme (Morinishi et al. (1998)JCP) MPI, i.e., distributed-memory parallelization, for 3D domain decomposition RCF(Reduced-Communication Forcing) to attain a stationary state (Onishi et al. (2011)JCP) Particle motion: Lagrangian tracking method Cell-index method for efficient collision detection MPI for 3D domain decomposition 3D domain decomposition Cell-index method (Allen & Tildesley (1987))

29 Flow simulation Flatness factor: F = ( u 1 x 1 ) 4 ( u 1 x 1 ) 2 2 Flow & Particle simulation Performance on ALTIX for 260,000 droplets in grids 10 7 Present code (N256) 10 6 Peak Performance 10% of Peak Performance MFLOPS Reliable & Fast 10 3 Good parallel performance Number of cores Present FDM is estimated to be x3.8 faster than conventional PSM (not shown here). REF:Onishi et al. (2011)JCP

30 Re λ = grids, 50million particles newly obtained data appears in the contribution paper? Collision data for Re λ ~540 ( grids, billion particles) is obtainable on ES2

31 g(r) St 2 St<<1 CASE-1 (Re λ =36) CASE-2 (Re λ =44) CASE-3 (Re λ =54) CASE-4 (Re λ =83) St 10 Problem: (g(r) - 1) / (Re λ St -2 ) g(2r) for St= is in between St~1 CASE-1 (Re λ =36) CASE-2 (Re λ =44) CASE-3 (Re λ =54) CASE-4 (Re λ =83) St St<<1 and St~1, and parameterized fully-empirically. (g(r) - 1) / (Re λ St -1 ) 1/ St >>1 CASE-1 (Re λ =36) CASE-2 (Re λ =44) CASE-3 (Re λ =54) CASE-4 (Re λ =83) St Empirical, but with some physical support 31

32 MSSG (Multi-Scale Simulator for the Geoenvironment) Non-hydrostatic atmos-ocean coupled model Yin-Yang grid High-resolution cloud simulations (LES) with MSSG- Bin scheme useful to see the turbulence role in clouds Δ=25m simulations are feasible on the ES2 DNS for colliding droplets in high-re flows useful to check the applicability of turbulent collision models to cloud turbulence with Re λ =10 3~4 Data for up to Re λ =340 has been obtained, and one for Re λ =540 is coming. -These atmos. flows have energy scales L of O(1m). Turbulence models validated by the DNS for L=O(10m) will strengthen the Δ=O(10m) cloud simulations, on O(10 PFLOPS) supercomputers!

How To Calculate Turbulent Collision

How To Calculate Turbulent Collision 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) Turbulent collision kernel