Turbulence-cloud droplet interaction in cloud micro-physics - - PowerPoint PPT Presentation

Turbulence-cloud droplet interaction in cloud micro-physics simulator

Izumi Saito, Toshiyuki Gotoh, Takeshi Watanabe

Nagoya Institute of Technology, Nagoya, Japan

2018/07/09 15th Conference on Cloud Physics (2018/07/09-13)

This work is supported by: KAKENHI: 15H02218 HPCI: hp160085, hp170189 JHPCN: jh170013 JAMSTEC

2

〜1m aerosol

small ice crystals

cloud droplets

collision/ coalescence

rain drops

Turbulent Mixing

evap.

condensatjon

buoyancy

非一様分布 間欠性 よどみ点 渦 dry wet

Turbulence, Mixing, Transport, and Droplet dynamics

Spectral method＋Lagrangian dynamics

Collision/Coalescence T wo phase fmow : LBM

0.5 mm < r < 1m 1ms < t < 20 min.

Molecular dynamics

Cloud microphysics simulator

Low temperature High temperature Rayleigh- Benard Convection (Turbulence)

Chandrakar et al (2016、PNAS)（C16）

• Moist R-B convection （turb.）
• Aerosol injection at const. rate
• Condensation nucleation

→Condensation growth →Removal （⇒steady state）

Drop Diameter PDF

large small

C16: Statistical theory and experimental results

Langevin Model

Chandrakar et al (2016、PNAS)

System time scale

phase relax. time turb.

Purpose of the present study

• To compare DNS results with statistical

relationships proposed by Chandrakar et al. (2016, PNAS) for validation of our model.

Model configuration

Particle injection at constant rate Particle removal with residential time scale ⇒ Statistically steady state (External) supersaturation (Ss) fluctuation

PDF(Ss)

• Condensation growth/decay
• Lagrangian motion

PDF(r) Particle radius (r)

Governing equations for DNS

Force (Gaussian white) Aerosol effect

• Gravity
• Droplet inertia
• Collision
• Buoyancy

Liquid water + NaCl r=0.39 [μm] NaCl, r=50 [nm]

Injected aerosol particle： NaCl aq

0.39 [μm]

Parameters

Ss fluctuation without droplets Residential time scale Mean Ss in

• equilib. state

Box length RMS velocity Number of grids Integration time

(5 million steps)

Run Aerosol effect Injected particle radius [μm]

Mean radius [μm] Mean number density [/cm^3] Phase relax. time [s]

1 No 20 20 77 2.0 2 No 20 20 160 1.0 3 No 20 20 320 0.50 4 No 20 20 640 0.25 5 Yes 0.39 5.2 77 7.8 6 Yes 0.39 4.9 160 4.1 7 Yes 0.39 4.4 320 2.2 8 Yes 0.39 3.8 640 1.3

Experimental setups

Questions to be answered

• For DNS, is there a proper choice for τ_t (time scale representing

for turbulent mixing)? Yes. If so, is it equivalent to large-eddy turnover time, or velocity Lagrangian correlation time? No, but the difference is not so large (for our DNS results).

• What is a proper time scale for diffusion coefficient?

Lagrangian autocorrelation time for Ss.

• How aerosol effects could be included in theory?

By reflecting wall boundary condition (to a 1st approximation).

Brownian motion with reflecting wall Droplet growth in fluctuating Ss with aerosol effect How to include the aerosol effect in theory?

Siewert et al. 2017, JFM

(Steady state solution)

Steady state solution with source and sink

sink source turbulence Reflecting wall boundary condition: （＊ Factor 2 disappeared）

PDF for R Normalized PDF

Size distribution in steady state

Experimental results Theory

(Normalization)

Run 5

41 43 0.50 0.68 7.8

Run 6

37 38 0.45 0.63 4.1

Run 7

31 32 0.42 0.56 2.2

Run 8

24 26 0.38 0.47 1.3

Phase relaxation time scale System time scale Lagrangian autocorrelation time scale for Ss

Theory Exp. results

⇒Fairly good agreement

Summary

• Statistical relationships proposed by Chandrakar (2016, PNAS)

were carefully reexamined and used for validation of our DNS.

• There is a proper choice of τ_t in DNS, but it is slightly larger

(by about 25%) than the large-eddy turnover time.

• Scalar (supersaturation) Lagrangian autocorrelation time

should be used for time scale of diffusion coefficient.

• Aerosol effect can be included in theory by reflecting wall

boundary condition to a first approximation [consistent with Siewert et al. (2017, JFM) ].

• Theory and DNS results agree very well.

⇒ C16 statistical theory is useful also for DNS.