TURBULENT MIXING OF CLOUD WITH THE ENVIRONMENT:TWO-PHASE EVAPORATING FLOW AS SEEN BY PARTICLE IMAGING VELOCIMETRY

Szymon P. Malinowski1 Piotr Korczyk2, Tomasz A. Kowalewski21Institute of Geophysics, University of Warsaw, Poland

2Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland.

1. INTRODUCTIONWe present new experimental results that

demonstrate influence of evaporative cooling and buoyancy fluctuations on the anisotropy of small-scale turbulence in clouds (c.f. (Andrejczuk et al.,2004), (Andrejczuk et al., 2006), (Korczyk et al.,2006), (Malinowski et al., 2008)). In these papers results of the numerical and laboratory experiments with small-scale turbulent mixing of cloud with unsaturated environmental air are discussed. The key findings indicate importance of small-scale fluctuations of buoyancy. These fluctuations are caused by evaporation of droplets mixing and from droplet sedimentation. Effecting buoyancy forces influence small-scale turbulence in clouds, making it anisotropic and more vigorous than expected.

The set-up of the experiments described here is designed to mimic basic aspects of small-scale turbulent mixing of a cloudy air with unsaturated environment. Thermodynamic conditions reconstructed in the chamber are, however, slightly different from those typical for clouds due to requirements of the visualization technique. Nevertheless, we believe that documented small-scale anisotropy of turbulent motions calls for the experiment investigating its role in natural conditions.

2. EXPERIMENTAL SETUPThe experimental setup is based on experiences

gathered in earlier attempts (Malinowski et al.,1998), (Jaczewski and Malinowski 2005), (Korczyket al., 2006). In the laboratory mixing takes place inside a cloud chamber of dimensions of 1.0 m ×1.0 m×1.8 m, (Figs 1 and 2 , for the detailed description consult (Korczyk et al., 2006) and (Korczyk 2008)).

Saturated and negatively buoyant cloudy plume (containing droplets of ~10 μm diameter) enters the chamber through the round opening in the ceiling. The initial velocity of the plume is about 20cm/s at the inlet, and it increases to about 30 cm/s in the middle of the chamber in response to the buoyancy forces. LWC in the plume is typically more than 10 g/kg --- somewhat higher than in natural clouds. The plume's temperature is about 25oC, close to the

temperature of the unsaturated chamber air. Relative humidity of the clear air inside the chamber varies from 20% to 65% for different experiments. The plume descends through the chamber while mixing with the environment, creating complicated continuously evolving structures (eddies, filaments, etc.).

Fig.1 Cloud chamber with the laser producing planar sheet of light and CCD cameras.

Fig.2. The principle of the visualization technique. A pulsed laser with the suitable optical system produces planar sheet of light. Light scattered by cloud droplets is imaged with the CCD camera.Droplet spectra at the inlet to the cloud chamber have been measured by a microscopic technique: droplets were collected on a glass plate covered with the silicone oil and imaged with the microscope. The data were processed with the algorithm allowing for determination of droplet diameters. Results, presented in Fig. 3 indicate that initial droplet spectrum is not atypical for natural clouds.

Fig.3 Initial droplet spectrum. Vertical axis: relative mass, horizontal axis – droplet radius [μm]

Illuminating the chamber interior with 1.2 mm thick sheet of laser light enables imaging in a planar cross section through the scene with a high-resolution CCD camera. An example image from the experiment, covering an area of 9×6 cm2, is presented in Fig 4.

Fig 4: The negative of the image from the experimental chamber showing small-scale structures created in a process of cloud-clear air mixing. Imaged area corresponds to 9×6 cm2 in physical space.

The image reveals fine structures created in the process of turbulent mixing of the cloud with its unsaturated environment. One pixel corresponds to 1.2 mm deep volume with about 69×69 μm2 area in the plane of the laser-light sheet. Such elementary volumes occupied by droplets are represented by dark pixels; bright pixels correspond to volumes void of droplets.

Pattern recognition in two consecutive images separated by a known time interval allows to retrieve two velocity components in the image plane. This technique, referred to as Particle Image Velocimetry (PIV) (Raffel 1998), is widely adopted in experimental fluid mechanics. An original, accurate multi-scale PIV algorithm was developed for this experiment (Korczyk et al., 2006), (Korczyk 2008).

First, it identifies motions of large structures, and then analyzes the displacements within the structures. Application of the algorithm allows estimating the two components of velocity vector with spatial resolution of about 0.07 mm; i.e., an order of magnitude smaller than the Kolmogorov length scale, the value of which was estimated from the measurements at approximately 0.76 mm. Fig. 5 shows an example pattern of droplets superimposed on the retrieved velocity vectors.

Fig. 5. Two components of velocity field retrieved by means of PIV technique. 3. RESULTS

The data were collected in a series consisting of 50 experiments, each subject to slightly different thermodynamic conditions inside the chamber. For each experiment, at least 100 pairs of frames (tens of thousands of velocity vectors in each frame) were analyzed, in order to retrieve statistical properties of velocity fluctuations.

3.1. Anisotropy of turbulent velocity fluctuationsExperimental probability distribution functions

(PDF) of the velocity fluctuations in horizontal (u') and vertical (w') directions are summarized in Table 1. It follows, that PDF of w' is wider than the PDF of u'. The derived kurtosis and skewness indicate that both distributions are close to Gaussian. The ratio of velocity variances =0.46±0.07 (a mean over all 50 experiments) is consistent with the numerical simulations, discussed in (Malinowski et al., 2008). Mean Taylor microscales, estimated independently for horizontal (λ1) and vertical (λ3) velocity components, are 7.5±0.4 mm and 9.2±0.6 mm, respectively. These values, obtained from measurements resolving smallest scales of the flow, also indicate anisotropy in agreement with results of numerical simulations ((Malinowski et al., 2008) and references therein).

Table 1. Distribution of horizontal (u') and vertical (w') turbulent velocity fluctuations. Average from 50 experiments.

Standard deviation [cm/s]

Skewness Kurtosis

u' 5.4 -0.01 3.2

w' 8.0 -0.2 3.1

Fig.6 Longitudinal (upper panel) and transversal (lower panel) 2nd order structure functions of horizontal (red) and vertical (green, dashed) turbulent velocity fluctuations evaluated from PIV measurements 70 cm from the inlet to the cloud chamber.

More on anisotropy can be inferred from presented in Fig. 6 structure functions of turbulent velocity fluctuations calculated according to the formulas:

Here superscripts II and ┴ denote longitudinal and transversal directions, respectively; u and w are horizontal and vertical turbulent velocity fluctuations in the plane of the image; x and z are horizontal and vertical coordinates in the image; means averaging over many scenes. We see a considerable differences between the structures

along and across the flow. In the whole range of scales investigated the most variable are the horizontal differences of the vertical velocity.

3.2. Effects of evaporative cooling and liquid phase load.

Anisotropy of small-scale turbulence in the laboratory experiments is most likely the result of evaporative cooling at the cloud-clear air interface, but the impact of the other buoyancy effects cannot be ruled out. This is corroborated by additional experiments using the same laboratory setup but with non-evaporating oil (DEHS) droplets replacing cloud water (Korczyk 2008) of spectrum presented Fig. 7. The observed ratio in these experiments was 0.86±0.02, suggesting non-negligible impact of the buoyancy oscillations, due to weight of oil droplets in “oil cloud” filaments, on the observed small-scale anisotropy.

Fig.7 Spectrum of DEHS droplets. Vertical axis: relative mass, horizontal axis – droplet radius.

In order to analyze the role of evaporative cooling of water droplets at the cloud-clear air interface on the buoyancy fluctuations consider mixing diagrams of cloudy air entering the chamber with the clear air of various relative humidities (RH, Fig. 8).

Fig. 8. Mixing diagrams (vertical axis: density temperature, horizontal axis – mixing proportion of cloudy air) for conditions in the cloud chamber.

The TKE dissipation rate ε is estimated with use of PIV measurements from the relation:

;

where ν is kinematic viscosity of the air.The amplitude between the maximum and the

minimum density temperature at given RH of the environmental air indicates the potential for buoyancy oscillations due to both effects: evaporative cooling and liquid water load. It follows, that for the conditions in the chamber the maximum buoyancy fluctuations are at low relative humidities, at which evaporative cooling (at high liquid water loads in the chamber) is most efficient. In such a case a systematic relation between the relative humidity (in the range 20%-50% at which potential for buoyancy fluctuations changes) and some parameters of turbulence should be measurable. Fig. 9 documents such systematic relation. The dependence of the TKE dissipation rate on the relative humidity of the environmental air is evident.

Another result documenting effect of evaporative cooling on the intensity of the small-scale turbulence is shown in Fig. 10. It presents 2nd order structure function of horizontal velocity fluctuations for experiments with different relative humidities of the environmental air. At low RH, at which contribution of evaporative cooling to buoyancy fluctuations has its maximum, structure function indicates large velocity differences. These differences decrease with increasing RH.

CONCLUSIONSResults presented here confirm that small scale

buoyancy fluctuations cause anisotropy of small scale turbulence. Two effects which contribute to these fluctuations are identified: evaporative cooling and uneven spatial distribution of droplets in cloud and clear air filaments (uneven distribution of liquid phase load).

Effect of evaporative cooling depends on the thermodynamical properties of cloud and clear air. Mixing diagram of shows the possible range of buoyancy fluctuations due to evaporative cooling. Increased range of buoyancy fluctuations results in more intense turbulence.

Effect of mass load, documented in experiments with non evaporating droplets, requires more investigations.

Third effect, additional transport of liquid water due to sedimentation of droplets (Andrejczuk et al.,2006) may contribute to first two: evaporative cooling and mass load. All effects combined cause, that small-scale turbulence in non-uniform cloud is anisotropic with the privileged direction in vertical.

Fig.9 Dependence of the relative humidity (horizontal axis) in the cloud chamber on the TKE dissipation rate estimated from PIV measurements. Consecutive plots show results of measurements at 50cm, 60cm and 70cm from the inlet to the cloud chamber.

Fig. 10. Longitudinal 2nd order structure function of u for varying relative humidities of the environmental air, measured 30 cm from the inletReferences:Andrejczuk, M., W.W. Grabowski, S.P. Malinowski and P.K.

Smolarkiewicz, 2004: Numerical simulation of cloud-clear air interfacial mixing. J. Atmos. Sci., 61, 1726-1739.

Andrejczuk, M., W.W. Grabowski, S.P. Malinowski and P.K. Smolarkiewicz, 2006: Numerical Simulation of Cloud-Clear Air Interfacial Mixing: Effects on cloud- microphysics. J. Atmos. Sci., 63, 3204-3225.

Korczyk, P.M., S.P. Malinowski and T.A. Kowalewski,2006: Mixing of cloud and clear air in centimeter scales observed in laboratory by means of particle image velocimetry. Atmos. Res., 82, 173-182.

Korczyk. P., 2008: Effect of cloud water on small-scale turbulence - laboratory model (in Polish), PhD thesis, IPPT, Polish Academy of Sciences.

Jaczewski. A. and S.P. Malinowski, 2005: Spatial distribution of cloud droplets investigated in a turbulent cloud chamber. Q. J. Roy. Meteorol. Soc,. 131, 2047-2062.

Malinowski. S.P., M. Andrejczuk, W.W. Grabowski, P.K. Korczyk, T.A. Kowalewski and P.K. Smolarkiewicz,2008: Laboratory and modeling studies of cloud-clear air interfacial mixing: anisotropy of small-scale turbulence due to evaporative cooling. New J. of Physics, accepted..

Malinowski, S.P., I. Zawadzki and P. Banat, 1998: Laboratory observations of cloud-clear air mixing in small scales. J. Atmos. Oceanic. Technol., 15, 1060-1065.

Raffel, M., Ch.E. Willert and J. Kompenhans, 1998: Particle image velocimetry: a practical guide. Springer.

1. INTRODUCTION2. EXPERIMENTAL SETUP3. RESULTS3.1. Anisotropy of turbulent velocity fluctuations3.2. Effects of evaporative cooling and liquid phase load.

CONCLUSIONS