EGU General Assembly 2020
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Simulating collisions of charged cloud drops in an ABC flow

Torsten Auerswald and Maarten Ambaum
Torsten Auerswald and Maarten Ambaum
  • University of Reading, Department of Meteorology, Reading, United Kingdom of Great Britain and Northern Ireland (

Calculating the electric force between cloud drops is not straightforward. Since water drops are conducting, the electric force is not just simply the force between point charges, but instead the charge in each drop induces an infinite number of image charges in the other drop. The effect of these image charges can cause the electric force between two like charged cloud drops to become attractive on very short distances, when only applying Coulomb's law would result in a repulsive force. The attractive effect of image charges could potentially increase the collision rate of cloud drops. Within the United Arab Emirates Rain Enhancement Program (UAE REP) we are investigating the potential for rain enhancement by charging clouds.

Simulating the behaviour of cloud drops is numerically very expensive. A large number of drops needs to be simulated to obtain stable collision statistics. Additionally, the drops move in a complex turbulent environment with eddies spanning several orders of magnitude in size. Simulating the turbulent flow alone is an expensive task. Because of the typical sizes of cloud drops, their motion is predominantly influenced by the smallest turbulent scales in the flow. Therefore, Direct Numerical Simulation (DNS) is necessary and used to simulate the influence of turbulent flow on drop motion. In this work, instead of using DNS, we use an ABC flow to simulate the turbulent effect on cloud drops. This simple approximation for the turbulent flow allows to simulate the drop motion using much less computational resources then needed by DNS and therefore, allows to include the very expensive effect of electrical drop charge in our simulation of colliding drops in a turbulent environment.

To investigate the effect of electrical charge on drop collisions, a Lagrangian particle code for the interaction of cloud drops is used. It calculates the motion of individual drops based on the aerodynamical force due to the ABC flow and the gravitational force and registers drop collisions from which collision statistics can be calculated. In the cloud model all drops carry positive charges. The effect of the electric force is calculated by an approximation which uses Coulomb's law for the effect of the point charges and an additional term to approximate the effect of image charges which produce an attractive force on short distance.

Results for the collision kernel with and without charge will be presented. The effect of the additional term to Coulomb's law will be shown for different drop sizes and drop charges. It will be discussed if the attractive force for like charged drops on short distances can lead to an enhancement in drop collisions and under which conditions the effect is the largest.

How to cite: Auerswald, T. and Ambaum, M.: Simulating collisions of charged cloud drops in an ABC flow, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12408,, 2020


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  • CC1: Comment on EGU2020-12408, Stefan Chindea, 05 May 2020

    Thank you for the presentation, I find the work really interesting.

    1) does your modelling allow for drops to coalesce? [if YES, have you seen how the population size changes with time?]

    2) What are the conditions at the boundary of your simulation space? (Can they be ignored when looking at the "bulk" of particles?)

    • AC1: Reply to CC1, Torsten Auerswald, 05 May 2020


      Regarding 1: Yes our model can consider coalescence. However in these simulations we did not let the drops merge because we wanted to keep the drop density constant. But we are planning to also conduct simulations where the drop size spectrum can develop in time.

      Regarding 2: We are using triple periodic boundary conditions for the motion of the drops.

      • CC2: Reply to AC1, Stefan Chindea, 05 May 2020

        Thank you for your prompt replies. May I ask one last question... 3) Does the simulation allow for a background EField to be applied? (if yes, have you noticed a significant impact on the collision rates linked to small signal changes to the background EF?)

        • AC2: Reply to CC2, Torsten Auerswald, 05 May 2020

          That is a good question. We have not looked at that yet. But that would be another interesting aspect to look at. Sorry that I can't give you any answer here.

  • CC3: Comment on EGU2020-12408, Miguel Teixeira, 05 May 2020


    I notice that your ABC flow field model is very simple. Does the velocity field have a time dependence? Does it include multiple spatial scales? I was wondering if sythetizing a more realistic flow using a slightly more complicated, but still computationally cheap technique, such as Kinematic Simulation of Turbulence, would have any useful impact on the results. This creates a turbulent velocity field that satisfies mass conservation and a prescribed energy spectrum. Do you think your results would be sensitive, for example, to the existence of multiple scales of motion?

    • AC3: Reply to CC3, Torsten Auerswald, 05 May 2020

      Our flow model is very simple indeed. The ABC flow is stationary and consists of only one scale. But ABC flow is known to create chaotic trajectories for particles, and since it is an analytical solution of the Euler equation (unlike synthetic turbulence) it represents a physical flow and is very easy to implement. It is true that synthetic turbulence captures some aspects of real turbulence better (e.g. energy spectrum and instationarity). But many important features of real turbulence can't be captured by them either (e.g. higher moments, for Fourier methods the phase is random, in many cases intermittency is missing).

      We have not checked how the drop collision statistics change when using synthetic turbulence. It could be that some aspects would be improved (e.g. instationarity should improve the Radial Distribution Function according to Kunnen et al. 2013). But we compared our collision statistics from the ABC flow (without electric charge) to results from DNS and found that our collision kernels are very similar. So we think that for the purpose of studying an isolated microphysical process, like the electric charge, the ABC flow should provide reliable results. Of course, if the interaction with the turbulent flow is in focus, synthetic turbulence methods or DNS would be suited better.

      So the short answer would be: Synthetic turbulence would probably improve the simulation in some aspects but we found that for our purpose the ABC flow is very good and cheaper.

      Regarding the impact of more turbulence scales: I think that it would have an impact if we would use a larger range of drop sizes. Our comparison with DNS has shown that for the drop size range from 10 to 60 µm one scale seems to be sufficient. But I think the larger the size range the more important it is to have a turbulent flow with more scales.

      But it would definitely be interesting to see how different features of the flow would change the collision statistics.