Collisional droplet growth in a turbulent environment
by Tobias Bätge
Date of Examination:2023-07-25
Date of issue:2024-07-18
Advisor:Prof. Dr. Michael Wilczek
Referee:Prof. Dr. Michael Wilczek
Referee:Prof. Dr. Eberhard Bodenschatz
Persistent Address:
http://dx.doi.org/10.53846/goediss-10610
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Abstract
English
It is a long-standing problem to find the mechanisms how the onset of rain occurs as rapidly as observed in warm clouds. In the so-called size gap, where neither condensation nor gravitational settling can explain efficient growth, the collisions and coalescence of droplets enhanced by turbulence is believed to play an important role. The history of the flow experienced by particles governs their collisions. In particular, rare and highly intermittent structures inherent to turbulence can still dominate the overall collision rate. However, in theoretical studies of collision mechanisms, such as the sling effect or the lucky droplet on which we focus in this thesis, the effect of the flow history and intermittency has not been consistently quantified yet. The sling effect occurs when similar-sized inertial particles detach from the streamlines, leading to intersecting trajectories and collisions with high relative velocities. Lucky droplets denote statistical outliers that grow significantly faster than average droplets, decreasing the estimated duration until the onset of rain. For the quantification of the rate of sling events, we develop a quantitative criterion for sling events based on the velocity gradient history along particle paths. By combining theory and simulations, we show that the problem reduces to a one-dimensional localization problem as encountered in condensed matter physics. The reduction demonstrates that the smallest real eigenvalue of the velocity gradient tensor controls the creation of slings. We use fully resolved turbulence simulations to confirm our predictions and study the dependence on the Stokes number St, Reynolds number Reλ, and Froude number Fr or equivalently settling parameter Sv. We also estimate through extrapolations of our prediction to the parameter range relevant for typical clouds (St < 0.5, Sv < 10, and Reλ ∼ 103 − 104) that the rate of sling events at high Reynolds numbers increases an order of magnitude for small Stokes numbers. To estimate the effect of intermittency on lucky droplets, we investigate droplet growth for different conditions relevant to clouds in a joint computational and theoretical approach. We show that highly dissipative air parcels – present due to cloud intermittency – dominate the droplet growth. It is also those parcels where memory effects (due to correlations between consecutive collisions) can further accelerate the formation of lucky droplets. Thus, we show at the example of two key mechanisms, sling effect and lucky droplets, that intermittency could be a significant ingredient in the collisional growth of rain droplets. Accordingly, it may help to explain the bridging of the size gap.
Keywords: turbulence; particle-laden flows; computational fluid dynamics; cloud micro-physics; collision and coalescence
