Particle Collisions in Turbulent Mixed-Phase Clouds

To numerically investigate collisions of small and heavy particles settling in a turbulent environment we introduced a new setup which mimics grid generated turbulence in wind tunnel experiments. Direct numerical simulations of the flow field are conducted. First, the motions of 43 million spherical particles in 20 size classes were tracked in the turbulent flow using a point particle model. Collision statistics were gathered at different turbulence intensities in the spatially decaying turbulence (Kunnen et al., Atmos. Res. 127 (2013) 8-21). We found that turbulence can largely increase the gravitation-induced collision probabilities. The collision statistics were validated against other simulations (e.g. Ayala et al., New J. Phys. 10 (2008) 075015) and an experimental study with the same setup (Bord\'as et al., New J. Phys. 15 (2013) 045010). For the latter comparison the large database of numerically determined collision kernels was cast into a fit function (Siewert et al., Meteorol. Z. (2013) under review). With respect to cloud micro-physics the setup was interpreted as water drops in turbulent clouds. The fit function for the collision kernel can be used to study the impact of turbulence on the droplet growth in warm clouds. E.g., currently simulations with the Lagrangian cloud model of Riechelmann et al. (New J. Phys. 14 (2012) 065008) are performed to study the effects of turbulence on cumulus clouds. However, in mid-latitudes the formation and evolution of precipitation is the result of a chain of processes taking place in mixed-phase clouds. Due to the coexistence of supercooled water drops and ice particles in such clouds much less is known about the influence of turbulence on the particles. This is mainly due to the variable and complex shapes of the ice particles depending on the temperature, the supersaturation, and their life time. In the early stage ice crystals often have the shape of hexagonal plates or needles. In theoretical and numerical studies these are commonly approximated by ellipsoids (Pruppacher and Klett (1997) Microphysics of Clouds and Precipitation). Hence, we extend our particle model to deal with ellipsoids. Depending on the turbulence intensity the ellipsoids preferentially align with the direction of gravity. This is due to the complex coupling of the air turbulence and the particle sedimentation which also causes preferential sweeping, i.e., the increase of the settling velocities due to turbulence (Siewert et al., Atmos. Res. (2013), http://dx.doi.org/10.1016/j.atmosres.2013.08.011). The coupling of the rotational with the translational degree of freedom via the orientation-dependent particle drag also leads to different collision probabilities. Comparing spherical and ellipsoidal particles at the same mass and volume we find that collisions of ellipsoids are considerably more likely to occur. Unequally orientated ellipsoids have different gravitation induced settling velocities and due to their inertia they can come in contact with each other featuring these large relative velocities. The drastically increased mean radial relative velocity of ellipsoids (β ≠ 1) compared to spheres (β = 1) can be seen in the figure at the bottom. We expect that these turbulent effects apply to all kinds of non-spherical particles since the condition of orientation-dependent settling velocities is generally fulfilled. We hope that with these findings we can contribute to the understanding of the role of cloud turbulence on aerosols and the micro-physical as well as the macro-physical properties of mixed-phase clouds.