Cloud physics

Droplet evaporation

Turbulence affects how small water droplets grow and shrink in turbulent clouds. The size distribution the water droplets in ice-free clouds determines their radiative properties, a significant source of uncertainty in weather and climate models.  Evaporation and turbulent mixing cause a cloud to display large variations in droplet-number density, but quite small variations in droplet size. Yet direct numerical simulations of the joint effect of evaporation and mixing near the cloud edge predict quite different behaviors, and it remains an open question how to reconcile these results with the experimental findings.

To  infer the history of mixing and evaporation from observational snapshots of droplets in clouds is challenging  because clouds are transient systems.  We formulated a  statistical model that allows to infer important aspects of the history  of  observed droplet populations, highlighting the key mechanisms at work, and explaining the differences between observations and simulations.

[1] Key parameters for droplet evaporation and mixing at the cloud edge
J Fries, G Sardina, G Svensson & B Mehlig, Quarterly Journal of the Royal Meteorological Society 147 (2021) 2160-2172

Alignment of ice crystals settling in turbulent clouds

Small ice columns and platelets settling through quiescent cloudy air tend to align so that they fall with their broad sides down. In cirrus clouds, ice platelets can be very well aligned, the fluctuations of the crystal orientation with respect to the horizontal can be less than a few degrees. Baran (2012) points out that that aligned ice crystals affect the way in which clouds reflect radiation. High-altitude cirrus clouds tend to contain large ice mass. When such clouds cover a non-negligible part of the Earth's atmosphere, ice-crystal alignment could affect its radiation balance, but the magnitude of this effect remains to be understood.

One difficulty is that turbulence randomises the crystal orientations to some extent. How large is this effect? This depends not only on turbulence intensity, but also on the crystal size. Larger crystals settle more rapidly so that fluid-inertia effects matter more, and the dynamics of larger particles becomes inertial. We formulated a statistical model that incorporates these effects and allows to compute the width of the orientation distribution - in good agreement with results based on direct numerical simulations of turbulence.

The model allows to identify  different asymptotic parameter regimes. Estimations of parameter values for ice crystals in turbulent clouds show that they cover several of the identified regimes. The theory predicts how the degree of alignment depends on particle size, shape and turbulence intensity, and that the strong horizontal alignment of small crystals is only possible when the turbulent energy dissipation is weak.

[1] Experimental validation of fluid-inertia models for a cylinder settling in a quiescent flow
F Cabrera, MZ Sheikh, B Mehlig, N Plihon, M Bourgoin, A Pumir & A Naso, preprint arXiv:2107.05918

[2] Effect of particle inertia on the alignment of small ice crystals in turbulent clouds
K Gustavsson, MZ Sheikh, A Naso, A Pumir & B Mehlig, Journal of the Atmospheric Sciences (2021)

[3] Inertial torque on a small spheroid in a stationary uniform flow
F Jiang, L Zhao, HI Andersson, K Gustavsson, A Pumir, & B Mehlig, Physical Review Fluids 6 (2020) 024302

[4] Importance of fluid inertia for the orientation of spheroids settling in turbulent flow
M Zubair Sheikh, K Gustavsson, D Lopez, E Leveque, B Mehlig, A Pumir, & Aurore Naso, J. Fluid Mechanics 886 (2020) A9

[5] Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence
K Gustavsson, MZ Sheikh, D Lopez, A Naso, A Pumir & B Mehlig, New Journal of Physics 21 (2019) 083008

[6] Statistical model for the orientation of nonspherical particles settling in turbulence
K Gustavsson, J Jucha, A Naso, E Lévêque, A Pumir & B Mehlig, Physical Review Letters 119 (2017) 254501
(This model does not take into account the effect of fluid inertia.)

A stochastic model for growth histories of cloud droplets

Collisional and condensational growth of droplets in turbulence is difficult to simulate on a computer from first principles, because a large range of spatial scales must be resolved. In collaboration with the astrophysics group at NORDITA we analysed an approximate numerical method to simulate droplet growth in turbulence, the so-called super-particle method. Instead of following indivdual droplets through the flow, several droplets are subsumed into super droplets.  A stochastic model is used to determine which of the droplets inside two approaching super droplets collide.

Our analysis indicates that the model describes the stochastic collisional growth of ensembles of droplets in quiescent air reliably. Turbulent fluctuations are represented qualitatively. Under which circumstances the model works quantitatively remains an open question.

[1] Fluctuations and growth histories of cloud droplets: superparticle simulations of the collision-coalescence process
XY Li, B Mehlig, G Svensson, A Brandenburg & NEL Haugen, preprint arXiv:1810.07475

[2] Condensational and collisional growth of cloud droplets in a turbulent environment
XY Li, A Brandenburg, G Svensson, NEL Haugen, B Mehlig & I Rogachevskii, Journal of the Atmospheric Sciences 77 (2020) 337-353

[3] Effect of turbulence on collisional growth of cloud droplets
XY Li, A Brandenburg, G Svensson, NEL Haugen, B Mehlig, I. Rogachevskii, Journal of the Atmospheric Sciences 75 (2018) 3469-3487