However, in LES models the turbulence is resolved down to some filter scale. The sub-filter scale turbulence is needed to be modelled and parametrised. Now there are several sub-grid scale (SGS) models. The most commonly used SGS model was proposed by Smagorinski (1963) and Lilly (1966). The other approach in numerical modelling of turbulent air motion is direct numerical simulations (DNS). The principle advantage of DNS model is that the turbulence is completely resolved by numerically integrating the Navier-Stokes equations and no parameters are needed there. On the other hand, DNS model requires the number of grid cells, N, which is proportional to Reynolds number as N ~ Re9/4, i.e. N = 1018 for typical Reynolds number Re = 108. It makes DNS inoperative for modelling of atmospheric boundary layer. In turn, DNS can be considered as the ideal physical experiment in real atmospheric conditions, and it allows us to check a validity of SGS model and improve its parametrisation.

We use the high-order public domain code (Pencil-Code) which can be used both for DNS and for LES simulations. This is the open source PENCIL code, which implements a high order finite difference method for compressible hydrodynamic flows. The code is highly modular and comes with a large selection of physics modules. It is widely documented in the literature and has been used for many different application (Dobler et. al, 2006). Recently, a detailed chemistry module has been implemented, including an accurate description of all necessary quantities, such as diffusion coefficients, thermal conductivity, reaction rates (Babkovskaia et al., 2011). This module was well tested by using a commercial code (Chemkin) for calculations of a turbulent combustion process. Our new aerosol module, coupled to the PENCIL Code, is now prepared for calculating condensation dynamics of aerosol particles (Babkovskaia et al., 2015). In the simulations, the composition of the aerosol cores is assumed to be NaCl, which is a soluble aerosol and will dilute inside the droplets.

Originally, the PENCIL Code was developed for studying turbulent motions, so it is well suited for modelling the fluid mechanical processes in atmospheric clouds. Additionally, due to an accurate description of the chemistry, the PENCIL Code is a powerful tool for studying the aerosol dynamics in a turbulent medium with complicated chemical composition. The scientific goals for our model are to investigate the spatial distribution of aerosol particles, turbulent mixing of clouds with the environment and the influence of turbulence on aerosol dynamics (and vice versa).

**References (Publications from our group are highlighted in bold)**

**Babkovskai, N., Rannik, U., Phillips, V., Siebert, H., Wehner, B. and Boy, M.: A DNS study of aerosol and small-scale cloud turbulence interactions, Atmos. Chem. Pays., 16, 7889-7898, 2016.****Babkovskaia, N., Boy, M., Smolander, S., Romakkaniemi, S., Rannik, U. and Kulmala, M.: A study of aerosol activation at the cloud edge with high resolution numerical simulations. Atmospheric research 153, 49-58, 2015.**- Babkovskaia, N., Haugen, N., Brandenburg, A.: A high-order public domain code for direct numerical simulations of turbulent combustion. J. Comput. Phys., 230, 1-12, 2011.
- Dobler, W., Stix, M., Brandenburg, A.: Magnetic field generation in fully convective rotating spheres. Astrophys. J., 638, 336-343, 2006.
- The PENCIL Code, http://pencil-code.googlecode.com, 2001.
- Lilly, D.K.: The representation of small-scale turbulence in numerical simulation experiments. NCAR Manuscript, 281, 1966.
- Smagorinski, J.: General circulation experiments with the primitive equations, Mon. Wea. Rev., 91, 99–164, 1963.