Fractal reconstruction of the subgrid scales in turbulence models in applications to cloud microphysics

Modelling of small-scale turbulence in the atmosphere play a significant role in improving our understanding of cloud processes, thereby contributing to the development of better parameterization of climate models. One of the important problems is related to the transport of cloud particles, their activation and growth, which are influenced by small-scale turbulence motions. The idea presented in this work is to use fractal interpolation to reconstruct structures which are typically not resolved in the Large Eddy Simulations (LES) of clouds. Known filtered values of velocities on LES are basis of the reconstruction. The reconstructed small scales depend on the stretching parameter d, which is related to the fractal dimension of the signal. In many previous studies, the stretching parameter values were assumed to be constant in space and time. We modify this approach by treating the stretching parameter as a random variable with a prescribed probability density function (pdf). This function can be determined from a priori analysis of numerical or experimental data and within a certain range of wavenumbers it has a universal form, independent of the Reynolds number. We show, such modification leads to improvement in terms of reconstruction of two-point statistics of turbulent velocities. Preliminary results of simulations with Lagrangian particles (superdroplets) in the reconstructed field show the fractal model properly mimics the turbulent mixing processes at subgrid scales.