A Model Of A Homogeneous Isotropic Turbulent Flow And Its Application For The Simulation Of Cloud Drop Tracks

A model of a homogeneous isotropic turbulent flow is presented. The model provides different realizations of the random velocity field component with given correlation latitudinal and lateral functions and a spatial structure which obeys the Kolmogorov theory of homogeneous and isotropic turbulence. For the generation of the turbulent flow the structural function of the flow in the form suggested by Batchelor (Monin and Yaglom, 1975) was used. This function describes the spectrum of turbulence both in the viscous and inertial ranges. The isotropy and homogeneity of the velocity field of the model are demonstrated. The model is aimed at simulating the “fine” features of drop's (aerosol particles’) motion, such as the deviations of drops’ velocity from the velocity of the flow, detailed structures of drops’ tracks, related to drops’ (particles’) inertia. The model is intended also for the purpose of studying cloud drops’ and aerosol particles’ motion and their diffusional spreading utilizing the Monte Carlo methods. Some examples of drop tracks for drops of different size are presented. Drops’ tracks are very sophisticated, so that the relative position of drops falling initially from the same point can vary drastically. In some cases drops’ tracks diverge very quickly, in other cases all drops move within a turbulent eddy along nearly the same closed tracks, but with different speed. The concentration of drop tracks along isolated paths is found in spite of the existence of a large number of velocity harmonics. It is shown that drops (aerosol particles) tend to leave some areas of the turbulent flow apparently due to their inertia. These effects can possibly contribute to inhomogeneity of drops’ concentration in clouds at different spatial scales.