Simulations of drop fall in a homogeneous isotropic turbulent flow

Abstract

Drop motion in a turbulent flow is studied using a model of homogeneous and isotropic turbulence. The model permits us to generate different realizations of the random velocity field component with given latitudinal and lateral correlation functions and a spatial structure which obeys the Kolmogorov theory. For the generation of the turbulent flow, the structure function of the flow in the form suggested by Batchelor was chosen. This function describes the spectrum of turbulence both in the viscous and inertial subranges. Numerous examples of drop tracks for drops of different size demonstrate a significant influence of turbulence on different aspects of drop (as well as ice and aerosol particle) motion. The tendency of drop tracks to collect along isolated paths is demonstrated. The existence of areas of two types within a turbulent flow is revealed. Drops (aerosol particles) tend to leave the areas of enhanced turbulent flow vorticity and curvature apparently due to their inertia. At the same time, drops tend to “avoid” these areas. Interlacing of the tracks of small drops attributed to different deviations from the velocity of the flow due to the difference in drop inertia is demonstrated. The formation of significant turbulence-induced drop velocity deviations from the air velocity is demonstrated. Some statistical characteristics of drop movement in a turbulent flow are studied using the Monte Carlo method. The analysis of the spectra of relative drop velocity fluctuations reveals a pronounced maximum at frequencies depending on the drop size. The maximum in the horizontal velocity deviation spectra moves from a highest frequency of 20 Hz for a 10 μm drop to about 0.1 Hz for a 500 μm drop. To evaluate the contribution of turbulence (inertia) effects as compared to the effect of gravity, the ratio of root-mean-square drop velocity deviation (induced by turbulence) to the still-air terminal velocity was calculated for a wide spectrum of drop sizes. This ratio reaches its maximum for the smallest drops. Inertial flow acceleration seems to be the main factor leading to the formation of drop velocity deviations from the air velocity. The maximum value of the acceleration for the case considered was greater than 7 g. Possible turbulence effects on the drop spectrum broadening and warm rain formation, generation of drop concentration inhomogeneity and formation of areas of enhanced ice concentration within clouds, time and space inhomogeneity of precipitation rate, in-cloud scavenging rate, and mechanisms of rain enhancement under cloud seeding are discussed.