Where are rainfall drops falling in a turbulent wind field ?

Weather radars measure rainfall in altitude whereas hydro-meteorologists are mainly interested in rainfall at ground level. During their fall, drops are advected by the wind which affects the location of the measured field. In this study, we investigate the fall of rain drops in a turbulent wind field between an height of 1500m and the ground.

The equation governing a rain drop motion relates the acceleration to the forces of gravity and buoyancy along with the drag force. The latter depends non-linearly on the instantaneous relative velocity between the drop and the local wind; which yields to complex behaviour. In this work, the drag force is expressed in a standard way with the help of a drag coefficient, which is itself determined according to a Reynolds number. Corrections accounting for the oblateness of drops greater than 1-2 mm are implemented. Such corrections are validated through comparison of retrieved “terminal fall velocity” (i.e. without wind) with commonly used relationships in the literature.

An explicit numerical scheme is implemented to solve this equation for 3+1D turbulent wind field, and hence analyse the temporal evolution of the velocities and trajectories of rain drops during their fall. Two types of wind inputs are used : (i) Four months of 100 Hz 3D sonic anemometers data. (ii) Numerical simulations of space-time varying wind carried out with the help of Universal Multifractals which are a framework that has been widely used to characterize and simulate geophysical fields extremely variable over a wide range of scales such as wind.

The behaviour of drop velocities is then characterized through temporal multifractal analysis. It notably enables to highlight a scale, depending on the drop size, below which turbulent eddies have a limited impact on their motion. Finally the dispersion on the ground of drops all starting at the same location is quantified and consequences on rainfall remote sensing with radars discussed.

 

Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for partial financial support.