3D trajectories and velocities of rainfall drops in a multifractal turbulent wind field
Résumé
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. The governing equation of a rain drop's motion relates the acceleration to the forces of gravity and buoyancy along with the drag force. It depends non-linearly on the instantaneous relative velocity between the drop and the local wind, which yields complex behaviour. Here, the drag force is expressed in a standard way with the help of a drag coefficient expressed as a function of the Reynolds number. Corrections accounting for the oblateness of drops greater than 1-2 mm are suggested and validated through a comparison of the retrieved "terminal fall velocity" (i.e. without wind) with commonly used relationships in the literature. An explicit numerical scheme is then implemented to solve this equation for a 3+1D turbulent wind field, and hence analyse the temporal evolution of the velocities and trajectories of rain drops during their fall. It appears that multifractal features of the input wind are simply transferred to the drop velocity with an additional fractional integration whose level depends on the drop size, and a slight time shift. Using an actual high-resolution 3D sonic anemometer and a scale invariant approach to simulate realistic fluctuations of wind in space, trajectories of drops of various sizes falling form 1500 m are studied. For a strong wind event, drops located within a radar gate in altitude during 5 min are spread on the ground over an area of the size of a few kilometres. The spread for drops of a given diameter is found to cover a few radar pixels. Consequences on measurements of hydrometeorological extremes that are needed to improve the resilience of urban areas are discussed.
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