Laboratory Measurements of Small Raindrop Distortion. Part 2: Oscillation Frequencies and Modes

Abstract

The oscillation frequencies and modes of small raindrops (1.04?1.54-mm diameter) were determined from laboratory experiments using water drops generated at terminal velocity at a fall distance sufficient for initial oscillations to damp out. Frequency information was obtained from fall streaks photographed in backscatter light near the primary and secondary rainbows. Streak data was interpreted with the aid of ray tracing through drops with spherical harmonic perturbations. Axis ratio data was used in conjunction with analyses of spherical harmonic perturbations to help determine the oscillation modes. Two frequencies were present in all drop sizes. The significant oscillation modes for smaller drops (1.04?1.30 mm) were the transverse modes of the fundamental and first harmonic, whereas the significant oscillation modes for larger drops (1.40?1.54 mm) were the axisymmetric mode of the fundamental and the transverse mode of the first harmonic. Primary resonance appears to be responsible for the transverse modes because of the match in frequencies between the forcing and response and because the spatial pattern of the eddy shedding would tend to force these modes. Secondary resonance would account for the axisymmetric mode in larger drops, since this mode is a subharmonic of the forcing frequency and there is no requirement for the forcing pattern to match the response. Our study shows that small raindrops oscillate as a resonant response to eddy shedding. The postulated oscillation modes are consistent with scatter and means found in the laboratory data and would produce the trends in axis ratios inferred for small raindrops from field studies (Goddard and Cherry; Chandrasekar et al.). Since the discovered secondary resonance does not require a good frequency match, eddy shedding also may be the cause of raindrop oscillations detected in the field studies for much larger sizes.