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Laboratory Measurements of Axis Ratios for Large Raindrops

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  • 1 Atmospheric Environment Section, Illinois State Water Survey, Champaign, Illinois
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Abstract

The oscillations of moderate to large raindrops are investigated using a seven-story fall column with shape data obtained from multiple-strobe photographs. Measurements are made at a fall distance of 25 m for drops of D = 2.5-, 2.9-, 3.6-, and 4.0-mm diameter, with additional measurements at intermediate distances to assess the role of aerodynamic feedback as the source of drop oscillations. Oscillations, initiated by the drop generator, are found to decay during the first few meters of fall and then increase to where the drops attained terminal speed near 10 m. Throughout the lower half of the fall column, the oscillation amplitudes are essentially constant. These apparently steady-state oscillations are attributed to resonance with vortex shedding.

For D = 2.5 and 3.6 mm, the mean axis ratio is near the theoretical equilibrium value, a result consistent with axisymmetric (oblate/prolate mode) oscillations at the fundamental frequency. For D = 2.9 and 4.0 mm, however, the mean axis ratio is larger than the theoretical equilibrium value by 0.01 to 0.03, a characteristic of transverse mode oscillations. Comparison with previous axis ratio and vortex-shedding measurements suggests that the oscillation modes of raindrops are sensitive to initial conditions, but because of the prevalence of off-center drop collisions, the predominant steady-state response in rain is expected to be transverse mode oscillations.

A simple formula is obtained from laboratory and field measurements to account for the generally higher average axis ratio of raindrops having transverse mode oscillations. In the application to light to heavy rainfall, the ensemble mean axis ratios for raindrop sizes of D = 1.5–4.0 mm are shifted above equilibrium values by 0.01–0.04, as a result of steady-state transverse mode oscillations maintained intrinsically by vortex shedding. Compared to the previous axis ratio formula based on wind tunnel measurements, the increased axis ratios for oscillating raindrops amount to a reduction of 0.1–0.4 dB in radar differential reflectivity ZDR, and an increase of about 0.5 mm for a reflectivity-weighted mean drop size of less than about 3 mm.

* Additional affiliation: Department of Atmospheric Sciences, University of Illinois, Urbana–Champaign, Urbana, Illinois.

Corresponding author address: Kenneth V. Beard, Department of Atmospheric Sciences, UIUC, 105 S. Gregory St., Urbana, IL 61801.

Email: k-beard@uiuc.edu

Abstract

The oscillations of moderate to large raindrops are investigated using a seven-story fall column with shape data obtained from multiple-strobe photographs. Measurements are made at a fall distance of 25 m for drops of D = 2.5-, 2.9-, 3.6-, and 4.0-mm diameter, with additional measurements at intermediate distances to assess the role of aerodynamic feedback as the source of drop oscillations. Oscillations, initiated by the drop generator, are found to decay during the first few meters of fall and then increase to where the drops attained terminal speed near 10 m. Throughout the lower half of the fall column, the oscillation amplitudes are essentially constant. These apparently steady-state oscillations are attributed to resonance with vortex shedding.

For D = 2.5 and 3.6 mm, the mean axis ratio is near the theoretical equilibrium value, a result consistent with axisymmetric (oblate/prolate mode) oscillations at the fundamental frequency. For D = 2.9 and 4.0 mm, however, the mean axis ratio is larger than the theoretical equilibrium value by 0.01 to 0.03, a characteristic of transverse mode oscillations. Comparison with previous axis ratio and vortex-shedding measurements suggests that the oscillation modes of raindrops are sensitive to initial conditions, but because of the prevalence of off-center drop collisions, the predominant steady-state response in rain is expected to be transverse mode oscillations.

A simple formula is obtained from laboratory and field measurements to account for the generally higher average axis ratio of raindrops having transverse mode oscillations. In the application to light to heavy rainfall, the ensemble mean axis ratios for raindrop sizes of D = 1.5–4.0 mm are shifted above equilibrium values by 0.01–0.04, as a result of steady-state transverse mode oscillations maintained intrinsically by vortex shedding. Compared to the previous axis ratio formula based on wind tunnel measurements, the increased axis ratios for oscillating raindrops amount to a reduction of 0.1–0.4 dB in radar differential reflectivity ZDR, and an increase of about 0.5 mm for a reflectivity-weighted mean drop size of less than about 3 mm.

* Additional affiliation: Department of Atmospheric Sciences, University of Illinois, Urbana–Champaign, Urbana, Illinois.

Corresponding author address: Kenneth V. Beard, Department of Atmospheric Sciences, UIUC, 105 S. Gregory St., Urbana, IL 61801.

Email: k-beard@uiuc.edu

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