Further results concerning rain drop axis ratios and canting angles from wind-tunnel and 2D video disdrometer measurements

There remain several issues concerning the recently reported (80-m fall) drop shape measurements (Thurai et al., 2007) and canting angle measurements (Huang et al., 2008) from the 2D-video disdrometer (2DVD; Schönhuber et al., 2008). One of them concerns the axis ratios of drops below 2 mm, and another concerns the distribution of canting angles. In this paper, we present measurements from the experimental wind-tunnel facility based in Mainz, Germany, which provide important information on these two issues. The wind-tunnel facility enables us to conduct experiments on raindrop oscillations of freely suspended water drops floating inside the wind-tunnel (with laminar flow) at their terminal velocities (Szakall et al., 2010).

Regarding the first issue, the resolution of the 2DVD (~ 0. 2mm) does not permit drop axis ratios to be determined with high accuracy for small drops (<2 mm); nevertheless, field measurements in natural rain using 2D video disdrometer has shown enhanced variation (amplitudes) of drop axis ratios in the range of 1.5-2 mm range (Thurai et al., 2009). Additionally, Beard et al. (1991) had found from their 20 m fall laboratory measurements that the drops in a slightly different diameter range, 1.4 to 1.6 mm, tended to exhibit very large oscillation amplitudes because of resonance with the eddy shedding frequency in this size range. To investigate this further, the wind-tunnel facility has been used to determine the oscillation modes, the mean axis ratios, and the oscillation amplitudes of water drops in the diameter range 0.8-1.5 mm. These have been derived from a detailed analysis of the temporal variation of the axis ratios recorded with a high speed digital video camera.

Over 200 sets of measurements were made and we present the range of axis ratios for drop diameters between 1 and 2.2 mm. However, there were difficulties in axis ratio measurements for drop diameters in the 1.4 to 1.6 mm range because these drops exhibited unusual fall trajectory of a spiral which made it difficult to keep the drops in focus for long-term (i.e. a few hundred milliseconds) time series measurements. This may be related to the resonance and large amplitude oscillations which as mentioned earlier was found by Beard et al. (1991) for a similar range of drop diameters. It was attributed to eddy shedding frequency exactly matching the natural oscillation frequency of these sized drops. From the time series data (mainly for the larger drops), it is possible to see the typical beat frequency which shows that there are more active fundamental oscillation modes, the (2,0) and the (2,1) mode. In the frequency domain, one can also see the fundamental frequency of the oscillations, however the frequencies are so close to each other that it is difficult to distinguish between the (2,0) and the (2,1) modes (35 Hz and 34 Hz respectively). If the area of drop images are analyzed in the frequency domain, some inference about the (2,2) mode can also be made, which should have a frequency of 30 Hz (Feng and Beard, 1991).

Concerning the second issue, i.e. drop canting, the same wind-tunnel time series measurements have been used to determine the temporal variation of the canting angle, and subsequently the frequency spectrum, for several large drop diameters (> 4mm). The canting angle at any given time is estimated by rotating the whole image of the drop, fitting a rectangle to it and seeking the minimum value of the axis ratio of the fitted rectangle. From the time variation of this angle, the spectrum of the canting angle is determined to ensure that the oscillation mode does not affect the estimated canting and vice-versa. Also determined from the temporal variations of the canting angle (for different drop diameters) are the corresponding histograms. Generally, the mode of the histogram was at 0 deg. For a 4.6 mm drop, the standard deviation was around 5 deg, although the angles ranged from -10 deg to +10 deg. These values are in good agreement with the canting angles determined from the 80 m fall experiment using 2D video disdrometer (but it is possible that the (2,1) mode contributes to the wide spectrum of the estimated canting angles from the wind-tunnel measurements). It also appears that the hypothesis of steady state orientation of rain drops inferred from the 2D video disdrometer is supported by the wind-tunnel data.

References:

Beard, K. V., R. J. Kubesh and H. T. Ochs, 1991: Laboratory measurements of small raindrop distortion. Part 1: Axis ratio and fall behavior. J. Atmos. Sci., 48, 698–710.

Feng, J. Q. and K. V. Beard, 1991: A perturbation model of raindrop oscillation characteristics with aerodynamic effects, J. Atmos. Sci., 49, 1856-1868.

Huang, G-J., V. N. Bringi, M. Thurai, 2008. Orientation Angle Distributions of Drops after 80 m fall using a 2D-Video Disdrometer, J. Atmos. Oc. Tech., 25, pp. 1717-1723.

Schönhuber, M., G. Lammer, and Randeu, W.L. 2008. The 2D-Video-Distrometer, Chapter 1 in “Precipitation: Advances in Measurement, Estimation and Prediction”, Michaelides, Silas (Ed.), Springer, 2008. ISBN: 978-3-540-77654-3, 2008.

Szakall, M, S. K. Mitra, K. Diehl, S. Borrmann, 2010: Shapes and oscillations of falling raindrops – A review. Atmos. Res. 97, 416-425.

Thurai, M, G-J. Huang, V. N. Bringi, W. L. Randeu, and M. Schönhuber, 2007: Drop shapes, model comparisons, and calculations of polarimetric radar parame-ters in rain. J. Atmos. Ocean. Tech ., 24, pp. 1019-1032.

Thurai,M, V. N. Bringi and P. T. May, 2009: Drop shape studies in rain using 2-D video disdrometer and dual-wavelength, polarimetric CP-2 radar measurements in south-east Queensland, Australia, Paper P13.16, 34th Conference on Radar Meteorology, Williamsburg, VA, Oct. 2009.