Accelerations of Snowflakes in Atmospheric Turbulence

We present results from the first coincident measurements of surface-layer turbulence with individual snowflake physical properties and their trajectories. Data were obtained at a high-elevation mountain location in Utah between October 2020 and April 2021. In addition to a sonic anemometer, several new instruments were deployed including a Differential Emissivity Imaging Distrometer (DEID), which provides precise estimates of hydrometeor mass, density, size, and terminal velocity (Singh et al. 2021 in review). In addition a particle tracking system was deployed that consisted of a laser sheet and SLR camera. The particle tracking system captured hydrometeor vertical motions at a framerate of 120 Hz. The light sheet was positioned directly above the DEID hotplate system. For measurement of the settling velocity of snow particles, both Particle Tracking Velocimetry and Particle Imaging Velocimetry techniques were used depending on precipitation intensity. These data were used to investigate the vertical accelerations of snow particles as a function of Stokes number (St), Reynolds number based on the Taylor microscale (Re$_{\lambda}$), and snow particle Reynolds number (Re). St varied from 0.11 to 5.0, Re$_{\lambda}$ ranged from 50 to 4000, and Re from 50 to 1400. We found a wide range of settling velocities (0.01 to 5.04 m s$^{-1}$) as well as terminal velocities ranging from (0.09 to 5.15 m s$^{-1}$) owing to the high variation in particle density (6 to 390 kg m$^{-3}$) and size (0.8 to 12.2 mm). It was found that the probability distribution function (pdf) of normalized settling acceleration of ensemble averaged snow particles follows an exponential distribution (exp(-3/2 a/a$_{rms}$)) with an exponent slope of -3/2, which is independent of St and Re$_{\lambda}$. Remarkably, the same distribution, with the same exponent slope and independence of conditions was found when variations in the actual measured particle settling velocity were replaced by temporal variations in the mean particle terminal velocity as captured by the DEID alone, and estimated using Bohm et al. (1998) aerodynamic formulations for relating particle physical properties to their terminal velocity. The coincidence is surprising but the implication appears to be that snowflake accelerations are determined more by variations in the atmospheric distribution of snow particles rather than turbulence effects on individual snow particles. That said, turbulence itself presumably plays a role in determining particle size distributions, and it remains to be determined how turbulence perturbs individual snowflake settling speeds. References: Singh, D. K., Donovan, S., Pardyjak, E. R., and Garrett, T. J.: A differential emissivity imaging technique for measuring hydrometeor mass and type, Atmos. Meas. Tech., 2021. Bohm, H. P., 1998: A general equation for the terminal fall speed of solid hydrometeors. J. Atmos. Sci., 46, 24192427.