We use a novel experimental setup to obtain the vertical velocity and acceleration statistics of snowflakes settling in atmospheric surface-layer turbulence, for Taylor microscale Reynolds numbers ( ) between 400 and 67 000, Stokes numbers (St) between 0.12 and 3.50, and a broad range of snowflake habits. Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of St. Ensemble-averaged snowflake root mean square (rms) accelerations scale nearly linearly with St. Normalized by the rms value, the acceleration distribution is nearly exponential, with a scaling factor for the (exponent) of −3/2 that is independent of and St; kurtosis scales with , albeit weakly compared to fluid tracers in turbulence; gravitational drift with sweeping is observed for St < 1. Surprisingly, the same exponential distribution describes a pseudo-acceleration calculated from fluctuations of snowflake terminal fall speed in still air. This equivalence suggests an underlying connection between how turbulence determines the trajectories of particles and the microphysics determining the evolution of their shapes and sizes.
REFERENCES
1.
J. H. E.
Cartwright
and
O.
Piro
, “
The fluid mechanics of poohsticks
,” Phil. Trans. R. Soc. A
378
, 20190522
(2020
).2.
M.
Yudine
, “
Physical considerations on heavy-particle diffusion
,” Adv. Geophys.
6
, 185
–191
(1959
).3.
G.
Csanady
, “
Turbulent diffusion of heavy particles in the atmosphere
,” J. Atmos. Sci.
20
, 201
–208
(1963
).4.
M. R.
Maxey
and
J. J.
Riley
, “
Equation of motion for a small rigid sphere in a nonuniform flow
,” Phys. Fluids
26
, 883
–889
(1983
).5.
G.
Good
,
P.
Ireland
,
G.
Bewley
,
E.
Bodenschatz
,
L.
Collins
, and
Z.
Warhaft
, “
Settling regimes of inertial particles in isotropic turbulence
,” J. Fluid Mech.
759
, R3
(2014
).6.
L.
Pan
,
P.
Padoan
,
J.
Scalo
,
A. G.
Kritsuk
, and
M. L.
Norman
, “
Turbulent clustering of protoplanetary dust and planetesimal formation
,” Astrophys. J.
740
, 6
(2011
).7.
H.
Wang
and
J. N.
Harb
, “
Modeling of ash deposition in large-scale combustion facilities burning pulverized coal
,” Prog. Energy Combust. Sci.
23
, 267
–282
(1997
).8.
D. E.
Aylor
, “
The role of intermittent wind in the dispersal of fungal pathogens
,” Annu. Rev. Phytopathol.
28
, 73
–92
(1990
).9.
A.
Tohidi
, “
Experimental and numerical modeling of wildfire spread via fire spotting
,” Ph.D. thesis (
Clemson University
, 2016
).10.
R. M.
Williams
, “
A model for the dry deposition of particles to natural water surfaces
,” Atmos. Environ.
16
, 1933
–1938
(1982
).11.
J. T.
Turner
, “
Zooplankton fecal pellets, marine snow, phytodetritus and the ocean's biological pump
,” Prog. Oceanogr.
130
, 205
–248
(2015
).12.
S. A.
Rutledge
and
P. V.
Hobbs
, “
The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: A diagnostic modeling study of precipitation development in narrow cold-frontal rainbands
,” J. Atmos. Sci.
41
, 2949
–2972
(1984
).13.
S.-Y.
Hong
,
J.
Dudhia
, and
S.-H.
Chen
, “
A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation
,” Mon. Weather Rev.
132
, 103
–120
(2004
).14.
R. G.
Fovell
and
H.
Su
, “
Impact of cloud microphysics on hurricane track forecasts
,” Geophys. Res. Lett.
34
, L24810
, https://doi.org/10.1029/2007GL031723 (2007
).15.
D. L.
Mitchell
,
P.
Rasch
,
D.
Ivanova
,
G.
McFarquhar
, and
T.
Nousiainen
, “
Impact of small ice crystal assumptions on ice sedimentation rates in cirrus clouds and GCM simulations
,” Geophys. Res. Lett.
35
, 9806
, https://doi.org/10.1029/2008GL033552 (2008
).16.
J. A.
Finlon
,
G. M.
McFarquhar
,
S. W.
Nesbitt
,
R. M.
Rauber
,
H.
Morrison
,
W.
Wu
, and
P.
Zhang
, “
A novel approach for characterizing the variability in mass–dimension relationships: Results from MC3E
,” Atmos. Chem. Phys.
19
, 3621
–3643
(2019
).17.
D. J.
Posselt
,
F.
He
,
J.
Bukowski
, and
J. S.
Reid
, “
On the relative sensitivity of a tropical deep convective storm to changes in environment and cloud microphysical parameters
,” J. Atmos. Sci.
76
, 1163
–1185
(2019
).18.
A.
Cauteruccio
,
M.
Colli
,
M.
Stagnaro
,
L. G.
Lanza
, and
E.
Vuerich
, In-Situ Precipitation Measurements
(
Springer International Publishing
, 2021
), pp. 359
–400
.19.
J.
Grazioli
,
G.
Ghiggi
,
A.-C.
Billault-Roux
, and
A.
Berne
, “
MASCDB, a database of images, descriptors and microphysical properties of individual snowflakes in free fall
,” Sci. Data
9
, 186
(2022
).20.
E.
Bou-Zeid
,
W.
Anderson
,
G. G.
Katul
, and
L.
Mahrt
, “
The persistent challenge of surface heterogeneity in boundary-layer meteorology: A review
,” Boundary-Layer Meteorol.
177
, 227
–245
(2020
).21.
T.
Zeugin
,
Q.
Krol
,
I.
Fouxon
, and
M.
Holzner
, “
Sedimentation of snow particles in still air in stokes regime
,” Geophy. Res. Lett.
47
, e2020GL087832
(2020
).22.
P. K.
Wang
, Motions of Ice Hydrometeors in the Atmosphere: Numerical Studies and Implications
(
Spinger
, 2021
).23.
M. W.
McCorquodale
and
C. D.
Westbrook
, “
Trail part 2: A comprehensive assessment of ice particle fall speed parametrisations
,” Q. J. R. Meteorol. Soc.
147
, 605
–626
(2021
).24.
S.
Elghobashi
, “
On predicting particle-laden turbulent flows
,” Appl. Sci. Res.
52
, 309
–329
(1994
).25.
V.
Mathai
,
V. N.
Prakash
,
J.
Brons
,
C.
Sun
, and
D.
Lohse
, “
Wake-driven dynamics of finite-sized buoyant spheres in turbulence
,” Phys. Rev. Lett.
115
, 124501
(2015
).26.
A.
Nemes
,
T.
Dasari
,
J.
Hong
,
M.
Guala
, and
F.
Coletti
, “
Snowflakes in the atmospheric surface layer: Observation of particle–turbulence dynamics
,” J. Fluid Mech.
814
, 592
–613
(2017
).27.
J.
Li
,
A.
Abraham
,
M.
Guala
, and
J.
Hong
, “
Evidence of preferential sweeping during snow settling in atmospheric turbulence
,” J. Fluid Mech.
928
, A8
(2021
).28.
M.
Maxey
, “
The motion of small spherical particles in a cellular flow field
,” Phys. Fluids
30
, 1915
–1928
(1987
).29.
J.
Li
,
M.
Guala
, and
J.
Hong
, “
Snow particle analyzer for simultaneous measurements of snow density and morphology
,” arXiv:2209.11129 (2022
).30.
D. K.
Singh
,
E. R.
Pardyjak
, and
T. J.
Garrett
, “
Time-resolved measurements of the densities of individual frozen hydrometeors and of fresh snowfall
,” Atmos. Meas. Tech.
(submitted).31.
D. K.
Singh
,
S.
Donovan
,
E. R.
Pardyjak
, and
T. J.
Garrett
, “
A differential emissivity imaging technique for measuring hydrometeor mass and type
,” Atmos. Meas. Tech.
14
, 6973
–6990
(2021
).32.
T. I.
Alcott
and
W. J.
Steenburgh
, “
Snow-to-liquid ratio variability and prediction at a high-elevation site in Utah's Wasatch Mountains
,” Weather Forecast.
25
, 323
–337
(2010
).33.
J.
Hong
,
M.
Toloui
,
L. P.
Chamorro
,
M.
Guala
,
K.
Howard
,
S.
Riley
,
J.
Tucker
, and
F.
Sotiropoulos
, “
Natural snowfall reveals large-scale flow structures in the wake of a 2.5-MW wind turbine
,” Nat. Commun.
5
, 4216
(2014
).34.
R.
Hassanian
,
A.
Helgadottir
,
L.
Bouhlali
, and
M.
Riedel
, “
An experiment generates a specified mean strained rate turbulent flow: Dynamics of particles
,” Phys. Fluids
35
, 015124
(2023
).35.
F. D.
Dimotakis
,
P. E.
Debussy
, and
M. M.
Koochesfahani
, “
Particle streak velocity field measurements in a two-dimensional mixing layer
,” Phys. Fluids
24
, 995
(1981
).36.
H. P.
Böhm
, “
A general equation for the terminal fall speed of solid hydrometeors
,” J. Atmos. Sci.
46
, 2419
–2427
(1989
).37.
A. J.
Heymsfield
and
C.
Westbrook
, “
Advances in the estimation of ice particle fall speeds using laboratory and field measurements
,” J. Atmos. Sci.
67
, 2469
–2482
(2010
).38.
T. J.
Morrison
,
T.
Meisenheimer
,
T.
Garrett
,
D.
Singh
,
S.
Donovan
, and
E.
Pardyjak
, “
Relating storm-snow avalanche instabilities to data collected from the Differential Emissivity Imaging Disdrometer (DEID)
,” Cold Regions Sci. Technol.
210
, 103839
(2023
).39.
C.
Fierz
,
R. L.
Armstrong
,
Y.
Durand
,
P.
Etchevers
,
E.
Greene
,
D. M.
McClung
,
K.
Nishimura
,
P. K.
Satyawali
, and
S. A.
Sokratov
, “
The international classification for seasonal snow on the ground
” (2009
).40.
G. A.
Voth
,
A.
La Porta
,
A. M.
Crawford
,
J.
Alexander
, and
E.
Bodenschatz
, “
Measurement of particle accelerations in fully developed turbulence
,” J. Fluid Mech.
469
, 121
–160
(2002
).41.
J.
Bec
,
L.
Biferale
,
G.
Boffetta
,
A.
Celani
,
M.
Cencini
,
A.
Lanotte
,
S.
Musacchio
, and
F.
Toschi
, “
Acceleration statistics of heavy particles in turbulence
,” J. Fluid Mech.
550
, 349
–358
(2006
).42.
M.
Bini
and
W. P.
Jones
, “
Particle acceleration in turbulent flows: A class of nonlinear stochastic models for intermittency
,” Phys. Fluids
19
, 035104
(2007
).43.
Y.
Lin
and
H.
Xu
, “
Experimental investigation of pressure statistics in laboratory homogeneous isotropic turbulence
,” Phys. Fluids
35
, 065129
(2023
).44.
A.
La Porta
,
G. A.
Voth
,
A. M.
Crawford
,
J.
Alexander
, and
E.
Bodenschatz
, “
Fluid particle accelerations in fully developed turbulence
,” Nature
409
, 1017
–1019
(2001
).45.
J. M.
Mercado
,
V. N.
Prakash
,
Y.
Tagawa
,
C.
Sun
, and
D.
Lohse
, “
Lagrangian statistics of light particles in turbulence
,” Phys. Fluids
24
, 055106
(2012
).46.
S.
Vajedi
,
K.
Gustavsson
,
B.
Mehlig
, and
L.
Biferale
, “
Inertial-particle accelerations in turbulence: A Lagrangian closure
,” J. Fluid Mech.
798
, 187
–200
(2016
).47.
N. M.
Qureshi
,
U.
Arrieta
,
C.
Baudet
,
A.
Cartellier
,
Y.
Gagne
, and
M.
Bourgoin
, “
Acceleration statistics of inertial particles in turbulent flow
,” Eur. Phys. J. B
66
, 531
–536
(2008
).48.
G. A.
Voth
,
K.
Satyanarayan
, and
E.
Bodenschatz
, “
Lagrangian acceleration measurements at large Reynolds numbers
,” Phys. Fluids
10
, 2268
–2280
(1998
).49.
G.
Gulitski
,
M.
Kholmyansky
,
W.
Kinzelbach
,
B.
Lüthi
,
A.
Tsinober
, and
S.
Yorish
, “
Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 3. Temperature and joint statistics of temperature and velocity derivatives
,” J. Fluid Mech.
589
, 103
–123
(2007
).50.
A. N.
Kolmogorov
, “
The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
,” Dokl. Akad. Nauk. SSSR
434
(9
), 301
(1941
)51.
W.
Heisenberg
, “
Zur statistischen theorie der turbulenz
,” Z. Phys.
124
, 628
–657
(1948
).52.
R. A.
Shaw
and
S. P.
Oncley
, “
Acceleration intermittency and enhanced collision kernels in turbulent clouds
,” Atmos. Res.
59–60
, 77
–87
(2001
).53.
G.
Gulitski
,
M.
Kholmyansky
,
W.
Kinzelbach
,
B.
Lüthi
,
A.
Tsinober
, and
S.
Yorish
, “
Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 1. Facilities, methods and some general results
,” J. Fluid Mech.
589
, 57
–81
(2007
).54.
P. J.
Ireland
,
A. D.
Bragg
, and
L. R.
Collins
, “
The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects
,” J. Fluid Mech.
796
, 659
–711
(2016
).55.
V.
Mathai
,
E.
Calzavarini
,
J.
Brons
,
C.
Sun
, and
D.
Lohse
, “
Microbubbles and microparticles are not faithful tracers of turbulent acceleration
,” Phys. Rev. Lett.
117
, 024501
(2016
).56.
D.
Buaria
and
K. R.
Sreenivasan
, “
Scaling of acceleration statistics in high Reynolds number turbulence
,” Phys. Rev. Lett.
128
, 234502
(2022
).57.
U.
Nakaya
, “
Snow crystals
,” in Snow Crystals
(
Harvard University Press
, 2013
).58.
T. J.
Garrett
, “
Analytical solutions for precipitation size distributions at steady state
,” J. Atmos. Sci.
76
, 1031
–1037
(2019
).59.
K. N.
Rees
,
D. K.
Singh
,
E. R.
Pardyjak
, and
T. J.
Garrett
, “
Mass and density of individual frozen hydrometeors
,” Atmos. Chem. Phys.
21
, 14235
–14250
(2021
).60.
A. A.
Grachev
,
L. S.
Leo
,
S. D.
Sabatino
,
H. J.
Fernando
,
E. R.
Pardyjak
, and
C. W.
Fairall
, “
Structure of turbulence in katabatic flows below and above the wind-speed maximum
,” Boundary-Layer Meteorol.
159
, 469
–494
(2016
).61.
C.
Hang
,
D. F.
Nadeau
,
E. R.
Pardyjak
, and
M. B.
Parlange
, “
A comparison of near-surface potential temperature variance budgets for unstable atmospheric flows with contrasting vegetation cover flat surfaces and a gentle slope
,” Environ. Fluid Mech.
20
, 1251
–1279
(2020
).62.
L.
Benedict
and
R.
Gould
, “
Towards better uncertainty estimates for turbulence statistics
,” Exp. Fluids
22
, 129
–136
(1996
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
