A 3-D simulation of drifting snow in the turbulent boundary layer

Introduction Conclusions References Tables Figures


Introduction
The phenomenon of the loose snow particles traveling near the land surface under the action of wind is known as drifting snow.As a typical two-phase flow, drifting snow is widely distributed in the globe and has significant impacts on the natural environment and the social economy.On one hand, drifting snow is one of the main causes of the temporal and spatial variation of snow distribution, contributes greatly to the mass balance of the Antarctic ice sheets (Gallée et al., 2013), and further affects global climate system.The seasonal snow cover also deeply affects the hydrological balance in cold regions, thus is of glaciological and hydrological importance.On the other hand, drifting snow causes snow accumulation on the road and reduces visibility, which may seriously affect the traffic and human activities, and its resultant non-uniform distribution of snow layer may induce and aggravate various natural disasters, such as flood, avalanche, mudslides and landslide (Michaux et al., 20022001).These disasters may result in not only huge direct and indirect economic losses, but also human casualties.Thus, in-depth study on the drifting snow is considered to be essential to comprehensively understanding the ice mass balance and hydrological balance.
The transport processes of snow grains have been extensively investigated (Pomeroy et al., 1993; Clifton andLehning, 2008Lehning et al., 2002;Bavay et al., 2009).Many models were proposed by taking the snow particles as continuous phase (Uematsu et al., 1993;Mann, 2000;Taylor, 1998;Déry and Yau, 1999;Fukushima et al., 1999Fukushima et al., , 2001;;Xiao et al., 2000;Bintanja, 2000aBintanja, , 2000b)).Obviously, the above assumption is not in agreement with the real situation.In addition, these models could reveal neither the movement mechanisms of snow particles nor the factors affecting the behaviors of snow particles.These models have a significant role in promoting the drifting snow research although some information can not be acquired from these models, for example, the trajactory of particle and its movement mechanisms.
SubsequentlyRecently, Nemoto and Nishimura (2004) studied the snow drifting process based on particle tracking in a turbulent boundary layer and their 1-D model included four sub-processes: the aerodynamic entrainment of snow grains, grain-bed collision, grain trajectories and wind modification.Later, Zhang and Huang (2008) presented a steady state snow drift model combined with the initial velocity distribution function and analyzed the structure of drifting snow at steady state.
However, neither the details of the spatial variation of snow drifting nor the whole turbulent structure of wind field can be described due to limitation of their models.
3-D simulation of drifting snow gradually carried out in recent years.Gauer (2001) first simulated the blowing and drifting snow in Alpine terrain with Reynolds Averaged Navier-Stokes (RANS) approaches.Also, Schneiderbauer and Prokop (2011) developed the SnowDrift3D model based on RANS.Vionnet et al. (2014) went on a study of large-scale erosion and deposition using a fully coupled snowpack/atmosphere model.Groot et al. (2014) simulated the small-scale drifting snow with a Lagrangian stochastic model based on LES and the intermittency of drifting snow was mainly analyzed.FurthermoreAnd, snow particles were uniform size in most previous models, which is different from the natural situation.To date, a comprehensive study on drifting snow in the turbulent field is indispensable for a thorough understanding of the complex drifting snow.
In this paper, based on the model of Dupont et al. (2013) that developed for blown sand movement, the Advanced Regional Prediction System (ARPS, version 5.3.3),which is a middle-scale meteorological model, is applied in a small-scale for drifting snow and a series of adaptations are made for drifting snow simulation.we We performed a numerical study ofpresent a physical 3-D numerical model for drifting snow in the turbulent boundary layer based on the LES of Advanced Regional Prediction System (ARPS, version 5.3.3) by taking the 3-D motion trajectory of snow particles with mixed grain size, the grain-bed interaction, and the coupling effect between snow particles and wind field into consideration and used it to directly calculate the velocity and position of every single snow particle in turbulent atmosphere boundary layer, the transport rate and velocity distribution characteristics of drifting snow, and the mean particles size at different heights.The paper is structured as follows: Section 2 briefly introduces the model and methods; Section 3 illuminates the model validations; Section 3 4 presents the simulation results and discussions, and Section 4 5 is the conclusion.

Turbulent boundary layer
The ARPS developed by University of Oklahoma is a three-dimensional, non-hydrostatic, compressible LES model and has been used for simulating wind soil erosion (Vinkovic et al., 2006;Dupont et al., 2013).In this paper, it is used for modeling the drifting snow.
Snow saltation movement in the air is a typical two-phase movement, in which the coupling of particles and the wind field is a key issue.Vinkovic et al. (2006) introduced the volume force caused by the particles into Navier-Stokes equation of ARPS and The conservation equations of momentum and subgrid scale (SGS) turbulent kinetic energy (TKE) after filtering with considering the impact of the presence of particles on the flow field can be expressed as (Vinkovic et al., 2006;Dupont et al., 2013) where the tilde symbol indicates the filtered variables and the line symbol represents grid volume-averaged variables.i x ( 1, 2,3 i = ) stand for the streamwise, lateral, and vertical directions, respectively, i u refers to the instantaneous velocity component of three directions, ij d is the Kronecker symbol, div α means the damping coefficient, p and ρ are the pressure and density of air, respectively; g is the gravity acceleration, θ indicates the potential temperature, p c and v c are the specific heat of air at constant pressure and volume, respectively; t is time, ij t denotes the subgrid stress tensor, and i f is the drag force caused by the particles and can be written as (Yamamoto et al., 2001): where grid V is the grid cell volume, P N stands for the number of particles per grid, p m means the mass of particles, ( ) pi u t and ( ( ), ) i p u x t t represent the velocity of particles and the wind velocity at grain location at time t , respectively, and ( ) is an empirical relation of the particle Reynolds number p Re (Clift et al., 1978): It is worth noting that the inertia effect of snow particles is considered by evaluating the maximum particle response time, so the particle motion is the dynamical calculation of time step, which is guaranteed to be less than the maximum particle response time.

Aerodynamic Entrainment
Snow particles will be entrained into the air if the shear force produced by air flow is large enough.The number of entrainment N (per unit area per unit time) can be express as (Anderson and Haff, 1991): where t is the local surface shear stress and t t is the threshold shear stress.
Obviously, if t of every position in the computation domain is always smaller than t t , no particle can start-up and the drifting snow will not happened.The threshold shear stress can be described as 2 ( ) is more suited to snow as reported by Clifton et al. (2006).
The coefficient takes the form of The initial velocity of entrained particles follows a lognormal distribution with mean value * 3.3u ( * u is the friction velocity), which is consistent with the measurements of saltating snow in wind tunnel (Nishimura and Hunt, 2000) and has been adopted by drifting snow studies (Clifton and Lehning, 2008;Groot et al., 2014).
And the initial take-off angle can be described by a lognormal distribution with a mean value of The collision of saltating particles with the bed surface is a key physical process in saltation, as it will rebound with a certain probability and may splash new saltating particles into the air (Shao and Lu, 2000).Kok and Renno (2009) have proposed a physical splashing function based on the conservation of energy and momentum.Thus, the saltation process under various physical environments can be accurately simulated and applied to the mixed soils and drifting snow.

2 Rebounding
The grain-bed interaction is a stochastic process, in which the impact When a moving particles impact on the bed, it may rebound into air againmay rebound with a certain probability.If a particle rebounds into the air, it can be described using three variables: the velocity reb v , the angle toward the surface reb α and the angle toward a vertical plane in the streamwise direction reb b .
The rebound probability can be expressed as (Anderson and Haff, 1991): Recent experiment shows that the fraction of kinetic energy retained by the rebounding particle approximately follows normal distribution (Wang et al., 2008): where 2 2 0.45 and Renno, 2009).
The angle reb α approximately follows an exponential distribution.Although Kok and Renno (2009) suggest the mean value of reb α is 45  and it was used by Groot et al. ( 2014) for drifting snow, we choose a mean value depending on the mean particle size because many researches indicate that reb α relay on particle size (Rice et al., 1995;Zhou et al., 2006): For the velocity after rebound reb v , Kok and Renno (2009) indicate that the fraction of kinetic energy retained by the rebounding particle approximately follows normal distribution as follow: 2 2 ((45 22)%) Two angles are introduced in the rebound process to describe the rebound direction as mentioned above.The angle reb α approximately follows an exponential distribution.Although it is not affected by the impact velocity, it decreases exponentially with the increase of particle diameter (Rice et al., 1995;Zhou et al., 2006).The relationship of average value of rebound angle to particle diameter can be expressed as: where p d is measured in the unit of micrometer.
However, the angle reb b was rarely involved in previous studies and may not 带格式的: 缩进: 首行缩进: 1.5 字符 strongly affect the saltation process ( Dupont et al., 2013).Here we choose 0 15

3 Splashing
The newly ejected particles and the 'dead particles' (not rebounded) will reach equilibrium when the saltation process becomes stable.
The number of newly ejected particles is usually proportional to the impact velocity and can be written as (Kok and Renno, 2009): where a is a dimensionless constant in the range of 0.01-0.05.This value affect the 'saturation length' (total transport rate of drifting snow reached equilibrium) to a great extent.We find that 0.03 a = is closer to the observation of drifting snow in the wind tunnel (Okaze et al., 2012).While this parameter will not influence the steady state of drifting snow because we found the percentage of eject particles is always less than Once a new particle is splashed into the air, it can also be characterized by its velocity ej v , its angle toward the surface ej α and its angle toward a vertical plane in the streamwise direction ej b .
The speed of the ejected particles is exponentially distributed.Kok and Renno (2009) developed a physical expression of the average dimensionless speed of the ejected particle as follow: 1 exp 40 where ej λ is the average fraction of impacting momentum applied on the ejecting surface grains.We choose 0.15 ej λ = in this paper, which corresponds to the experimental observation of sand by Rice et al. (1995).
where ej λ is the average fraction of impacting momentum applied on the ejecting surface grains.We choose 0.15 ej λ = in this paper.Kok and Renno (2009) indicated that the angle ej α approximately follows an exponential distribution and its mean value is 50°, which was also adopted by Groot .

Simulation Details
In this paper we have performed some wind tunnel experiments to obtain the initialization data for the simulation as well as to compare the simulated results with experiment results.The The blowing snow process in the turbulent boundary layer is simulated and the simulation results are compared with the existent experiment results.Additionally, The the snow particles have circulatory motion in the lateral boundary and they will disappear when moving out of the outlet in the end of the domain..
The size distribution of snow particles in this paper is fitted to the experiment results obtained from field observations of SPC (Schmidt, 1984), that is where α and b are the shape and scale parameters of gamma-function distribution and we choose a value of 4.65 and 75.27, respectively.Every new ejection or entrainment particle will be given a random size from above distribution and will be tracked separately.The sizes of snow particles in the air are stochastically collected and the size distribution is presented in figure 2

Model validations
The wind profile is firstly obtained by the time averaging and spatial averaging of a time-series of wind velocities ( 5 ~10 t s = and the time interval is 0.01s ).As shown in figure 3, the method leads to similar wind profiles to that of wind tunnel experiment at different wind speeds.
Snow transport rate (STR) is one of the most important indicators of the strength of the drifting snow.This is mainly because the mean velocity of snow particles increases with height increasing, our measurement is mainly set at lower positions due to the limitation of instrument and thus part of high-speed particles are not being captured.
A more detailed statistics of the percentages of particles that moving at different velocities are showed in figure 6(c).The field observation of Greeley et al. (1996) showing that the proportions of saltating sand particles with velocity smaller than 1.5 / m s and greater than 4 / m s are greater than 59% and smaller than 3%, respectively.However, the proportion of snow particles with the velocity smaller than 1.5 / m s is in general smaller than 48% and the percentage of particles with velocity greater than 4 / m s increase with the increasing friction velocity.It can be found that the drifting snow has more high-speed particles than saltating sand, which is mainly because the density of snow particles are significant smaller than sand and they are more easily suspended and followed.
Finally, figure 7 shows the mean size of snow particles along height in the air at different friction velocities and compared with the experimental result of Gromke et al. (2014).All the data have been normalized to the average diameter of overall snow particles.It is clearly that the mean diameter of snow particles in the saltation layer slightly decreases with the height increasing, which is also consistent with the observation of previous works (Nishimura and Nemoto, 2005).However, it appears that the mean diameter increase with increasing height above the saltation layer.The main reason may be that the small particle trends to carry smaller inject velocity, while the larger particle is just the opposite due to the stronger inertia.The rebound velocity is proportional to the incident velocity and thus larger snow particle will rebound with a bigger initial velocity.

Analysis of the flow fieldThe interaction between turbulent and particle motion
Almost all the flows at atmospheric boundary layer are turbulent.Therefore, the simulation of turbulent boundary layer is the key and basis for accurately simulating the drifting snow.Enough time is supplied for forming a stable turbulent boundary layer before particles taking off.The computational region is relative small and the inflow contains the real turbulent fluctuation.The turbulent fluctuations will affect the movement of snow particles and the particle motion will influence the development of turbulent.showing only slight influence on the saltation height, saltation distance and landing position of snow particles.This is consistent with the sand saltation in the turbulent boundary layer performed by Dupont et al. (2013).On the other hand, we can see from figure 10 that the wind velocity is significantly decreased in the drifting snow region due to the reaction force of the snow particles, while the TKEs are obviously enhanced during snow drifting.This result is attributed to the fact that velocity gradient is obviously changed when the drifting snow formed (Okaze et al., 2012).
It can be observed from Figure 3 that homogeneous turbulent fluctuations are distributed in the fully developed boundary layer.When the stable drifting snow is formed, the wind velocity will significantly decrease in the drifting snow region due to the reaction force of the snow particle and the turbulent fluctuations gradually become non-uniform in the drifting snow region.This is mainly due to the presence of the snow streamers-resulted great difference in the number concentration of snow particles at different positions (details are shown in Section 3.2).
In addition to the turbulent fluctuation, the wind profile can also be obtained by the time averaging and spatial averaging of a time-series of wind velocities and the time interval is 0.01 s ).As shown in Figure 4, the method leads to similar wind profiles to that of wind tunnel experiment at different wind speeds.
When the turbulent boundary layer is fully developed, the snow particles will be released and the motion feature of snow particles could be further obtained.

1 The formation of Snow snow streamers
The saltation process, either in the field or in the wind tunnel, exhibits a temporospatial discontinuity.This discontinuity is affected by many factors such as turbulent fluctuation, topography, surface moisture, roughness elements, etc (Stout and Zobeck, 1997;Durán et al., 2011).Different fromMost previous models which are unable to clearly describe the drifting snow structure, .our 3-D model could be used to directly calculate the The 3-Dmotion trajectory of every snow particle is calculated and further intuitively demonstrate the overall structure of snow saltation layers could be intuitively demonstrated because it describes the macroscopic performance of a large amount of drifting snowsaltating particles.It can be observed from Figure 6 11 that snow streamers with high saltating particle concentration obviously swing forward along the downwind direction, merging or bifurcating during the movement.It can also be found that the snow streamers with elongated shape differ greatly in length, but only 0.1~0.2m in width.
From the corresponding slices of wind velocity cloud map, it can be seen that many low-speed streaks exist in the near-wall region of the turbulent boundary layer.By comparing the concentration and corresponding velocity cloud map, it is hard to decide the relationship between particle concentration and local wind velocity, which is just like the sand streamers reported by Dupont et al. (2013).This may be due to the complex motion of the snow particles and hysteretic change of local wind.However, the shapes of snow streamers are quite different from that of sand streamers.For example, the snow streamers trend to be longer and thinner in the turbulent boundary layer.itcan be found that the particle concentration shows a direct proportional relationship with the local wind velocity, that is, only few snow particles present in the low-speed streaks.
The in-homogeneous take off and splash of the snow particles in the turbulent wind field are the main reasons for the formation of snow streamers.The shape and size of streamers largely depend on the flow structure of the turbulent boundary layer.
In addition, during the full development of drifting snow, the saltating particles and wind field are in the state of dynamic balance due to the feedback effect of each other.
When the number concentration of snow particles at a certain position is high enough, the local wind velocity will be significantly reduced, resulting in a lower splash level.
Thus the streamer will gradually weaken or even disappear.In contrast, the local wind speed in the low concentration region will increase, which enhances the splash process, so the snow particles will grow rapidly and form a streamer.Furthermore, the fluctuating velocity may also change the movement direction of snow particles.All the above reasons together cause the serpentine forward of the snow streamers.

Snow transport rate
Snow transport rate (STR) is one of the most important indicators of the strength of the drifting snow.In this simulation, the snow particles will be collected if they pass through the section located at 3 during the time of 10 20 t s =  . ; while at the height of 0.2 m, the former is 176.32 times greater than the latter.Therefore, it is concluded that the significant increase of snow particles at the higher position is the major contributor to the increase of STR at higher wind speed mainly because the snow particles in the higher speed flow field can acquire more energy from the air and will rebound with a higher velocity.

Velocity of snow particles
As one of the most important aspects to evaluate the accuracy of a drifting snow model, the velocity information (especially in the spanwise direction) of snow particles in the air is worthy of attention although it is seldom given in previous models.The location and velocity of every snow particle can be obtained, and the most important of all, the spanwise velocity of snow particles can be directly obtained in our simulation.The velocity distribution of snow particles in the air and the initial take-off velocity of the ejected particles are given in Section 3.4.1 and Section 3.4.2,respectively.

Velocity of snow particles in the air
The velocity distribution of snow particles in the air is shown in Figure 9 , the proportions of snow particles with the velocity smaller than 1.5 / m s and greater than 4 / m s are 65.07%and 1.76%, respectively, consistent with a field observation of Greeley et al. (1996) showing that the proportions of saltating particles with velocity smaller than 1.5 / m s and greater than 4 / m s are greater than 59% and smaller than 3%, respectively.
It should be noted that the high-speed particles in our simulation are significantly more than those captured in the experiments (Figure 9(b)).This is mainly because the concentration of snow particles decreases with height increasing, making it increasingly difficult to be captured the high-speed snow particles.proportion of snow particles in the air with higher spanwise velocity increases with friction velocity increasing.Furthermore, it can be seen that when the friction velocity is small, the absolute value of spanwise velocity increases decreases with increasing height; while the law is just the opposite for large friction velocity.And the spanwise velocity of snow particles is in an order of magnitude less than that of the streamwise in general velocity.The variation in the spanwise velocity with height at different friction wind velocity is not obvious.The main reason for this is that turbulent fluctuations are fairly minimal when the wind speed is small, and they exert an increasingly stronger with the growing wind speed.
From the above analysis it is quite evident that the velocity distribution of snow particles in the air is not sensitive to the wind velocity.The main reason for that is the wind velocity in the full development drifting snow slightly varies due to the reaction force of snow particles in the air.

Take-off velocity of snow particles
Then, the The initial take-off velocities speed distributions of snow particles in Although there is no obvious difference in take-off velocity at different wind velocity, we can see that a large amount of particles may saltate at higher saltation 带格式的: 首行缩进: 0 字符 height and greater friction wind speed.It may be inferred that turbulent fluctuation plays an important role in the lifting of snow particles.

Diameter distribution of snow particles in the air
The snow particles with mixed size close to natural situation are applied in our simulation.In this section, the size distribution of snow particles in the air is analyzed.m) is unchanged with the height increasing, which is consistent with the conclusion obtained by Gromke et al. (2014).However, the mean diameter of snow particles with height above 0.05 m exhibits a growing trend with height increasing, similar to the results observed by Sedmit (1984).This is mainly because larger particles withstand greater drag force in the air during the movement process and have higher impact velocity.Therefore, they will rebound with higher initial velocity because the rebound velocity is proportional to the incident velocity.

5 Conclusions
In this study, thewe establish a 3-D drifting snow model process with mixed particle size in the turbulent boundary layer is performed, simulate the development process of drifting snow with mixed particle size and draws the following main conclusions: (1) Turbulent fluctuation may significantly affect the trajectory of small snow particles with equivalent diameter 100 (2) The drifting snow in a turbulent boundary layer is very intermittent.Fully developed drifting snow swings forward toward the downwind in the form of snow streamers and the wind velocity is proportional to the concentration of snow particles at different locations of the turbulent boundary layer.
(3) The change of spanwise velocities of snow particles along streamwise and spanwise directions increase with the height relay on the friction velocity, .and the latter spanwise velocity is one order of magnitude less than the former streamwise direction in general.In addition, the velocity distribution is not sensitive to the wind speed.
(4) The mean diameter of snow particles in the air is obviously distributed in layers.It is constant for snow particles with height less than 0.05 m, but shows a gradual increase trend for snow particles with height above 0.05 m.
Groot et al.(2014) indicate that these value are more accurate for drifting snow.whereimp vis the impact velocity of particle, B and γ are the experienced parameters 3% in the fully developed drifting snow.D is the typical particle size ( where a is a dimensionless constant in the range of 0.01-0.05(here 0.03 a =), D is the typical particle size ( p d in this paper, imp m is the mass of impacting particle and ej m is the average mass of ejection grains. development of the fully developed turbulent wind field region with a steady turbulent boundary layer and provides a steady turbulent turbulent characteristics separating from our wind tunnel results are added on the initial logarithmic velocity profile at beginning and the inlet velocity of fluid will be equal to the wind velocity at the location of 5 x m = after 5 seconds which realizes a long distance development of the turbulent boundary layer.The second zone is the blowing snow blowing region from 6 loose snow layer is set on the ground.In this model, the grid has a uniform size of 0the vertical direction.The grid is stretched by cubic function to acquire more detailed information of the surface layer and the smallest grid is 0layer over a snow bed is generated using tThe actual computation time is 30 seconds, in which the first 10s and the second 10s are respectively used for the development of turbulent boundary layer and the drifting snow, and the last 10s for data statistics.The dynamic Smagorinsky-Germano 带格式的: 缩进: 首行缩进: 0 字 符, 定义网格后自动调整右缩进, 行距: 单倍行距, 到齐到网格 带格式的: 字体: Calibri, 五号 带格式的: 字体: Times New Roman, 小四, 非倾斜 带格式的: 缩进: 首行缩进: 0 字 符 subgrid-scale (SGS) model is used in the simulation.by setting the soil type, reasonable roughness and an initial field with turbulent fluctuations.For the flow field, we applied the rigid ground boundary condition at the bottom, the open radiation boundary in the top, the periodic boundary condition in the spanwise direction, the open radiation boundary condition at the end of the domain along the streamwise direction.The forced boundary is applied in the inflow as mentioned above.and the periodic boundary condition in the inflow with the cycle location at 5.0 x m = .The initial wind database is obtained from the experimental results of wind tunnel.
are in consistence with those observational results of the natural snow(Omiya et al., 2011).whereα and b are the shape and scale parameters of gamma-function distribution, respectively.Here, the diameters of 2617 snow particles are counted and their distribution is presented in Figure2in the domain at the initial moment of drifting snow.The processes of snow blowing with the friction wind velocity of 带格式的: 首行缩进: 0 字符 0.179 ~0.428 / u m s = are performed with the environmental temperature of 10 C −  and initial relative humidity of 90%.And we found the lower bound of friction velocity for a drifting snow is approximately 0.18 / m s for this situation.The processes of snow blowing with the wind velocity of * 0.179 ~0.428 / u m s = are performed at environmental temperature of 10 C −  and initial relative humidity of 90%.
figure 6, in which (a) is the average velocity of snow particles along the streamwise direction as a function of height and (b) displays the corresponding velocity probability distribution of snow particles.It can be observed from figure 6(a) that the average velocity of snow particles along the streamwise direction increases with the height increasing, in which the experiment data has been calibrated by wind speed.Good accordance with the experimental results until below 0.02m mainly because mid-air collision near bed surface is high frequency and loses energy.It can be seen from figure 6(b) that the probability distribution of snow particles' velocity along the streamwise direction obeys the unimodal distribution.In other words, it distributes mainly at 0 4 / m s  and the amount of snow particles moving in the opposite direction is basically less than 3% of the total snow particles.Meanwhile, the probability distribution basically does not change with the friction wind speed, in agreement with our experiment.It should be noted that the high-speed particles in this simulation are significantly more than those captured in the experiments (figure 6(b)).

Figure
Figure 3 8 shows the cloud map of velocity along the streamwise direction ( * 0.428 / u m s = ) (a) before the snow particles take off (t=5s10s) and (b) when the drifting snow has been sufficiently developed (t=20s25s).The slice elicited by arrows displays the velocity cloud map of U U-direction at height 0.001 H m = .Figures 38(a-1) and 38(a-2) show the contour surface map ( 0.5 / m s ± ) of wind velocity along spanwise direction and vertical direction, respectively, at time 10 t s = , and Figures figures 38(b-1) and 38(b-2) show the corresponding results at time 25 t s = .At the same time, the typical trajectories of snow particles are represented in figure 9, in which the diameter of (a) and (b) are 100 μm and 300 μm, respectively.The blue dotted line denotes the motion trajectory that is not affected by the turbulence and it is calculated by another drifting snow model (Zhang and Huang, 2008) with the same take-off velocity and wind profile.It can be seen from figure9that turbulence can significantly affect the trajectories of snow particles with diameter smaller than 100 μm, and may drive these snow particles moving up to 5~6 m during one saltation process.By contrast, the trajectories of larger snow particles are less affected by the turbulent fluctuation,

Figure 5
Figure 5(a) and 5(b) show the typical trajectories of snow particles with diameter of 100 μm and 300 μm, respectively, in which the blue dotted line denotes the motion trajectory that is not affected by the turbulence.It can be seen that turbulence can significantly affect the trajectories of snow particles with diameter smaller than 100 μm, and may drive snow particles with diameter of 100 μm moving 5~6 m during one Figure 7(a) shows the time evolution of STR per width in different friction wind velocity.It can be seen that the STR per width increases rapidly and reaches a dynamic equilibrium state in a short time.With the friction wind speed increasing, the time needed to reach the equilibrium state also increases.During the transport process, STR per width also slightly fluctuates and its fluctuation amplitude is proportional to the friction wind velocity, mainly owing to the intermittent behavior of drifting snow.At the same time, it can be observed from Figure 7(b) that the STR per width increases with friction wind velocity increasing, in consistence with the existing experiment results.The average particle concentrations under different friction wind velocities as a function of height are shown in Figure 8(a).It is clear from the figure that the average particle concentrations at different friction wind velocity similarly fluctuate with height, that is, they decrease with height increasing.And the greater the friction wind velocity, the greater the maximum height the snow particles can achieve.Further analysis shows that the difference of average particle concentrations under different friction wind speed is proportional to height.For example, at the height of 0.001 m, the average particle concentration at friction wind velocity of * 0.361 / u m s = is 2.86 times greater than that at friction wind velocity of * 0.215 / u m s =

Figure 8
Figure 8(b) shows the relationship of STR per unit area to the saltation height.As shown in Figure 8(b), the variations in the STR per unit area with height at different friction wind speeds are equivalent, that is, the STR per unit area decreases with height increasing.However, the STRs per unit area differ greatly at the same height at different friction wind speeds.In the same condition, the STRs per unit area at height Figure 9(b) that the probability distribution of snow particles' velocity along the streamwise direction obeys the unimodal distribution.In other words, it distributes mainly at 0 3 / m s  and the amount of snow particles moving in the opposite direction is less than 3% of the total snow particles.Meanwhile, the probability distribution does not change with the friction wind speed, in agreement with our experiment.In this work, at friction wind velocity of * 0.288 / u m s = , the proportions

Firstly, the spanwise
velocity of snow particles in the air is analyzed.As shown in Figure figure 10 11shows the spanwise velocity of snow particles in the air, where (a) is the distribution of the absolute value of spanwise velocity along the elevation and (b) is the corresponding probability distribution of snow particles' velocity.It is observed from figure 12(a) that the mean velocity along spanwise basically increases with the increasing wind speed.This can also be certified from figure 12(b) that the three directions are acquired due to they are (including rebound particles) widely used in the numerical model.The probability distributions of lift-off velocity in a fully developed drifting snow field are presented in Figure1113, in which the (a), (b), (c) and (d) show the distributions of streamwise, spanwise, vertical and resultant velocities, respectively.It is clear that all the velocity components obey the unimodal distribution.The vertical lift-off velocity and areis basically not affected by the friction wind velocity while the initial take-off speed along streamwise and spanwise trend to increase with the increasing wind speed.This provides a reference for use the probability distributions of initial take-off speed.

Figure 12
Figure12shows the size distributions of snow particles in the air at different friction velocities, and their comparison with the experimental results.All the data have been normalized to the average of overall snow particles due to different characteristics of snow particles in different experiments.To avoid the random error, those data with snow particle influx less than little influence on that of particles with larger size.And the saltating particles can strengthen the turbulent fluctuation.

Figure 2 .
Figure 2. Equivalent diameter probability distribution of snow particles.

Figure 3 .
Figure 3.The wind profile at (a) U e =10m/s and (b) U e =12m/s.

Figure 4 .
Figure 4. Variation of the snow transport rate (STR) per width with (a) development distance and (b) friction wind velocity.

Figure 5 .
Figure 5.The STR per unit area versus height at different friction wind velocities.

Figure 6 .
Figure 6.(a)Variation of the average velocity of snow particles along streamwise direction as a function of height, (b) the velocity probability distribution of snow particles and (c) the percentage of particles in different velocity vs friction wind velocities.

Figure 7 .Figure 38 .
Figure 7.The mean equivalent diameter distribution of snow particles in the air vs height.

Figure 4 .
Figure 4.The wind profile at (a) U e =8m/s and (b) U e =10m/s.

Figure 10 .
Figure 10.The TKE profile (a) and wind profile (b) at different time, in which the wind data between 13~15m along the downstream is used ( * 0.428 / u m s =).

Figure 611 .
Figure 611.The top view of the particle concentration and the horizontal section of wind velocity cloud map at corresponding moment ( * 0.357 / u m s = , one dark spot stands for a snow particle and the height of horizontal section is 0.001 H m =).

Figure 7 .
Figure 7. Variation of the snow transport rate (STR) per width with (a) time and (b) friction wind velocity.

Figure 8 .
Figure 8.(a) The average particle concentrations and (b) STR per unit area versus the height at different friction wind velocities.

Figure 9 .Figure 1012 .
Figure 9. (a)Variation of the average velocity of snow particles along streamwise direction as a function of height and (b) the velocity probability distribution of snow particles.

Figure 1113 .
Figure 1113.Distribution of the initial (a) streamwise, (b) spanwise, (c) vertical directions and (d) resultant take-off velocity of snow particles.

Figure 12 .
Figure 12.The mean equivalent diameter distribution of snow particles in the air vs height.