平坦床面上风雪流运动的力学机理分析
|
摘要
根据床面雪粒粘连程度的不同,建立不同的起动模型,并讨论温度在-30°C-0℃的范围内,起动风速与粒径、温度以及积雪时间的关系。结果表明:当其他因素不变时,临界起动风速随着雪粒粒径的增大而增大;在一定积雪时间内,临界起动风速随时间增加而增加,最终达到一个稳定的值;在温度低于零度时,临界起动风速随雪表温度的增大而增加。
建立单颗雪粒的运动模型,分别讨论了在不同情况下各种因素对雪粒运动轨迹的影响。结果表明:除重力和拖曳力外,saffman力、magnus力、静电力以及运动随机性对雪粒的运动也有重要的影响,并且随着风速、雪粒粒径、密度的变化各因素的影响程度也发生不同程度的变化。
基于对雪粒起动、运动机理的分析,结合初速度分布函数,建立稳态的风雪流计算模型,并对稳定状态下的风雪流结构进行分析,将分析的结果与风洞试验的测量值进行了比较,结果显示:风雪流发展稳定后,运动雪粒对风场有较为明显的修正作用;稳定状况下雪粒的数浓度和水平质量通量均随高度呈负指数分布,并且在考虑saffman力、magnus力以及静电力以后计算结果更接近实测值。当运动随机性较大时,其对雪粒的数浓度和水平质量通量的计算结果会有明显影响。
通过击溅函数模拟了风雪流的发展过程,讨论了不同风速下风雪流发展时间的变化,模拟所得的稳定状态下的输雪通量与实验结果吻合较好。
According to the adhesion degree of snow grains on the bed, this paper have established different initiation models and respectively analyzed the relationship between threshold wind velocity and particle size, temperature and snow cover time at the temperature range of - 30℃- 0℃. The results show that when other factors do not change, the critical threshold wind velocity will increase with the particle size of snow grains, the critical threshold wind velocity increase with time of snow cover, and reach a steady value finally; when the temperature below zero, the critical threshold wind velocity will increase with the temperature of snow surface.
Established a movement model of single snow particle and discussed the influence of various factors on motion trajectory of snow particle at different situations. The results show that besides the gravity and the drag force, the saffman force, the magnus force, the electric field force as well as motion randomicity also have important influence to a snow grain movement, which changes with different wind speed, particle size and particle density.
Based on the analysis of threshold and movement mechanism of a snow particle, a computation model of the evolution process of wind-snow drift has been established, combined with initial velocity distribution function we analyze the structure of the snow drift and compare it with the value of cold wind tunnel test. The result demonstrated that after the wind blow snow develops to a stable state, the movement of snow grains has the obviously effects on the wind field; snow grain number's density and the horizontal quality flux obey the negative exponent distribution with height, and the computed results will be closer to the actual when the effects of Saffman force Magnus force and electric field force are taken into consideration. Furthermore the motion randomicity of mobile particle has obvious effects on the computed results too.
On the basis of splash function, we simulated the evolution of snow drift and calculated the time for the entire system to reach a steady state of snow drift at several wind speeds. Compared to the experimental results of snow flux in steady state, it suggests that the simulating results are good accordance with the experimental results.
建立单颗雪粒的运动模型,分别讨论了在不同情况下各种因素对雪粒运动轨迹的影响。结果表明:除重力和拖曳力外,saffman力、magnus力、静电力以及运动随机性对雪粒的运动也有重要的影响,并且随着风速、雪粒粒径、密度的变化各因素的影响程度也发生不同程度的变化。
基于对雪粒起动、运动机理的分析,结合初速度分布函数,建立稳态的风雪流计算模型,并对稳定状态下的风雪流结构进行分析,将分析的结果与风洞试验的测量值进行了比较,结果显示:风雪流发展稳定后,运动雪粒对风场有较为明显的修正作用;稳定状况下雪粒的数浓度和水平质量通量均随高度呈负指数分布,并且在考虑saffman力、magnus力以及静电力以后计算结果更接近实测值。当运动随机性较大时,其对雪粒的数浓度和水平质量通量的计算结果会有明显影响。
通过击溅函数模拟了风雪流的发展过程,讨论了不同风速下风雪流发展时间的变化,模拟所得的稳定状态下的输雪通量与实验结果吻合较好。
According to the adhesion degree of snow grains on the bed, this paper have established different initiation models and respectively analyzed the relationship between threshold wind velocity and particle size, temperature and snow cover time at the temperature range of - 30℃- 0℃. The results show that when other factors do not change, the critical threshold wind velocity will increase with the particle size of snow grains, the critical threshold wind velocity increase with time of snow cover, and reach a steady value finally; when the temperature below zero, the critical threshold wind velocity will increase with the temperature of snow surface.
Established a movement model of single snow particle and discussed the influence of various factors on motion trajectory of snow particle at different situations. The results show that besides the gravity and the drag force, the saffman force, the magnus force, the electric field force as well as motion randomicity also have important influence to a snow grain movement, which changes with different wind speed, particle size and particle density.
Based on the analysis of threshold and movement mechanism of a snow particle, a computation model of the evolution process of wind-snow drift has been established, combined with initial velocity distribution function we analyze the structure of the snow drift and compare it with the value of cold wind tunnel test. The result demonstrated that after the wind blow snow develops to a stable state, the movement of snow grains has the obviously effects on the wind field; snow grain number's density and the horizontal quality flux obey the negative exponent distribution with height, and the computed results will be closer to the actual when the effects of Saffman force Magnus force and electric field force are taken into consideration. Furthermore the motion randomicity of mobile particle has obvious effects on the computed results too.
On the basis of splash function, we simulated the evolution of snow drift and calculated the time for the entire system to reach a steady state of snow drift at several wind speeds. Compared to the experimental results of snow flux in steady state, it suggests that the simulating results are good accordance with the experimental results.
引文
1 Anderson,R.S.,and P.K.Haff,1988,Simulation of eolian saltation,Science,241,820-823.
2 Anderson R S,and Haft P K.1991.Wind modification and bed response during saltation of sand in air.Acta.Mech.,(Supp.)1:21-25.
3 Anderson R S,Sorensen M,and Willetts B B.1991.A review of recent progress in our understanding of Aeolian sediment transport.Acta.Mech..suppl.,1:1-19.
4 Arthur W J,1975.Snow cover and avalanches in the high alpine zone of Western United States.Low Temp.Sei Sappere.In:Physics of snow and ice.V.1,Part a,1511-1168.
5 Butterfield,G.R.(1991),Grain transport rates in steady and unsteady turbulent airflows,Acta Mech.Suppl.,1,97-122.
6 Budd,W.F.,Dingle,W.R.J.,Radok,U.,1966.The Byrd snow drift project:outline and basic results.Studies in Antarctic Meteorol.Am.Geophys.Union,Antarctic Res.Ser.9,71-134.
7 B.W.Morstad,E.E.Adams,L.R.McKittrick,2007.Experimental and analytical study of radiafion-recrystallized near-surface facets in snow.Cold Regions Science and Technology 47 90-101
8 Bagnold R A.1941.The physics of blown sand and desert dune.Methuen,London.
9 Chepil,WS,1958.The use of evenly spaced hemispheres to evaluate aerodynamic forces on a soil surface.Trans.Am.geophys.Un 39,397-404.
10 Chepil,WS,1959.Equilibrium of soil grains at the threshold of movement by wind.Proceedings,Soil Science Society of America,Vol.23,No.6,p.422-28
11 D.S.Schmidt,R.A.Schmidt and J.D.Dent1 1999:Electrostatic Force in Blowing Snow.Boundary-Layer Meteorology,1999-Springer
12 Daiji E,1970.Measure of snow drift using parallel trenches.MGA22:99-106.
13 Edson,J.B.,Fairall,C.W.,1994,Spray droplet modeling.Part 1:Lagrangian model simulation of the turbulent transport of evaporating droplets.J.Geophys.Res.,99:25295-25311.
14 Hobbs P V,MASON B J,1964.The sintering and adhesion of ice[J].Philosophy Magazine,9(3):181-197
15 Hobbs,P.V.Ice physics.1974,Oxford,Clarendon Press.
16 Hunt,J.C.R.,andA.H.Weber,1979.A Lagrangian statistical analysis of diffusion from a ground-level source in a turbulent boundary layer,Q.J.R.Meteorol.Soc.,105,423-443.
17 J.H.M.Beyers,P.A.Sundsbo,T.M.Harms.2004.Numerical simulation of three-dimensional transient snow drifting around a cube[J].Journal of Wind Engineering and Industrial Aerodynamics,No.92,725-747
18 Jensen,D.C.1956.On the cohesion of ice,p.110.M.S.Thesis,Pennsylvania State University.
19 Judith J.J.Doorschot and Michael Lehning 2002.Equilibrium saltation:mass fluxes,aerodynamic entrainment,and dependence on grain properties.Boundary-layer meteorology 104:111-130.
20 Judith J.J.Doorschot_ and Michael Lehning,2002,Equilibrium altation:mass fluxes,aerodynamic entrainment,and dependence on grain properties.Boundary-Layer Meteorology 104:111-130.
21 Kobayashi,D.,1972.Studies of Snow Transport in Low-Level Drifting Snow.Contributions from the Institute of Low Temperature Science,Hokkaido University,Ser.A,Vol.24,pp.1-58.
22 K.Nishimura and J.C.R.Hunt,2000.Saltion and incipient suspension above a flat particle bed below in turhnlent boundary layer.J.Fluid Mech.vol 417,pp.77-102.Printed in the United Kingdom.
23 Konosuke Sugiura,Kouichi Nishimura,Norikazu Maeno and Tadashi Kimura,1998,Measurements of snow mass flux and transport rate at different particle diameters in drifting snow.Cold Regions Science and Technology 27,.83-89
24 Kuroiwa,D.,1975.Mechanics and structure of snow as a dispersed system.Snow Mechanics Symposium;Proceedings of the Grindelwald Symposium,Grindelwald,Bemese Oberland (Switzerland)April 1974:International Association of Hydrological Sciences Publication No 114,p 3-15,1975.8 fig,2 tab,15 ref.
25 Legg,B.J.,Raupach,M.R.,1982,Markov-chaln simulation of particles in inhomogeneous flows:The mean drift velocity variance.Boundary Layer Meteorol.,24:3-13.
26 McEwan,I.K.,and B.B.Willetts 1991,Numerical model of the saltation cloud,Acta Mech.Suppl.,1,53-66.
27 McEwan, I. K., and B. B. Willetts (1993), Adaptation of the near-surface wind to the development of sand transport, J. Fluid Mech., 252,99-115.
28 M. Nemoto and K. Nishimura 2001, Direct Measurement of shear stress during snow saltation. Boundary-Layer Meteorology 100:149-170.
29 M. Nemoto and K. Nishimura 2004 :Numerical simulation of snow saltation and suspension in a turbulent boundary layer. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, D18206, doi:10.1029/2004JD004657,2004
30 Magono, C. and Kikuchi, K., 1980. Some observations of snowfall and meteorological conditions in Arctic Canada. Mon. Weather Rev. 108, pp. 1656-1664
31 Michaux, JL; Naaim-Bouvet, F; Kosugi, K; Sato, A; Sato, T.2002.Study in a climatic wind tunnel (Cryospheric Environment Simulator) of the influence of the type of grain of snow and of the flow on the formation of a snow-drift HOUILLE BLANCHE-REVUE INTERNATIONALE DE LEAU, (6-7): 79-83
32 Nemoto, M., and K. Nishimura ,2001. Direct measurement of shear stress during snow saltation, Boundary Layer Meteorol., 100,149-170.
33 Ning Huang, Xiaojing Zheng, 2003, Theoretical simulation of developing process of wind-blown sand movement, Key Engineering Materials, vol. 243-244: 589-594
34 Ning Huang, Xiao Jing Zheng, and You-He Zhou, 2006, Simulation of wind-blown sand movement and probability density function of liftoff velocities of sand particles, Journal of Geophysical research, vol. 111,
35 Ning Huang, Xiaojing Zheng, and You-He Zhou, 2006, A Multi-objective Optimization Method for Probability Density Function of lift-off Speed of Wind-blown Sand Movement, Advances in Engineering Software, vol. 37 (1): 32-40
36 Ning Huang, Yali Zhang, and Robert D'Adamo, 2007, A model of the trajectories and mid-air collision probabilities of sand particles in a steady-state, Journal of Geophysical research, vol. 112, D08206,
37 Owen P R. 1964. Saltation of uniform grains in air. J. Fluid Mech., 20: 225-242.
38 P.A.Sundsbo , 1998. Numerical simulations of wind deflection fins to control snow accumulation in building steps[J]. Journal of Wind Engineering and Industrial Aerodynamics, No. 74-76,543-552.
39 Ronald D Tablet,1994.Design Guidelines for the control of blowing and Drifting snow[M].Strategic Highway Program national Research council Washington,DC.
40 S.A.Savelyev,Gordon,1 J.Hanesiak,T.Papakyriakouand E A.Taylor,2006 Blowing snow studies in the Canadian Arctic Shelf Exchange Study,2003-04.HYDROLOGICAL PROCESSES Hydrol.Process.20,817-827.
41 S.Alhajraf.2004.Computational fluid dynamic modeling of drifting particles at porous fences[J].Environmental Modelling &Software,No.19,163-17
42 Shao,Y.,and A.Li 1999,Numerical modeling of saltation in the atmospheric surface layer,Boundary Layer Meteorol.,91,199-225.
43 S.Thordarson & H.Norem,2000.Simulation of two-dimensional wind flow and snow drifting application for roads:part Ⅰ[C].Snow Engineering,Hjonh-Hansen,Holant,Laset & Norem Rottardam ISBN 90 5809 148 1
44 Schmidt,D.S.and Dent.J.D.,1993,'A Theoretical Prediction of the Effects of Electrostatic Forces on Saltating Snow Particles',Ann.Glaciol.18,234-238.
45 Schmidt.R.A.,1980:Threshold wind-speeds and elastic impact in snow transport.Journal of Glaciology,vol.26,Issue 94,pp.453-467
46 Schmidt,R.A.,1981.Estimate of threshold windspeed from particle size in blowing snow.Cold Regions Science and Technology 4,187-193.
47 Skuli Thordarson 2002,Wind Tunnel Experiments and Numerical Simulation of Snow Drifting around an Avalanche Protecting Dam.Environmental Fluid Mochanics 2:265-289,2002.
48 Sugiura.K.,and N.Maeno 2000,Wind-tunnel measurements of restitution coefficients and ejection number of snow particles in drifting snow:Determination of splash functions,Boundary Layer Meteorol.,95,123-143.
49 Thomas K.Thiis.2000.A comparison of numerical simulations and full-scale measurements of snowdrifts around building[J].Wind and Structures,No.2,73-81
50 Thomas K.Thiis.1997.Experimental validations of numerical simulations of snowdrifts around buildings and in terrain[D].Doctoral Dissertation,Norwegian University of Science and Technology,Trondheim,Norway.
51 Ungar J,and Haff P K.1987.Steady state saltation in air.Sedimentology,34:289-299.
52 Wang Yanlong,Xie Zichu,Zhang Zhizhong,1980.Prevention of avalanch in the Guns Valley in Tienshan,China.Journal of Glaciology,26(94):520-521.
53 White F M.1974.Viscous fluid flow.McGraw-Hill Book Company,New York.
54 Wilson,J.D.,and B.L.Sawford 1996,Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere,Boundary Layer Meteorol.,78,191-210.
55 Xie Li,Zheng Xiaojing,2007.Impact action of soft particles on crust in wind erosion,Proceeding of International Conference on Science and Technology for Desertification Control,1:63-72.
56 XJ Zheng,L He,J Wu,2003,Vertical profiles of mass flux for windblown sand movement at steady state,Journal of Geophysical Research,vol.109,B01106
57 Xiaojing Zheng,Li Xie and Zou Xue-Yong.2006,Theoretical prediction of liftoff angular velocity distributions of sand particles in wind-blown sand flux.Journal of Geophysical research,D11109.
58 Xiaojing Zheng,Ning Huang(通讯联系人)and You-He Zhou,2003,Laboratory measurement of electrification of wind-blown sands and simulation of its effect on sand saltation movement,J.Geophys.Res.,vol.108 D(10):4322
59 Xiaojing Zheng,Ning Huang(通讯联系人),YouHe Zhou,2006,The effect of electrostatic force on the evolution of sand saltation cloud,The European Physical Journal E.vol.19:129-138
60 X.J.Zheng,L.H.He,and J.J.Wu,2004,Vertical profiles of mass flux for windblown sand movement at steady state,Journal of Geophysical Research,109,1301106.
61 Xue-Yong Zou,Hong Cheng,Chun-Lai Zhang,Yan-Zhi Zhao,2007.Effects of the Magnus and Saffman forces on the saltation trajectories of sand grain.Geomorphology 90 11-22
62 YH Zhou,WQ Li,XJ Zheng 2006,Particle dynamics method simulations of stochastic collisions of sandy grain bed with mixed size in aeolian sand saltation,Journal of geophysical research,vol.111,D15108
63 Zheng Xiaojing,He Lihong,and Wu Jianjun,2003,The feature of stratification in the blowing sand cloud,Chinese Science Bulletin,48(14):1493-1498.
64 Zheng Xiaojing,Xie Li and Zhou Youhe.2005.Exploration of probability distribution of velocities of saltating sand grains based on the stochastic grain-bed collisions.Physics letters A.334:107-118.
65 何丽红,2005.风-沙-电的多场耦合效应及其对风沙跃移运动的影响.兰州大学博士论文.
66 黄宁,2002.沙粒带电及风沙电场对风沙跃移运动影响的研究.兰州大学博士论文.
67 黄宁,郑晓静,2006.风沙跃移运动发展过程及静电力影响的数值模拟.力学学报,Vol.38,No.2
68 孔珑,2004.两相流体力学,北京:高等教育出版社.
69 马高生,黄宁,2006.风雪流临界起动风速的研究,,兰州大学学报(自然科学版)Vol.42,No 6,130-134
70 米德生,1990.中国冰、雪、冻土图的编制,冰川冻土,12(2):175-181.
71 王显祎,2003.公路风吹雪的成因机理分析[D].东北林业大学硕士论文.
72 王彦龙,张志忠,谢自楚,1979.雪崩及其防治。北京:科学出版社,1-144.
73 王中隆,1983.我国雪害及防治研究,山地研究,1(3)
74 王中隆,1988.中国积雪、风吹雪和雪崩研究,冰川冻土,10(3)
75 王中隆,2001中国风雪流及其防治研究.兰州:兰州大学出版社,
76 王中隆,白重媛,陈元,1982.天山地区风雪流运动特征及其预防研究.地理学报,37(1)
77 王中隆,李长治,1995.艾肯达坂风雪流形成机制及其治理.中国沙漠,15(2)
78 王中隆,潘遐华,陈元等,1978.风雪流及其防治。北京:人民交通出版社,1-120.
79 王中隆,潘遐华,刘贤万,1988.路堑和隧道风雪流的风洞模拟实验研究,地理学报,43(3)
80 王中隆,张志忠,1999.中国风吹雪区划,山地学报,17(4)
81 王萍,2004.风沙流悬移沙尘扩散的湍流随机模拟.兰州大学硕士论文
82 吴正,1987.风沙地貌学.北京:科学出版社.
83 杨焕霞,2000.风吹雪跃移运动的稳态数值模型.西北师范大学学报:自然科学版.Vol.36NO.3
84 邢茂,郭烈锦2003,紊流风场中起跳沙粒的轨迹特征.中国沙漠,,23(6):628-631.
85 由长福,祁海鹰,徐旭常,2002,Basset力研究进展与应用分析.应用力学学报,VOl.19NO.2
86 张林林,2005.公路风吹雪雪害仿真技术研究.吉林大学硕士论文.
87 张祥松,施雅风,1996.中国的冰雪灾害及其发展趋势.自然灾害学报,5(2)
88 张祥松,王中隆,王彦龙,1990.中国冰雪灾害研究的回顾与展望,见:第四纪全国冰川冻 学术会议论文选集.北京:科学出版社。
89 郑晓静,王萍2006,风沙流中沙粒随机运动的数值模拟研究.中国沙漠26(2):84-188.
90 周春堰著 孙祥海等译,1987.《计算流体力学导论》上海交通大学出版社
2 Anderson R S,and Haft P K.1991.Wind modification and bed response during saltation of sand in air.Acta.Mech.,(Supp.)1:21-25.
3 Anderson R S,Sorensen M,and Willetts B B.1991.A review of recent progress in our understanding of Aeolian sediment transport.Acta.Mech..suppl.,1:1-19.
4 Arthur W J,1975.Snow cover and avalanches in the high alpine zone of Western United States.Low Temp.Sei Sappere.In:Physics of snow and ice.V.1,Part a,1511-1168.
5 Butterfield,G.R.(1991),Grain transport rates in steady and unsteady turbulent airflows,Acta Mech.Suppl.,1,97-122.
6 Budd,W.F.,Dingle,W.R.J.,Radok,U.,1966.The Byrd snow drift project:outline and basic results.Studies in Antarctic Meteorol.Am.Geophys.Union,Antarctic Res.Ser.9,71-134.
7 B.W.Morstad,E.E.Adams,L.R.McKittrick,2007.Experimental and analytical study of radiafion-recrystallized near-surface facets in snow.Cold Regions Science and Technology 47 90-101
8 Bagnold R A.1941.The physics of blown sand and desert dune.Methuen,London.
9 Chepil,WS,1958.The use of evenly spaced hemispheres to evaluate aerodynamic forces on a soil surface.Trans.Am.geophys.Un 39,397-404.
10 Chepil,WS,1959.Equilibrium of soil grains at the threshold of movement by wind.Proceedings,Soil Science Society of America,Vol.23,No.6,p.422-28
11 D.S.Schmidt,R.A.Schmidt and J.D.Dent1 1999:Electrostatic Force in Blowing Snow.Boundary-Layer Meteorology,1999-Springer
12 Daiji E,1970.Measure of snow drift using parallel trenches.MGA22:99-106.
13 Edson,J.B.,Fairall,C.W.,1994,Spray droplet modeling.Part 1:Lagrangian model simulation of the turbulent transport of evaporating droplets.J.Geophys.Res.,99:25295-25311.
14 Hobbs P V,MASON B J,1964.The sintering and adhesion of ice[J].Philosophy Magazine,9(3):181-197
15 Hobbs,P.V.Ice physics.1974,Oxford,Clarendon Press.
16 Hunt,J.C.R.,andA.H.Weber,1979.A Lagrangian statistical analysis of diffusion from a ground-level source in a turbulent boundary layer,Q.J.R.Meteorol.Soc.,105,423-443.
17 J.H.M.Beyers,P.A.Sundsbo,T.M.Harms.2004.Numerical simulation of three-dimensional transient snow drifting around a cube[J].Journal of Wind Engineering and Industrial Aerodynamics,No.92,725-747
18 Jensen,D.C.1956.On the cohesion of ice,p.110.M.S.Thesis,Pennsylvania State University.
19 Judith J.J.Doorschot and Michael Lehning 2002.Equilibrium saltation:mass fluxes,aerodynamic entrainment,and dependence on grain properties.Boundary-layer meteorology 104:111-130.
20 Judith J.J.Doorschot_ and Michael Lehning,2002,Equilibrium altation:mass fluxes,aerodynamic entrainment,and dependence on grain properties.Boundary-Layer Meteorology 104:111-130.
21 Kobayashi,D.,1972.Studies of Snow Transport in Low-Level Drifting Snow.Contributions from the Institute of Low Temperature Science,Hokkaido University,Ser.A,Vol.24,pp.1-58.
22 K.Nishimura and J.C.R.Hunt,2000.Saltion and incipient suspension above a flat particle bed below in turhnlent boundary layer.J.Fluid Mech.vol 417,pp.77-102.Printed in the United Kingdom.
23 Konosuke Sugiura,Kouichi Nishimura,Norikazu Maeno and Tadashi Kimura,1998,Measurements of snow mass flux and transport rate at different particle diameters in drifting snow.Cold Regions Science and Technology 27,.83-89
24 Kuroiwa,D.,1975.Mechanics and structure of snow as a dispersed system.Snow Mechanics Symposium;Proceedings of the Grindelwald Symposium,Grindelwald,Bemese Oberland (Switzerland)April 1974:International Association of Hydrological Sciences Publication No 114,p 3-15,1975.8 fig,2 tab,15 ref.
25 Legg,B.J.,Raupach,M.R.,1982,Markov-chaln simulation of particles in inhomogeneous flows:The mean drift velocity variance.Boundary Layer Meteorol.,24:3-13.
26 McEwan,I.K.,and B.B.Willetts 1991,Numerical model of the saltation cloud,Acta Mech.Suppl.,1,53-66.
27 McEwan, I. K., and B. B. Willetts (1993), Adaptation of the near-surface wind to the development of sand transport, J. Fluid Mech., 252,99-115.
28 M. Nemoto and K. Nishimura 2001, Direct Measurement of shear stress during snow saltation. Boundary-Layer Meteorology 100:149-170.
29 M. Nemoto and K. Nishimura 2004 :Numerical simulation of snow saltation and suspension in a turbulent boundary layer. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, D18206, doi:10.1029/2004JD004657,2004
30 Magono, C. and Kikuchi, K., 1980. Some observations of snowfall and meteorological conditions in Arctic Canada. Mon. Weather Rev. 108, pp. 1656-1664
31 Michaux, JL; Naaim-Bouvet, F; Kosugi, K; Sato, A; Sato, T.2002.Study in a climatic wind tunnel (Cryospheric Environment Simulator) of the influence of the type of grain of snow and of the flow on the formation of a snow-drift HOUILLE BLANCHE-REVUE INTERNATIONALE DE LEAU, (6-7): 79-83
32 Nemoto, M., and K. Nishimura ,2001. Direct measurement of shear stress during snow saltation, Boundary Layer Meteorol., 100,149-170.
33 Ning Huang, Xiaojing Zheng, 2003, Theoretical simulation of developing process of wind-blown sand movement, Key Engineering Materials, vol. 243-244: 589-594
34 Ning Huang, Xiao Jing Zheng, and You-He Zhou, 2006, Simulation of wind-blown sand movement and probability density function of liftoff velocities of sand particles, Journal of Geophysical research, vol. 111,
35 Ning Huang, Xiaojing Zheng, and You-He Zhou, 2006, A Multi-objective Optimization Method for Probability Density Function of lift-off Speed of Wind-blown Sand Movement, Advances in Engineering Software, vol. 37 (1): 32-40
36 Ning Huang, Yali Zhang, and Robert D'Adamo, 2007, A model of the trajectories and mid-air collision probabilities of sand particles in a steady-state, Journal of Geophysical research, vol. 112, D08206,
37 Owen P R. 1964. Saltation of uniform grains in air. J. Fluid Mech., 20: 225-242.
38 P.A.Sundsbo , 1998. Numerical simulations of wind deflection fins to control snow accumulation in building steps[J]. Journal of Wind Engineering and Industrial Aerodynamics, No. 74-76,543-552.
39 Ronald D Tablet,1994.Design Guidelines for the control of blowing and Drifting snow[M].Strategic Highway Program national Research council Washington,DC.
40 S.A.Savelyev,Gordon,1 J.Hanesiak,T.Papakyriakouand E A.Taylor,2006 Blowing snow studies in the Canadian Arctic Shelf Exchange Study,2003-04.HYDROLOGICAL PROCESSES Hydrol.Process.20,817-827.
41 S.Alhajraf.2004.Computational fluid dynamic modeling of drifting particles at porous fences[J].Environmental Modelling &Software,No.19,163-17
42 Shao,Y.,and A.Li 1999,Numerical modeling of saltation in the atmospheric surface layer,Boundary Layer Meteorol.,91,199-225.
43 S.Thordarson & H.Norem,2000.Simulation of two-dimensional wind flow and snow drifting application for roads:part Ⅰ[C].Snow Engineering,Hjonh-Hansen,Holant,Laset & Norem Rottardam ISBN 90 5809 148 1
44 Schmidt,D.S.and Dent.J.D.,1993,'A Theoretical Prediction of the Effects of Electrostatic Forces on Saltating Snow Particles',Ann.Glaciol.18,234-238.
45 Schmidt.R.A.,1980:Threshold wind-speeds and elastic impact in snow transport.Journal of Glaciology,vol.26,Issue 94,pp.453-467
46 Schmidt,R.A.,1981.Estimate of threshold windspeed from particle size in blowing snow.Cold Regions Science and Technology 4,187-193.
47 Skuli Thordarson 2002,Wind Tunnel Experiments and Numerical Simulation of Snow Drifting around an Avalanche Protecting Dam.Environmental Fluid Mochanics 2:265-289,2002.
48 Sugiura.K.,and N.Maeno 2000,Wind-tunnel measurements of restitution coefficients and ejection number of snow particles in drifting snow:Determination of splash functions,Boundary Layer Meteorol.,95,123-143.
49 Thomas K.Thiis.2000.A comparison of numerical simulations and full-scale measurements of snowdrifts around building[J].Wind and Structures,No.2,73-81
50 Thomas K.Thiis.1997.Experimental validations of numerical simulations of snowdrifts around buildings and in terrain[D].Doctoral Dissertation,Norwegian University of Science and Technology,Trondheim,Norway.
51 Ungar J,and Haff P K.1987.Steady state saltation in air.Sedimentology,34:289-299.
52 Wang Yanlong,Xie Zichu,Zhang Zhizhong,1980.Prevention of avalanch in the Guns Valley in Tienshan,China.Journal of Glaciology,26(94):520-521.
53 White F M.1974.Viscous fluid flow.McGraw-Hill Book Company,New York.
54 Wilson,J.D.,and B.L.Sawford 1996,Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere,Boundary Layer Meteorol.,78,191-210.
55 Xie Li,Zheng Xiaojing,2007.Impact action of soft particles on crust in wind erosion,Proceeding of International Conference on Science and Technology for Desertification Control,1:63-72.
56 XJ Zheng,L He,J Wu,2003,Vertical profiles of mass flux for windblown sand movement at steady state,Journal of Geophysical Research,vol.109,B01106
57 Xiaojing Zheng,Li Xie and Zou Xue-Yong.2006,Theoretical prediction of liftoff angular velocity distributions of sand particles in wind-blown sand flux.Journal of Geophysical research,D11109.
58 Xiaojing Zheng,Ning Huang(通讯联系人)and You-He Zhou,2003,Laboratory measurement of electrification of wind-blown sands and simulation of its effect on sand saltation movement,J.Geophys.Res.,vol.108 D(10):4322
59 Xiaojing Zheng,Ning Huang(通讯联系人),YouHe Zhou,2006,The effect of electrostatic force on the evolution of sand saltation cloud,The European Physical Journal E.vol.19:129-138
60 X.J.Zheng,L.H.He,and J.J.Wu,2004,Vertical profiles of mass flux for windblown sand movement at steady state,Journal of Geophysical Research,109,1301106.
61 Xue-Yong Zou,Hong Cheng,Chun-Lai Zhang,Yan-Zhi Zhao,2007.Effects of the Magnus and Saffman forces on the saltation trajectories of sand grain.Geomorphology 90 11-22
62 YH Zhou,WQ Li,XJ Zheng 2006,Particle dynamics method simulations of stochastic collisions of sandy grain bed with mixed size in aeolian sand saltation,Journal of geophysical research,vol.111,D15108
63 Zheng Xiaojing,He Lihong,and Wu Jianjun,2003,The feature of stratification in the blowing sand cloud,Chinese Science Bulletin,48(14):1493-1498.
64 Zheng Xiaojing,Xie Li and Zhou Youhe.2005.Exploration of probability distribution of velocities of saltating sand grains based on the stochastic grain-bed collisions.Physics letters A.334:107-118.
65 何丽红,2005.风-沙-电的多场耦合效应及其对风沙跃移运动的影响.兰州大学博士论文.
66 黄宁,2002.沙粒带电及风沙电场对风沙跃移运动影响的研究.兰州大学博士论文.
67 黄宁,郑晓静,2006.风沙跃移运动发展过程及静电力影响的数值模拟.力学学报,Vol.38,No.2
68 孔珑,2004.两相流体力学,北京:高等教育出版社.
69 马高生,黄宁,2006.风雪流临界起动风速的研究,,兰州大学学报(自然科学版)Vol.42,No 6,130-134
70 米德生,1990.中国冰、雪、冻土图的编制,冰川冻土,12(2):175-181.
71 王显祎,2003.公路风吹雪的成因机理分析[D].东北林业大学硕士论文.
72 王彦龙,张志忠,谢自楚,1979.雪崩及其防治。北京:科学出版社,1-144.
73 王中隆,1983.我国雪害及防治研究,山地研究,1(3)
74 王中隆,1988.中国积雪、风吹雪和雪崩研究,冰川冻土,10(3)
75 王中隆,2001中国风雪流及其防治研究.兰州:兰州大学出版社,
76 王中隆,白重媛,陈元,1982.天山地区风雪流运动特征及其预防研究.地理学报,37(1)
77 王中隆,李长治,1995.艾肯达坂风雪流形成机制及其治理.中国沙漠,15(2)
78 王中隆,潘遐华,陈元等,1978.风雪流及其防治。北京:人民交通出版社,1-120.
79 王中隆,潘遐华,刘贤万,1988.路堑和隧道风雪流的风洞模拟实验研究,地理学报,43(3)
80 王中隆,张志忠,1999.中国风吹雪区划,山地学报,17(4)
81 王萍,2004.风沙流悬移沙尘扩散的湍流随机模拟.兰州大学硕士论文
82 吴正,1987.风沙地貌学.北京:科学出版社.
83 杨焕霞,2000.风吹雪跃移运动的稳态数值模型.西北师范大学学报:自然科学版.Vol.36NO.3
84 邢茂,郭烈锦2003,紊流风场中起跳沙粒的轨迹特征.中国沙漠,,23(6):628-631.
85 由长福,祁海鹰,徐旭常,2002,Basset力研究进展与应用分析.应用力学学报,VOl.19NO.2
86 张林林,2005.公路风吹雪雪害仿真技术研究.吉林大学硕士论文.
87 张祥松,施雅风,1996.中国的冰雪灾害及其发展趋势.自然灾害学报,5(2)
88 张祥松,王中隆,王彦龙,1990.中国冰雪灾害研究的回顾与展望,见:第四纪全国冰川冻 学术会议论文选集.北京:科学出版社。
89 郑晓静,王萍2006,风沙流中沙粒随机运动的数值模拟研究.中国沙漠26(2):84-188.
90 周春堰著 孙祥海等译,1987.《计算流体力学导论》上海交通大学出版社