Environmental Science and Engineering Subseries: Environmental Science Series Editors: R. Allan U. Förstner W. Salomons

Transcription

1 Environmental Science and Engineering Subseries: Environmental Science Series Editors: R. Allan U. Förstner W. Salomons

2 Xiaojing Zheng Mechanics of Wind-blown Sand Movements 123

3 Prof. Xiaojing Zheng Lanzhou University 222 South Tianshui Rd Lanzhou, Gansu People s Republic of China xjzheng@lzu.edu.cn ISSN ISBN e-isbn DOI / Springer Dordrecht Heidelberg London New York Library of Congress Control Number: c Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: lntegra Software Services Pvt. Ltd., Pondicherry Printed on acid-free paper Springer is part of Springer Science+Business Media (springer.com)

4 Foreword Ever since 1930s, human beings have been plagued by disasters caused by desertification and accompanying dust storms. Although basically a result of the evolution of the local inherent environmental conditions, all forms of desertification are also related to the economic development and influenced by global climate changes. Damages caused by desertification not only hinder the economic development, but also aggravate man s living condition. Therefore, the United Nations passed the 3337 General Assembly Resolution on Plan of Action to Combat Desertification in 1975, and desertification has become one of the major concerns of all nations since 1970s. In China, the government has also attached great importance to studies on desertification and ways to control desertification. Since the establishment of the Sand Control Team by Chinese Academy of Sciences (CAS) in 1950 s, disciplines involved have been extending from merely physical geography to multi-disciplinary combination of atmospheric science, ecology and mechanics, etc. Nowadays, many scientists and technologists plunge into the multi-disciplinary studies on desertification, they are from various national and provincial research institutions, Universities, and China Meteorological Administration (CMA). In the past 50 years, they have accumulated many experiences on monitoring and controlling of desertification, and also achieved a lot laudability progresses in theoretical researches on desertification. The physics of wind-blown sand is an issue of basic researches in desertification controlling and sand and dust storm prediction. As early as the 1930s, Bagnold, the British scientist, summarized and classified his field measurements and wind tunnel experiments. In his The Physics of Blown Sand and Desert Dune (1941), he established an initial system of windblown sand research, laying a foundation in related studies and the engineering application in the controlling of soil wind erosion and desertification. Theoretically speaking, desertification or wind-induced soil erosion is a dynamic process of spatial-temporal evolution manifested by the group behavior of wind-forced sand movement, in which many factors are involved. These factors, to name just a few of them, are the granular characteristic of sand particles, the coupling effect among sand motions, the driving wind field and moving boundary of the landforms, the trans-scale

5 VI Foreword (from micrometer-scale sand particles to centimeter-scale sand ripples, and even to ten-meter sand dunes) characteristics, the nonlinearity (the turbulent characteristics in the near-surface layer, the interaction among wind field, sand motions and thermal effect, and the nonlinearity caused by moving boundary, etc.), and the randomness (the random size distribution of sand particles, the spatial and temporal randomness of wind field, and the stochastic of turbulence, etc.). Due to the extreme complex nature of sand transportation, it remains a most challenging task to scientists, and we still have a long way to go before asserting that we have fully understood its mechanism and rules. Fortunately, achievements in non-linear science and computing technology render further in-depth studies of these complex issues possible with the rapid advancement of science and technology. Moreover, the urgent demand to increase the efficiency of desertification controlling and to vouch for the accuracy of sand (dust) storm monitoring and forecasting also promote studies on the mechanism of wind-blown sand movement in a more quantitative and more profound way. In the last decade, Professor Xiaojing Zheng, the author of this book, with her team has been working painstakingly on wind-blown sand movement. They started with a basic analysis of its underlying mechanical processes, and then undertook systematical and thorough studies on the formation and evolutional processes of the wind-blown sand flux in the nearsurface boundary layer. They have made some remarkable progresses which evolve and renew the extant theories of the physics of wind-blown sand forward to be more reasonable and sophisticated. Based on a summary of the major achievements since Bagnold, the author, in this book, elaborates her with her team s latest researches into the mechanism of wind-blown sand movement. Professor Zheng with her team s main achievements include establishing the kind of statistical method and the stochastic particle-bed collision model to obtain the lift-off velocity distribution function of sand particles, promoting the quantitative investigation on the phenomenon of wind-blown sand electrification and its impact by their experimental measurements and theoretical estimations, realizing the quantitative simulations on the formation and evolution of wind-blown sand flux relating to wind erosion, dust devil, sand ripples and sand dune fields. Furthermore, they formulated some analytical methods and presented experimental results from the mechanical approach, regarding the erecting of straw checkerboard barriers and sand fences, and the formation of soil crust. These remarkable achievements have not only profoundly revealed the underlying dynamic mechanism of wind-blown sand movement but also provided a kind of essential methods for effective design of sandcontrol engineering, which makes a very significant contribution to the physics of wind-blown sand.

6 Foreword VII Frequently plagued by raging disastrous sand and dust storms, China vigorously facilitates studies on the controlling of desertification, incubating national projects dedicating to the monitoring, the understanding and forecasting of dust storms. Scientists from CAS, CMA and some universities have made joint efforts to approach related issues from the perspective of atmospheric dynamics, such as the weather system dynamics, climatological statistics, monitoring method and predicting model of dust storms. They have established a comprehensive system, from dust monitoring to predicting, and applied it to operational service. It is worth mentioning that dust emission scheme is one of the key factors in dust storm forecast and closely related to the fashion of wind-blown sand movement in the near surface layer, which, in turn, is based on the analytic methods and corresponding studies on sand transportation illustrated in this book. Therefore, Professor Zheng s work is also very instructive for investigation on dust storms. In my own research on the dust storm, especially on the dust emission scheme, I have probed into similar issues that Professor Zheng discusses in her work. Professor Zheng and I exchanged ideas on several occasions, and have reached an understanding out of those elaborate talks that both of us are trying to find a solution to an identical problem. Our approaches may differ, but we do share same ideas and benefit from each other s research. We have also been more than once enlightened by Professor Zheng s work. Last but not least, I have to point out that the complex scientific issues involved in mechanics of wind-blown sand movement, such as multi-scale process, multi-physics field coupling effect, randomness, nonlinearity, and so on, are also paramount concerns shared by scientists working in some other fields. The solution to these problems calls for joint efforts of scientists from different disciplines. Professor Zheng s work is a rewarding attempt to provide answers to some of those questions, and certainly sets, as we have realized, a valuable example for the study of other perplexing dynamical systems, aside from solving these intractable scientific issues in mechanics of wind-blown sand movement. Qingcun Zeng Academician of CAS Institute of Atmospheric Physics, CAS December 2008

7 Preface Sand (dust) movement driven by wind force as a natural phenomenon can be seen everywhere in arid desert, farmland, seashore or even broader regions on the earth and other planets including the Mars, Venus, Titan and so on. This kind of aeolian process is usually constituted by three parts including the uplifting from the surface of the earth, atmospheric dispersion, and deposition back to the surface. Whilst wind-blown sand (dust) movement contributes to the formation of the Loess Plateau and the growth of marine fauna and flora, it also causes a series of disasters such as soil nutrient loss, physical damage to farmland, deterioration of air quality, abrasion of engineering facility, etc. These above-mentioned disasters and environmental problems arising from wind-blown sand (dust) movement, to which scholars from many scientific fields other than geographers have paid more and more attention, have always been a governmental as well as a public concern since the 20 th century. Despite great achievements have been made in controlling and managing the wind-blown sand hazard in some developed countries, for example, in the United States and Canada, desertification and pollution caused by wind-blown sand movement still remain to be the most serious, most urgent issues in developing countries, especially in China, as the global climate changes. The transportation of sand (dust) materials by wind force is influenced by a lot of factors: climate, soil type, vegetation cover and soil utilization, to name just a few. Due to its critical dependency, hysteretic nature and high spatial-temporal discontinuity, it is a typical complex natural flow of multi-phases, multi-component media, multi-scale nonlinearity under complex boundaries as well as a comprehensive dynamical system presenting multiple characteristics such as non-linearity, statistical property, diversity, self-similarity, criticality, etc., in which the multi-physics field coupling (wind field, temperature field, wind-blown sand electric field caused by charged sand particles) and multi-processes interaction (atmospheric, ecological, chemical, human activity, and so on) co-exist. Scientific research concerning the transportation of sand (dust) materials by wind force involves issues like multi-scale and multi-field coupling, stochastic and nonlinear process, and complex system, etc., which are also crucial issues confronted by other disciplines. Despite the large amount of progress

8 X Preface achieved through long-period field observations, wind-tunnel experiments and theoretical analysis as well as some famous monographs (i.e. Bagnold, 1941; Greeley and Iversen, 1985; Pye and Tsoar, 1990; Shao, 2000; Zeng, et al., 2006, etc.) published, there is still a long way to travel before we arrive at a comprehensive and profound understanding on the mechanism of sand (dust) movement and form a precise prediction of its real physical process; further still, a lot more obligations need to fulfill before we realize an effective simulation and reproduction of the evolution of wind-blown sand flux and aeolian landforms. Hence, the research approach which combines experiments, modelling and quantitative analysis, as a predominance of mechanics, is probably to the advantage of a deeper understanding of the physical process and basic rules of wind-blown sand environmental problems. Taking this advantage of mechanics into consideration, my team and I have devoted to the research of several typical issues related to aeolian processes during the past decade from a mechanical perspective. Apart from a summary of recent considerable achievements, this book mainly intends to introduce our recent research on the wind-blown sand movement through theoretical modelling, quantitative analysis and computer simulation. The first chapter of this book briefly introduces the situation of desertification and wind-blown sand disasters in China, especially North-western China. Chapter 2 summarizes the characteristics of the wind field in the atmospheric boundary layer with a particular emphasis on the turbulent property of the wind field. Chapter 3 devotes to the introduction of researches on sand s lifting off the sand bed surface, including the linear and angular velocity of sand particles lifting from the bed, their distribution and the representation of the particle-bed collision process. Chapter 4 is a description of the wind-blown sand electrification and its effect on sand saltation movement. Chapter 5 is dedicated to an analysis of the forces on sand particles and their trajectories, and is also an introduction to the experiment and theoretical prediction of sand transport rate, and in particular, the electric and thermal effect on the development of wind-blown sand flux, as well as the prediction of sand movement and transport intensity under a fluctuating wind field. Chapter 6 and 7 are devoted to the introduction of the formation and evolution of some typical aeolian landforms like ripples and dunes. Chapter 8 presents the mechanical analysis method to estimate the efficiency of sand prevention methods. This book aims at serving as a reference for researchers and graduate students who major in geo-related sciences, such as physics of wind-blown sand, environmental science, geophysics, atmospheric science, etc., mechanics as well as applied mathematics, broadening the readers horizon on the latest development of the quantitative research on wind-blown sand

9 Preface XI movement and enhancing their competence to apply basic methods in this field. What I strive for is provide some methods and principles which may be helpful to researchers interested in the wind-blown sand movement and other environmental issues via this book, which, on one hand, may help researchers and students of geology and atmospheric science understand what can be absorbed from mechanics to push investigations on windblown sand movements in a more rational and quantitative manner and on the other hand, provide researchers and students expertise in mechanics, mathematics, physics and environment-related engineering with a smooth access to the research field of wind-blown sand movement. In this case, both parties mentioned above can unit their efforts to promote an understanding of the mechanism of wind-blown sand (dust) movements and push forward the development of this interdisciplinary research. By the way, with the publication of this book, I would also hope that more and more scholars and experts in the world will pay their attention, further their professional suggestions and actions to aeolian environmental problems in China. Since the first day I set foot in the field of wind-blown sand movements, I have been inspired by some scholars in Geosciences and atmospheric sciences as follow: Prof. D. A. Gillette of National Oceanic and Atmospheric Administration (USA), Prof. Y. P. Shao of the Institute of Geophysics and Meteorology, University of Cologne, Academician H. L. Sun and D. H. Qin, Dr. P. Cui, Dr. Z. H. Lin, Dr. T. Wang, Dr. J. J. Qu, Dr. Y. Q. Ling, Dr. Z. B. Dong of Chinese Academy of Sciences (CAS) and Academician Y. T. Chen of China Earthquake Administration as well as Dr. X. Y. Zou of Beijing Normal University. Besides, some scholars in Mechanics like Prof. K. Moffat, ex-president of the International Union of Theoretical and Applied Mechanics (IUTAM, ), Prof. F. Hussain (Member of the National Academy of Engineering and the Academy of Sciences for the Developing World) of the University of Houston, and several ex- Presidents of the Chinese Society of Theoretical and Applied Mechanics (CSTAM), including Academician Z. M. Zheng, Y. L. Bai, and E. J. Cui, etc., also offered me very important assistance. I would like to take the opportunity to express my gratitude to them. In particular, I would like to appreciate Academician H. Zhou of Tianjin University, Academician Q. C. Zeng of the Institute of Atmospheric Physics, CAS, and Academician J. C. Li, President of CSTAM, who not only provided much important and detailed guidance, but also paid much attention to my research work. All these concern and encouragement have been urging me keep going forward. The research work in this book is co-financed by the project of the Ministry of Science and Technology of China (No.2009CB421304,

10 XII Preface No.2006DFA03640), the Natural Science Foundation of China (NSFC, No , No ) and the Science Foundation of Ministry of Education of China (No ). I would like to express my acknowledgement on these supports and also would like to thank Dr. P. W. Ji, Dr. Q. G. Meng, Dr. S. G. Zhan, and Dr. Q. Q. Liu of NSFC. Besides, sincere thanks are due to my students as follows: N. Huang, L. Xie, T. L. Bo, J. H. Zhang, P. Wang and W. Zhu, etc., who assisted me to collect relevant materials. I appreciate Mr. M. Lion from Canada and Mr. N. Virgo from the United Kingdom for the proofreading of this book, and due to Dr. Agata Oelschläger from Springer-Verlag, Germany for the publishing work and Mr. N. Cheng for the typesetting of this book. Finally, I would like to express my sincere thanks to Prof. Y. H. Zhou, Director of the Key Laboratory of Mechanics on Western Disaster and Environment (Lanzhou University) for his long-term support. Lanzhou University Lanzhou, P. R. China January 2009 Xiaojing Zheng

11 Contents Chapter 1 Wind-Blown Sand Environment Desert and Desertification Desert Desertification Harms of Wind-Blown Sand Environment Wind Erosion Sand (Dust) Storm Examples: Dunhuang, Minqin, Maqu Dunhuang Minqin Maqu...16 Chapter 2 Flows of the Near-Surface Boundary Layer An Introduction to Fluid Mechanics Viscosity of a Fluid Properties of Flow Basic Equations of Fluid Mechanics Conservation of Mass (Continuity Equation) Conservation of Momentum Conservation of Energy Basic Equations of Turbulence Models of Turbulence Approaches of Turbulent Numerical Simulation Basic Characteristics of the Atmospheric Boundary Layer Observations of the Atmosphere Boundary Layer Basic Equations of the Atmospheric Boundary Layer Basic Equations Aerodynamic Roughness Characteristics of the Flow Field on the Wind-Blown Sand Boundary Layer Effect of Sand Dunes on the Flow Field Wind Gusts near the Earth s Surface Analysis of the Wind Gusts...47

12 XIV Contents Prediction Model I: Wind Gusts Vary with Time Prediction Model II: Wind Gusts Vary with Height...58 Chapter 3 Sand Motion near the Sand Bed Surface Threshold Wind Velocity for Sand Motion Mechanism of the Entrainment of Sand Particles Threshold Wind Velocity of Sand Motion Factors Affecting the Threshold Wind Velocity Experimental Research on the Lift-off of Sand Particles Experiments on Particle-Bed Collision with Artificial Sand Measurements of the Linear Velocities of Lift-off Particles Measurement of the Angular Velocities of Saltating Particles Stochastic Model of Particle-Bed Collision Stochastic Model Soft-Particle Approach for Collision Process Hard-Particle Approach for Collision Process Analytical Solution of Lift-off Velocity Probability Distribution of Lift-off Velocities Splash Function Splash Function for Uniform Sands Splash Function for Mixed Sands...98 Chapter 4 Wind-Blown Sand Electrification Charged Sand Particles and their Charging Mechanisms Observations and Measurements Charging Mechanisms of Sand Particles Measurements of Wind-Blown Sand Electric Field Atmospheric Electric Field Field Observation of Wind-Blown Sand Electric Field Wind Tunnel Measurement of Wind-Blown Sand Electric Field Theoretical Calculation of Wind-Blown Sand Electric Field Electric Field Due to Sand Particles Moving in Air Electric Field Due to Sand Particles in Sand Bed Total Electric Field Due to Charged Sand Particles in Wind-Blown Sand Flux Effects of Charged Sand Particles Effects on the Entrainment of Sand Particles Effects on Electromagnetic Wave Propagation...128

13 Contents XV Chapter 5 Wind-Blown Sand Flux and its Prediction Forces on Saltating Sand Particles Sand Saltation The Effect of Wind-Blown Sand Electric Field on Sand Saltation The Effects of Particle s Mid-Air Collisions on Sand Saltation Trajectories Saltation Trajectory and Saltation Activity in a Fluctuating Wind Field The Criterion of Saltation and Suspension Experiments and Observations on Sand Transport Rate Theoretical Simulations on the Evolution of Wind-Blown Sand Flux Dust Devil Chapter 6 Aeolian Geomorphology and its Simulation Aeolian Sand Ripples Observations of Aeolian Sand Ripples The Basic Characteristics of Aeolian Sand Ripples The Formation Mechanism of Aeolian Sand Ripples Continuous Models for Aeolian Sand Ripples The Anderson s Continuous Model The Granular Surface Flow Model Discrete Models for Aeolian Sand Ripples Cellular Automata Model (Anderson-Bunas Discrete Model) Discrete Element Model (Landry-Werner Model) Coupled Mapping Lattice Model (Nishimori-Ouchi Model) Discrete Particle Tracing Method (DPTM) Model Basic Method Major Simulation Results Chapter 7 Aeolian Geomorphology and its Simulation Aeolian Sand Dunes Aeolian Sand Dunes and Observation Results Classification of Sand Dunes The Observation of Sand Dune Migration Observation on the Dynamical Behavior of Sand Dunes Influence Factors Continuum Sand Dune Model...232

14 XVI Contents 7.3 Simulation of Sand Dune Field Coupled Mapping Lattice Method Cellular Automaton Method Numerical Simulation of Sand Dune Field Discrete Numerical Simulation of Sand Dune Field Simulation Results Chapter 8 Mechanical Analysis on the Efficiency of Sand Prevention Methods Sand Fence Straw Checkerboard Barriers The Mechanical Properties of Crust The Survey on the Mechanical Properties of Crust The Destruction of Saltating Sand to Crust References Author Index Subject Index...305

15 Sy m b o ls In this text, hundreds of different physical quantities are included in various formulations. Use of the same letters or symbols for different concepts has been unavoidable. Choice of notation was affected by the desire to retain commonly used notations familiar in each field of study, while at the same time avoiding ambiguity by making a single choice where two or more symbols for the same quantity are known to exist in the literature. Main symbols commonly used in this text are listed below, unless otherwise defined in the text, the meaning of symbols, are understood: x,y,z Cartesian coordinates S T viscous dissipation u(u,v,w) velocity vector of fluid term (velocity component in λ Τ thermal conductivity coordinates x,y,z) γ d atmospheric dry adiabatic x i ith coordinate (i = 1, 2, lapse rate 3) k T thermal diffusivity e the unit vector of the e internal energy coordinates with e i in the direction of x i c p heat capacity at constant pressure of fluid μ viscosity of fluid phase μ t turbulent viscosity or g gravity acceleration eddy viscosity coefficient R Molar gas constant t time ν kinetic viscous of fluid Δt time interval Re Reynolds number l m Prandtl mixing length ρ density k Karman constant ν kinetic viscous of fluid σ k Prandtl number of the U characteristic velocity turbulent fluctuation of fluid or velocity momentum L length ε turbulent dissipation H height rate P thermodynamics pressure c concentration of solid phase in two phase T temperature flow f body force vector P 0,ρ 0,T 0 pressure, density and T surface force tensor temperature of static heat flux atmosphere q T

16 XVIII Symbols p,ρ,t d variation of thermodynamic quantities caused by flow u *t threshold friction velocity for baresand(soil) surface u *0 surface friction velocity u * friction velocity of (u *t ) V threshold friction velocity for vegetated u t u *a friction velocity of wind in saltation layer z 0 z s equivalent roughness or movable bed roughness in wind blown τ 0 τ a N s N a σ number flux of saltation particle from surface bed number flux of particles entrained directly by the aerodynamic force of air flow standard deviation or basal-to-frontal area ratio of vegetation fluid S k skewness K x kurtosis I turbulence surface T g wind gusts period threshold fluid velocity D particle diameter at height z ρ s density of sand particle D s diameter of sand particle in wind-blown sand m s mass of sand particle aerodynamic roughness V s volume of sand particle length V s resultant velocity vector x, yz, of sand particle (velocity component sand in coordinates x,y,z) shear stress at the upper θ angle of sand velocity boundary of the to the horizontal or saltation layer in wind- potential temperature blown sand η porosity of the sand shear stress in the satation bed or fence layer τ c critical fluid shear stress τ s vertical momentum flux produced by sand movement H s thickness of mean saltation E kinetic energy of moving particle or Young s modulus of crust α dune u *crest velocity acceleration factor on the dune friction velocity on dune top

17 Symbols XIX u * friction velocity of the inflow far away from β,α k impact and contact angle of sand in the dune process of impact F D aerodynamic drag force with bed surface F g gravity force ω spin angular velocity F L aerodynamic lift force N r, N e numbers of rebound F M Magnus force and ejected sand particles F E electric force F s Saffman force V im Impact velocity of Basset force sand particle F B F i F pn F fτ F rn,f rτ F x C D C L inter-particle force normal contact force in the process of particle colliding tangential friction force in the process of particle colliding normal and tangential damping forces in the process of particle colliding force acting on the wind per volume resulted from sand transport λ V roughness density, frontal area index of σ V χ N ej V r, V e V V x,v y,v z mean number of sand particles jumping from the bed per impact rebound velocity and ejected velocity of sand particle from bed, respectively resultant lift-off velocity of sand particle from bed E s wind sand electric E x,e y,e z field vector aerodynamic drag coefficient E a atmospheric electric field aerodynamic lift coefficient E a0 atmosphere electric field at ground level δ e density of surface charges at ground vegetation roughness level basal-to-frontal area ratio ε 0 electrical permittivity of roughness ele- of air ment or vegetation ε s permittivity of sand angle between the wind particle direction and the normal C q charge-to-mass ratio line of the bed sur- of charged sand parti- face cle α surface slope angle q c particle charge

18 XX Symbols ρ q volume charge density RSI ripple symmetry index σ q surface charge density RI ripple index 1 2 E sz, E sz electric field produced λ wavelength of sand by saltating and suspending ripple particle, re- spectively α ss,α ls stoss and lee slope angle of sand ripple E cz electric field produced by sand particles in sand bed V d migration velocity of sand dune E i electric field of incident H supply thickness of sand electromagnetic supply wave penetrating in the h tun height of wind tunnel spherical sand particle u ax axial wind velocity of σ w w st P sal σ s w τ L T L * vertical velocity standard deviation of air parcel terminal settling velocity of sand particle saltation parameter h 0 l max wind tunnel straw height of straw checkerboard barrier maximum distance of two adjacent straw grids of straw checkerboard barrier elastic deflection of crust because of salta- vertical velocity standard w e deviation of sand particle tion impact Lagrangian time scale W(t) creep deflection function of air parcel of crust modified Lagrangian p(.) collision probability time scale of air parcel of saltating particle along the sand particle trajectory f(.) distribution function I s processional moment Q sand transport rate of sand particle q mass flux of sand Subscripts Unsuperscripted or Superscripts ij tensor (ˉ) mean of the physical quantity s sand ( ) fluctuation of the physical quantity f fluid (.) time rate ( ) second derivative with respect to time