The Physics of Blown Sand and Desert Dunes

THE NATURE OF THE PROBLEM THIS book results from an attempt to explain on a basis of experimental physics some of the many strange phenomena produced by the natural movement of sand over the dry land of the Earth. The subject is but one aspect of a far wider problem which is still very imperfectly grasped-the transport of solid particles of any kind by fluids in general. Here the difficulty has been, and still is, that no one branch of science has attempted to deal with the problem as a whole, or to co-ordinate the vast amount of piecemeal work by students of different outlook in many unrelated fields. The carriage of silt by rivers has received a great deal of attention from engineers. But owing to the difficulties of direct measurement, to the expense and labour of conducting full-scale experiments, and to a failure to find agreement as to the basic quantities upon which a theoretical edifice may be built, the published results are far from satisfactory. Little has emerged except empirical formulae; and these are rarely capable of reliable application to conditions other than those under which they were evolved. The drifting of snow is of direct interest to transport authorities in many countries, to meteorologists engaged in the study of rainfall, to ski-runners and to mountaineers. Yet no means has been found whereby the precipitation can be gauged, or the rate of drift related to the strength of the wind.

I The Physics of Grain Movement.- 1 Sand and Dust.- 1 The Order of Size of Small Particles. Use of the Logarithmic Scale.- 2 The Definition of Grain Size.- 3 The Suspension of Small Particles. The Distinction between Sand and Dust.- 4 The Composition of Natural Sand. The Prevalence of Quartz.- 5 The Origin and Formation of Sand Grains.- 2 The Behaviour of Sand Grains in the Air.- 1 The Phenomenon of Sand-Driving.- 2 Susceptibility of The Grains to Wind Forces.- 3 Experimental Verification.- 4 The Paths Traced by Sand Grains through the Air.- 5 Experiments on the Bouncing Properties of Quartz Grains.- 6 Saltation.- Appendix I Calculation of the Susceptibility.- Appendix II Calculation of Grain Motion.- 3 Wind-Tunnel Observations.- 1 The Design of a Special Wind Tunnel for Sand Experiments.- 2 Method of Operation.- 3 Observation of the Grain Paths. Method of Illumination.- 4 Saltation Over a Loose Sand Surface, Initiated by Grain Impact.- 5 Saltation Initiated by Direct Wind Action.- 6 Saltation at Higher Wind Speeds.- 7 The Surface Creep.- 8 Surface Ripples.- 9 Saltation Over Hard Ground.- 10 Three Types of Grain Motion: Suspension, Saltation, and Surface Creep.- 4 The Surface Wind.- 1 The Measurement of Wind Velocity.- 2 The Surface Drag.- 3 Streamline and Turbulent Flow.- 4 The Transition Condition. the Reynolds’ Number.- 5 The Distribution of Wind Velocity with Height.- 6 The Surface Roughness.- 7 The Drag Velocity V*. V* Also a Measure of the Velocity Gradient.- 8 Change of Wind Speed Caused by Change of Surface Texture.- 9 The Boundary Layer.- 5 The Effect of Sand Movement on the Surface Wind.- 1 Changes in the Velocity Distribution.- 2 The Characteristic Grain Path.- 3 The Drag Caused by Moving Sand. Relation Between V’* and Rate of Sand Movement.- 4 Relation Between Wind Velocity and Rate of Sand Movement.- 5 Increase of Sand Movement Over Surfaces Containing Large Grains.- 6 Sand Movement Under Water Compared With That in Air.- 7 The Suspension of Sand Grains in Air.- 6 Confirmatory Measurements in the Desert.- 1 The Apparatus Used.- 2 Measurement of the Rate of Sand Movement.- 3 Results.- 7 Threshold Wind Speed and Size of Sand Grain.- 1 The Fluid Threshold for Uniform Sand.- 2 The Fluid Threshold for Very Small Grains.- 3 Immobility of Settled Dust and Loess.- 4 The Fluid Threshold for Natural Sand of Mixed Grain Size.- 5 The Impact Threshold Wind.- 8 Summary of the Physics of Grain Movement.- 1 The Forces Acting on Single Particles.- 2 The Size of Natural Particles in Terms of the Equivalent Spherical Diameter.- 3 The Turbulence of the Fluid.- 4 Suspension, and Transport Along the Floor. Distinction Between Dust (OR SILT) and Sand.- 5 Turbulent Flow Near the Bed.- 6 The Drag ?, and the Drag Velocity V*.- 7 Flow Over a Flat Surface Whose Texture Changes Across a Transverse Border. The Boundary Layer.- 8 The Fluid Threshold of Flow Required to Move Grains on the Bed.- 9 Sand Movement in Air and Water. The Saltation Drag.- 10 Sand Movement in Air. Wind Velocity Distribution.- 11 The Impact Threshold.- 12 Saltation and Surface Creep. Sand Flow in Terms of Wind Strength.- 13 The Mean Grain Path of the Saltation and the Wave-Length of the Surface Ripple in Air.- II Small-Scale Effects. Grain Size Distribution. Surface Ripples and Ridges.- 9 Grading Diagrams.- 1 Mechanical Analysis.- 2 The ‘ Percentage-Smaller ’ Diagram.- 3 The Block Diagram.- 4 The Differential Diagram.- 5 The Log Diagram.- 6 Symmetrically Graded Sands. Comparison With the ‘ Normal Probability Curve ’.- 7 Regular and Mixed Sands.- 8 Grain Diameter Defined by Sieve Aperture. a Method of Adjustment of Sieve Calibration.- 10 Grading Changes in Non-Uniform Sand.- 1 The Cycle of Sand Movement. Removal, Transportation, and Deposition. Three Modes of Deposition: Sedimentation, Accretion, and Encroachment.- 2 Grading Experiments, and the Representation of the Results.- 3 Grading Changes due to Wind Action During the Cycle of Sand Movement.- 4 Summary of Grading Changes in Regular Sands.- 5 Grading Changes Due to Mechanical Movement of Grains Down a Slip-face.- 6 How do Irregular Sands Become Regular ?.- 7 Incomplete Sands.- 11 Surface Ripples and Ridges.- 1 Sand Waves and Water Waves Not Analogous.- 2 Classification of Sand Ripples and Ridges.- 3 Instability of a Flat Sand Surface. Effect of Changes in the Angle of Incidence of the Descending Saltation.- 4 Surface Creep Dependent on the Angle of Incidence of the Saltation.- 5 Ripples Formed Under Equilibrium Conditions: (a) Factors Controlling the Wavelength; (b) Wind Strength and Characteristic Grain Path; (c) The Ripple Height and Shape Depend on the Surface Grading.- 6 Ripples during Deposition.- 7 Ripples and Ridges During Sand Removal: (a) Limited Removal—Coarse, Steep-Faced Ripples; (b) Removal Maintained by an Oncoming Saltation—Unlimited Growth of Ridges; (c) Ridges in Very Strong Winds.- 8 Ripple-Less Sand Mixtures. The Surfaces of Sand Sheets.- 9 The Transverse Alignment of Sand Ripples in Air.- 10 Sand Ripples in Air and Water Compared.- 11 Ripples in Snow.- 12 Ripples in Very Fine Sand.- III Large-Scale Effects. Sand Accumulation. Dunes. Internal Structure, Etc..- 12 Conditions for the Growth of a Sand Surface.- 1 Limitations to the Experimental Study of Dune Formation.- 2 The Supply of Material for Dune-Building. Nature of the Desert Floor.- 3 Sand Storage on a Pebble floor.- 4 Deposition by Accretion on an Existing Patch of Bare Sand.- 5 Explanation of Sand Accretion on a Flat Surface in Terms of the wind Velocity Picture. Distinction Between ‘ Gentle ’ and ‘ Strong ’ Winds.- 6 The Effect of Varying Wind Direction.- 7 Sand Drift Over a Uniform Surface is Unstable Across a Transverse Section. Sand-Strip Formation. Dune-Building by a Uni-Directional Wind.- 8 Surrounding Surface Not Immobile. Inhibition of Dune Growth by the Spread of Coarse Grains over the Sand Surface.- 9 Fluctuations in the Rate of Sand Movement Over a Sand Surface. The Minimum Size of Sand Dunes.- 10 The Influence of Vegetation.- 11 The Prevailing Sand-Driving Wind. The Long-Period Sand Movement as a Vector-Sum Of Movements During ‘ Strong ’ and ‘ Gentle ’ Winds.- 13 Sand Shadows and Sand Drifts. General Factors on Which Dune Shape Depends.- 1 Types of Sand Accumulation.- 2 Sand Shadows Behind Obstacles.- 3 Sand Drifts Between Obstacles.- 4 Sand Drifts Below Cliffs.- 5 The Influence of Cross-Winds on Dune Shape as Suggested By the Behaviour of Under-Cliff Sand Drifts.- 6 True Dunes as Deformable Wind Obstacles. General Considerations Affecting the Shape they Assume. The Longitudinal Cross-Section. (a) Gentle Winds; (b) Strong Winds; (c) Long-Period Mean Wind—Relation Between Rate of Sand Flow Over Dune, and The Shape of the Dune; (d) Formation of The Slip- Face; (e) The Effect of The Slip-Face on Dune Formation; The Rate of Advance.- 7 The Instability of a Long Transverse Dune.- 14 The Barchan Dune.- 1 The Crescentic or Barchan Dune. The Observed Wind Distribution Over It.- 2 The Shape and Position of the Slip-Face.- 3 The Minimum Height of The Slip-Face.- 4 The Trailing Wing-Tips. The Lateral Sand Movement Away from the Axis. Sand Leaves the Dune in Two Streams.- 5 Non-Uniform Distribution of Sand Supply. Complex Barchans. Fuljis.- 6 The Size and Height of Barchans, and Their Rate of Advance.- 7 The Effect of Winds from the Reverse Direction.- 8 Barchan Belts.- 9 Ice Barchans.- 15 The Longitudinal or Seif Dune. The Whaleback.- 1 The Transition from the Barchan to the Seif Dune Forms.- 2 The Seif Shape Varies According to the Long-Period Wind Régime.- 3 Movement of the Seif Dune.- 4 Growth of a Seif Dune. Grading of Sand Over the Cross-Section. Formation of a Plinth of Coarse Sand at the Base.- 5 Seif Dune Chains. Height, Length, Repetition Distance, and Alignment.- 6 Whalebacks or Sand Levees. The Egyptian Sand Sea.- 7 The Transverse Repetition Distance Between Seif Dune Chains.- 8 The Formation of Barchans in the Longitudinal Troughs between Multiple Seif Chains, where the Effect of Cross-Winds is Excluded.- 9 Dune Systems and Wind Direction.- 16 The Internal Structure of Sand Deposits.- 1 Consistency of the Deposited Material.- 2 Laminar Structure Revealed by the Differential Rate of Water Seepage through Layers of Varying Grain Grading.- 3 Structure of Beds Deposited by Accretion. Their Firmness. Similarity to Wind-Packed Snow.- 4 Grading Changes due to Shearing. Structure of an Avalanched Encroachment Deposit.- 5 Structure of a Barchan Dune.- 6 Structure of Seifs and Whalebacks.- 7 Structure and Growth of Sand Sheets.- 8 Water Retention and Vegetation Dependent on the Internal Structure.- 17 ‘ Singing Sands ’.- 1 ‘ Whistling ’ Beach Sand.- 2 The ‘ Song ’ or Booming of Desert Sands.- 3 What Controls the Note, and How Does the Sound Arise ?.