Table Of ContentTHE PHYSICS OF
BLOWN SAND AND DESERT DUNES
THE PHYSICS
OF BLOWN SAND AND
DESERT DUNES
by
R. A. BAGNOLD, F.R.S.
CHAPMAN & HALL
NEW FETTER LANE, LONDON EC4
I I
First published June 26th I94I
Reprinted four times
Reprinted I973
sojtcover reprint of the hardcover 1S f edition 1973
Published by Chapman f!j Hall Ltd
II New Fetter Lane, London EC4P 4EE
ISBN-13: 978-94-{)09-5684-1 e-ISBN-13: 978-94-009-5682-7
DOl: lO.l0071978-94-()09-5682-7
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may be printed, or reproduced or utilized in
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other means, now known or hereafter invented,
including photocopying and recording, or in
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without permission in writing from the
Publisher.
Distributed in the U.S.A. by
Halsted Press, a Division of
John Wiley f!j Sons, Inc. New York
PREFACE TO 1954 REPRINT
THE completion of the original manuscript of this book
coincided with the beginning of World War II and with
my own departure on military service in the Middle East.
The number of copies which it was possible to print in
1941 was, for obvious reasons, small. And by the time
many of those interested had returned to their normal
pursuits the edition had become exhausted. The decision
of the publishers to print a second edition will therefore,
it is hoped, be welcomed.
Considerable re-writing would have been possible,
but for several reasons I have retained the original text,
subject to a few minor corrections. As regards the first
half of the book time has not altered or appreciably
extended the experimental facts concerning the movement
of sand by wind. When at some future date the subject
matter may come to be re-written, I feel it should be in
the form of an entirely new book dealing much more
generally with the movement of any kind of solid grains
in any fluid, that of sand in air or in water being covered
as special cases. Though my recent experimental work
has lain in this direction the time is not yet ripe for such
an enterprise.
As regards the second half of the existing book which
deals with full-scale dunes and other sand forms, few if
any new facts have emerged. Further progress here
must, I think, be in the nature of surmise only, until
local wind, and possibly temperature, records taken over
fairly long periods are available for the very near vicinity
of dunes of various types, and until our knowledge of
the meteorology of deserts is more thorough than at
present. The sandy regions of the world are economi
cally unimportant; and were it not for the recent oil
v
VI BLOWN SAND AND DESERT DUNES
developments in the Middle Eastern deserts and for the
nuisance caused to these vast operations by blown sand
and dunes there would be little hope of the required data
being collected. Under present conditions we may,
however, look forward with some confidence to a start
being made on sound and well-organized lines.
But intriguing though the shapes and movement of
desert dunes may be, the physics of wind-blown sand
has a potentially wider interest much nearer home. On
the first page of the Introduction, written fourteen years
ago, I referred to the wider problem of the transport of
granular material of any kind by fluids in general, to the
case of its carriage by liquids, both in rivers and, indus
trially, through pipes, and to the greater difficulties of
observation in this case. These difficulties have been so
great that research on lines conventional to hydraulic
engineers has advanced very little our knowledge of the
basic principles involved. There is, however, an essential
unity underlying the internal dynamics of the flow of all
fluids, whether gases or liquidi', and this unity must
extend to the interaction between the fluid flow and the
movement of grains within it. Clearly, therefore, the
difficult hydraulic problem should be approached by
viewing it in as wide a perspective as possible. If by
so doing we can find general relationships or physical
laws which hold good in very different parts of the field
of view, these must provide the clues by which the
difficult hydraulic problem may be solved.
In the case of wind-blown sand the grains are some
2,000 times as heavy as the fluid. In that of water
driven natural sand the immersed weight of the grains
is only one and a half times the weight of the fluid.
Since no really intermediate pair of substances exist a big
difference in the behaviour of the grains in the two fluids
is only to be expected. It is possible in the laboratory
to go much further. \Ve can make an artificial sand
which is only just heavier than water. Or more .simply
we can load \vater with, say, common salt till it is only
just lighter than a sand made of crushed plastic-Perspex
PREFACE Vll
or polystyrene. In this way we can experiment with a
granular material whose immersed weight is only a few
thousandths of that of the fluid. Under these conditions
the grains take a minute or more to settle a few inches
to the bed. Yet at this opposite extremity of the scale
of relative density many of the experimental difficulties
met with in the case of natural sand in water are found
to disappear. Curiously enough much of the same
technique is applicable as was used in the case of wind
blown sand. Experimenting on these lines one finds
that some phenomena barely detectable in one case
become grossly exaggerated in the other, and vice-versa,
but that several quite simple relationships are common
to both these extreme cases.
The results of this work is approaching the stage of
publication. From them a fairly clear picture is emerging
of the general principles of the fluid transport of solids.
But at the same time it is becoming apparent that in the
intermediate and much more economically important
case the real simple picture may long remain obscured
from direct vision by practical experimental difficulties.
Our knowledge of some aspects of it may have to remain
indirect, derived from the two extreme cases.
One of the~e is the case of wind-blown sand. Being
simple, cleanly and easily dealt with experimentally with
out elaborate apparatus, it seems likely to become an
essential stepping stone to knowledge which is yearly
more needed both by industry and by engineers.
R. A. B.
July, I953
CONTENTS
PAGE
INTRODUCTION: THE NATURE OF THE PROBLEM XV
PART I
THE PHYSICS OF GRAIN MOVEMENT
CHAPTER I
SAND AND DUST
I THE ORDER OF SIZE OF SMALL PARTICLES. USE OF THE
LOGARITHMIC SCALF. I
2 THE DEFINITION OF GRAIN SIZE 3
3 THE SUSPENSION OF SMALL PARTICLES. THE DISTINCTION
BETWEEN SAND AND DUST 5
4 THE COMPOSITION OF NATURAL SAND. THE PREVALENCE
OF QUARTZ 7
5 THE ORIGIN AND FORMATION OF SAND GRAINS 8
CHAPTER 2
THE BEHAVIOUR OF SAND GRAINS IN THE AIR
I THE PHENOMENON OF SAND-DRIVING 10
2 SUSCEPTIBILITY OF THE GRAINS TO WIND FORCES 12
3 EXPERIMENTAL VERIFICATION IS
4 THE PATHS TRACED BY SAND GRAINS THROUGH THE AIR 16
5 EXPERIMENTS ON THE BOUNCING PROPERTIES OF QUARTZ
GRAINS 16
6 SALTATION 19
APPENDIX I CALCULATION OF THE SUSCEPTIBILITY 21
APPENDIX II CALCULATION OF GRAIN MOTION 23
IX
x BLOWN SAND AND DESERT DUNES
CHAPTER 3
WIND-TUNNEL OBSERVATIONS PAGE
I THE DESIGN OF A SPECIAL WIND TUNNEL FOR SAND EXPERI
MENTS 25
2 METHOD OF OPERATION 27
3 OBSERVATION OF THE GRAIN PATHS. METHOD OF
ILLUMINATION 28
4 SALTATION OVER A LOOSE SAND SURFACE, INITIATED BY
GRAIN IMPACT 3 I
5 32
SALTATION INITIATED BY DIRECT WIND ACTION
6 SALTATION AT HIGHER WIND SPEEDS 33
7 THE SURFACE CREEP 33
8 SURFACE RIPPLES 35
9 SALTATION OVER HARD GROUND 35
10 THREE TYPES OF GRAIN MOTION: SUSPENSION, SALTATION,
AND SURFACE CREEP 37
4
CHAPTER
THE SURFACE WIND
I THE MEASUREMENT OF WIND VELOCITY 38
2 THE SURFACE DRAG 42
3 STREAMLINE AND TURBULENT FLOW 43
4 THE TRANSITION CONDITION. THE REYNOLDS' NUMBER 46
5 THE DISTRIBUTION OF WIND VELOCITY WITH HEIGHT 47
6 THE SURFACE ROUGHNESS 49
7 THE DRAG VELOCITY v• . V. ALSO A MEASURE OF THE
VELOCITY GRADIENT SO
8 CHANGE OF WIND SPEED CAUSED BY CHANGE OF SURFACE
TEXTURE 53
9 THE BOUNDARY LAYER 55
5
CHAPTER
THE EFFECT OF SAND MOVEMENT ON THE SURFACE WIND
CHANGES IN THE VELOCITY DISTRIBUTION 57
2 THE CHARACTERISTIC GRAIN PATH 62
3 THE DRAG CAUSED BY MOVING SAND. RELATION BETWEEN
V~ AND RATE OF SAND MOVEMENT 64
CONTENTS Xl
5
CHAPTER
THE EFFECT OF SAND MOVEMENT ON THE SURFACE WIND
-continued
PAGE
4 RELATION BETWEEN WIND VELOCITY AND RATE OF
SAND MOVEMENT 68
5 INCREASE OF SAND MOVEMENT OVER SURFACES CONTAINING
LARGE GRAINS 71
6 SAND MOVEMENT UNDER WATER COMPARED WITH THAT IN
~ ~
7 THE SUSPENSION OF SAND GRAINS IN AIR 75
CHAPTER 6
CONFIRMATORY MEASUREMENTS IN THE DESERT
I THE APPARATUS USED 77
2 MEASUREMENT OF THE RATE OF SAND MOVEMENT 79
3 RESULTS 81
CHAPTER 7
THRESHOLD WIND SPEED AND SIZE OF SAND GRAIN
I THE FLUID THRESHOLD FOR UNIFORM SAND 85
2 THE FLUID THRESHOLD FOR VERY SMALL GRAINS 89
3 IMMOBILITY OF SETTLED DUST AND LOESS 90
4 THE FLUID THRESHOLD FOR NATURAL SAND OF MIXED
GRAIN SIZE 92
5 THE IMPACT THRESHOLD WIND 94
CHAPTER 8
SUMMARY OF THE PHYSICS OF GRAIN MOVEMENT
I THE FORCES ACTING ON SINGLE PARTICLES 96
2 THE SIZE OF NATURAL PARTICLES IN TERMS OF THE
EQUIVALENT SPHERICAL DIAMETER 97
3 THE TURBULENCE OF THE FLUID 97
4 SUSPENSION, AND TRANSPORT ALONG THE FLOOR. DISTINC-
TION BETWEEN DUST (OR SILT) AND SAND 98
5 TURBULENT FLOW NEAR THE BED 98
6 THE DRAG T, AND THE DRAG VELOCITY v. 99
xu
BLOWN SAND AND DESERT DUNES
CHAPTER 8
SUMMARY OF THE PHYSICS OF GRAIN MOVEMENT-contd.
PAGE
7 FLOW OVER A FLAT SURFACE WHOSE TEXTURE CHANGES ACROSS
A TRANSVERSE BORDER. THE BOUNDARY LAYER 100
8 THE FLUID THRESHOLD OF FLOW REQUIRED TO MOVE GRAINS
ON THE BED 100
9 SAND MOVEMENT IN AIR AND WATER. THE SALTATION DRAG 102
10 SAND MOVEMENT IN AIR. WIND VELOCITY DISTRIBUTION 104-
II THE IMPACT THRESHOLD 104
12 SALTATION AND SURFACE CREEP. SAND FLOW IN TERMS OF
WIND STRENGTH lOS
13 THE MEAN GRAIN PATH OF THE SALTATION AND THE WAVE-
LENGTH OF THE SURFACE RIPPLE IN AIR 106
PART II
SMALL-SCALE EFFECTS. GRAIN SIZE
DISTRIBUTION. SURFACE RIPPLES AND RIDGES
CHAPTER 9
GRADING DIAGRAMS
I MECHANICAL ANALYSIS 107
2 THE' PERCENTAGE-SMALLER' DIAGRAM 109
3 THE BLOCK DIAGRAM 110
4 THE DIFFERENTIAL DIAGRAM I I I
S THE LOG DIAGRAM 113
6 SYMMETRICALLY GRADED SANDS. COMPARISON WITH THE
'NORMAL PROBABILITY CURVE' II6
7 REGULAR AND MIXED SANDS 118
8 GRAIN DIAMETER DEFINED BY SIEVE APERTURE. A METHOD
OF ADJUSTMENT OF SIEVE CALIBRATION 123
