Natural Aerodynamics

337 Pages·1958·23.27 MB·English

by  R. S. Scorer (Auth.)

INTERNATIONAL SERIES OF MONOGRAPHS ON
AERONAUTICAL SCIENCES AND SPACE FUGHT
CHAIRMEN
T. VON KARMAN H. DRYDEN
Advisory Group for Aeronautical National Advisory Committee
Research and Development, for Aeronautics,
North Atlantic Treaty Organization, 1512 H Street Northwest,
Palais de Chaillot, Paris 16, Washington 25, D.C.,
France U.S.A.
HONORARY ADVISORY BOARD
UNITED KINGDOM UNITED STATES
A. G. Pugsley E. H. Heinemann
H. Roxbee Cox W. F. Milliken
A. M. Ballantyne C. Kaplan
E. T. Jones F. Clauser
W. S. Farren W. Diehl
W. J. Duncan E. R. Sharp
B. P. Mullins R. Bisplinghoff
G. W. H. Gardner C. B. Millikan
F. W. Page T. P. Wright
H. B. Squire W. C. Nelson
A. J. Murphy J. R. Markham
A. D. Baxter L. E. Root
W. S. Hemp J. Stack
W. P. Jones N. J. Hoff
G. B. Lachmann P. M. Fitts
C. S. Draper
GERMANY G. Stever
J. R. Dempsey
H. Görtier G. P. Sutton
A. W. Quick
G. Bock
FRANCE .
ITALY M. Roy
L. Malavard
G. Gabrielli
HOLLAND
AUSTRALIA
L. P. Coombes H. J. van der Maas
JAPAN SWEDEN
I. Tani B. K. O. Lundberg
CANADA
D. C MacPhail
D. L. Mordell
H. C. Luttman
J. J. Green
NATURAL
AERODYNAMICS
R. S. SCORER
Reader in Applied Mathematics
Imperial College
London
PERGAMON PRESS
NEW YORK · LONDON
PARIS . LOS ANGELES
1958
PERGAMON PRESS INC.
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Copyright
©
1958
R. S. Scorer
Library of Congress Card Number 57-14447
Printed in Great Britain at The Chapel River Press, Ando ver, Hants.
PREFACE
THESE chapters began to take shape during extramural courses
given in the Department of Meteorology at Imperial College.
These lectures were advanced in the sense that they described
very largely the results of recent*research, yet they were given to
audiences composed of aviators, engineers, geographers, meteoro­
logists, mathematicians, and indeed some with no advanced
scientific training at all but with an interest in the subject and a
mechanical turn of mind. With such a variety of interests in
mind the aim has been to develop the basic concepts listed in the
chapter headings, all the time taking examples from out of doors
air motion as illustrations. Consequently many special topics
which could be included in the title have been omitted. For
instance, breathing in man and animals could easily occupy a
chapter; but however fundamental to life it is not a fundamental
hydrodynamical process in terms of which other phenomena can
be understood, and it is hoped that readers interested in breathing
will be able to pursue their studies more fruitfully by making use
of the ideas which are discussed here. The index is intended to
guide those enquiring about a particular phenomenon to the
fundamental processes which make the phenomenon what it is.
The chief difficulty is the complexity of the subject. The air
is so free that it finds a great variety of ways in which to move.
The mathematics of any problem in air motion soon become very
complicated, and I have therefore tried to show how one can argue
what it is necessary to specify in order that there shall exist
solutions to the problems posed and to explain qualitatively what
the answers are, rather than duplicate the mathematical treatment
which may be found in one or more of the very good books
available. Yet many of the problems discussed have not yet been
satisfactorily solved, and they offer a great opportunity for mathe­
maticians and experimentalists in natural aerodynamical research.
On account of the elementary nature of the treatment it was not
thought necessary to give references to original papers, and
though a few books are suggested for further reading it is probably
best that everyone should explore the literature for himself as far
as possible because if he reads this book he is often likely to find
the best stimulus in what has not been read by its author.
v
VI PREFACE
Though the basic concepts of hydrodynamics are the same
whatever the fluid and its surroundings, we are concerned here
with air motion in Nature ; we find that we have to think rather
differently from the mathematician who plays on paper with
imaginary * perfect ' fluids or the engineer who makes machines
for special tasks. Our study is not purely academic. It is of
great use in the control of air pollution for example: we
must know our enemy. Natural Aerodynamics can also be a
fascinating hobby, especially in these days of steam and smoke
which make visible the ever varied and delightful behaviour of
the air. Unless we are mathematicians we have to employ a
certain amount of ' black-boxery ' in our thinking. We recognise
that in certain circumstances the results deduced and stated by
experts will follow: we cannot always be concerned with the
details of how the black box (in this case the expert's reasoning)
converts its intake into its output; but we are satisfied that the
detailed design of the black box is within the comprehension of
another fairly ordinary person, understand that it is consistent
with our general philosophical principles, and that the results of
using the box are of a kind we would reasonably expect. Thus a
geographer may prefer to slide over the more mathematical parts
of Chapter 8 and be content to understand the conclusions, con­
vincing himself that they are at least plausible. He can then
make use of the known properties of vorticity to interpret his
observations of Nature.
Many readers may have misgivings about Chapter 2, and it can
quite well be left out without detriment to the understanding of
the other chapters. But it is placed early in the book for two
reasons : first it comes logically as an extended example of inertia
forces and does not depend upon the concepts developed later,
and secondly it seemed desirable to say something about how the
wind contrives to blow (though not much about why, for that is
the special province of meteorology) before going on to the many
consequences of the existence of wind. There are many
obscurities which may tax the imagination of engineers versed in
fluid mechanics because the full consequences of the earth's
rotation are not well known. For example, we all understand
that cold air is heavier than warm air and that the pressure is due
to the weight of air above. We would therefore ' expect ' that an
PREFACE vii
inrush of cold air into a depression would be the best way to make
the pressure rise and fill it up. Yet this is not so ; on the contrary
such inrushes are a common cause of deepening of depressions
and of rejuvenation of their circulations, and it is the arrival of
warm air which often makes the pressure rise rapidly and cause
the cyclone to disappear! It is interesting that by studying the
motion of the troposphere in connections such as this we can
deduce that active cold fronts must drag the stratosphere down­
wards while it must often be carried upwards ahead of warm
fronts. Such deductions would be impossible if we were satisfied
with the simple idea that the pressure is due to the weight of air
above : we have in fact to think of the up and down motion of the
air above as being governed very largely by what goes on below,
Possibly this chapter will be useful to meteorologists because the
dynamics of unbalanced flow are not usually given the emphasis
due in ordinary textbooks.
The conservative reader may boggle at the digressions from the
business of natural aerodynamics into topics with kindred philo­
sophical content. If the reader is of an enquiring turn of mind
he will be curious about all of Nature, including ourselves, our
behaviour, and our way of thinking. To penetrate the details of
appearance and find simpler universal processes is a delight
granted to all who study scientifically, and the delight is greater
according to the power of the imagination. Those unnecessary
paragraphs will, I hope, lead the reader into many further irrele-
vancies of thought where he will glimpse a little of the beauty
of the world of conjecture and become less fierce in his dogmas.
As the subject advances the difficulties increase. If we allow
ourselves to pose a problem and then press on regardless of the
consequences to an answer, we may find that we have displayed in
all its glory our mathematical skill (or someone else's), but only
solved a triviality. Often a little more thought can lead us to
frame a more meaningful question whose answer is more useful
and easier to obtain. Indeed we never know until we have the
answer whether a question is worth asking. The * wouldn't it be
nice to know . . .' attitude is unscientific. We have to become
gradually acquainted with Nature's ways, and many sophisticated
mathematical treatments are pointless because they assume at the
beginning that we know what we want to know. Insight into
viii PREFACE
natural dynamics is worth a great many mathematical techniques
in pursuing research in which experiments are necessary.
Finally I must acknowledge debts of gratitude. First to the
Meteorological Office for enrolling me during the war and pre­
senting me with the impossible task of forecasting the weather.
It is a stimulating experience for a scientist, more particularly a
mathematician, to have to find within a given time, answers to
questions which are always beyond his powers, but which he
instinctively feels ought to be within his grasp. Secondly to
Sir Geoffrey Taylor, who, however new a problem one takes to
him for discussion, always seems to have thought about it long
ago and in a few grand remarks brings some order to one's con­
fused thinking. Thirdly to Mr. F. H. Ludlam, a keen observer
of Nature, who believes in the poetry of science, and is prepared to
consider almost any fantastic suggestion and suggest that almost
any accepted theory is fantastic. Fourthly to Professor P. A.
Sheppard, an encyclopaedic critic of anything to do with
meteorology, a sympathetic listener who gives no quarter in
argument, and has a zest for the excitements of reality. ..Finally
to the gliding fraternity among whom there are experts and cranks,
whose mad theories about the atmosphere are always based on sound
observations of Nature that seem to have eluded everyone else, and
who will not believe anything until it has been proved to them with­
out mathematics—good company indeed for any mathematician !
The Pergamon Press have in all matters proceeded expeditiously,
avoiding those delays which frustrate so many authors. I would
particularly like to thank Mr. W. R. Buchanan, who has converted
about 150 pencil sketches and diagrams into excellent drawings.
Among these drawings the instrumental records shown on
pages 224 and 252 are Crown copyright, and the permission of the
Controller of Her Majesty's Stationery Office to reproduce them
is gratefully acknowledged. I would also like to thank Dr.
Ryozaburo Yamamoto, of the Meteorological Research Institute,
Kyoto University, for kindly sending me a copy of one of his
microbarograph records of a hydrogen bomb explosion: it is
displayed on page 224.
Imperial College R. S. S.
November 1957
LIST OF PLATES
Plate Facing
No. page No.
1 Bubbles of air rising in water 148
2 Wing-tip vortex condensation trails 149
3 Clouds of air bubbles rising in water 164
4 A growing thermal 165
5 A growing thermal 165
6 The growth of cumulus over a thermal source 200
7 Smoke plumes at inversions 201
8 Plume with large efflux velocity 208
9 Plumes coning 208
10 Plumes looping 209
11 Bifurcation of a hot plume 212
12 Bifurcation of a wet plume 212
13 Downwash and its avoidance 212
14 Converging buoyant plumes 213
15 Cumulation and thermalling 228
16 Puffing 229
17 Pileus clouds over thermals 229
18 The erosion of a thermal 260
19 Laminated wave cloud 261
20 Bursting freezing water drops 261
21 Fallstreaks, thermals and mamma 276
22 Mamma and the fallout front 277
XI
ERRATA
Page 280, line IB for positive read negative
Page 280, line 14 for negative read positive
Page 281, line 4 for positive read negative
CHAPTER 1
INERTIA FORCES
Newton's laws and the pressure gradient
NEWTON stated that if one piece of matter, A, exerts a force on
another piece, B, then B exerts an equal and opposite force on A.
This is simply to say that forces cannot be dissipated without
trace, as had been thought previously. If B does not gain
velocity under the eflFects of the force delivered by A it can only
be because there exist other forces on B equal and opposite to
those delivered by A. But if there are no such other forces B
will be seen to accelerate in the direction of the force due to A.
The important point is that whether B moves or not it exerts a
force on A equal and opposite to A's force on it. B is able to
offer such a force because it possesses mass, or inertia, and as far
as A is concerned it does not matter whether the force offered
by B is due to inertia or friction or anything else; A's experience
is still the same,
The inertia of a body therefore produces forces upon any other
object which exerts a force upon it to change its velocity. Such
forces are as real as any other. Indeed they are fundamental in the
sense that their existence enables us easily to measure force in
terms of the fundamental mechanical dimensions of mass, length,
and time. Of course, we could regard force as a fundamental
dimension in the place of one of the other three. It would be
quite logical, though not so convenient practically, to dispense
with time as a basic dimension and use force in its place. The
unit of time would then be the square root of the distance travelled
by a unit mass under the influence of a unit force in a constant
direction. Time has been popular in the past as the fourth
dimension into which men have dreamed of wandering out of the
present, but such adventure would have an exact counterpart in
the experiences of a person who could, by some magic, avoid
offering a force in return to any exerted upon him, that is to say
have no inertia, no mass. From other people's point of view he
1