Leslie Howarth OBE. 23 May 1911

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Downloaded from http://rsbm.royalsocietypublishing.org/ on January 20, 2017
Leslie Howarth OBE. 23 May 1911 −− 22
September 2001
J. T. Stuart
Biogr. Mems Fell. R. Soc. 2009 55, 107-119, published 3 September 2009
originally published online September 3, 2009
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LESLIE HOWARTH OBE
23 May 1911 — 22 September 2001
Biogr. Mems Fell. R. Soc. 55, 107–119 (2009)
LESLIE HOWARTH OBE
23 May 1911 — 22 September 2001
Elected FRS 1950
BY J. T. STUART FRS
Department of Mathematics, Imperial College London, Huxley Building,
180 Queen’s Gate, London SW7 2AZ, UK
Leslie Howarth was born in Lancashire and studied at Accrington Grammar School and the
University of Manchester, where he graduated in mathematics. Sydney Goldstein (FRS 1937)
had a great impact on him, and he migrated with Goldstein to the University of Cambridge.
There he studied for the Mathematical Tripos and then for a PhD under the guidance of
Goldstein, gaining the Smith’s Prize in the process. The 1930s were a golden age for fluid
dynamics, both theoretical and experimental, partly because of the rapid rise of aviation in both
Europe and North America. Howarth rapidly developed a formidable international reputation,
producing a string of theoretical and computational papers at the cutting edge of research in
the study of boundary layers in aerodynamics and fluid dynamics. In 1937–38 he spent a year
in the USA at the California Institute of Technology, working with Theodore von Karman
(ForMemRS 1946), during which they produced a remarkable paper of lasting importance in
the theory of turbulence. During World War II Howarth worked for several UK government
agencies, but afterwards he moved from Cambridge to the University of Bristol, where he
developed a strong research school in theoretical fluid dynamics and applied mathematics.
EARLY YEARS AND BACKGROUND
Leslie Howarth was born in Bacup, Lancashire, on 23 May 1911, being the son of Fred
Howarth, who was a civil engineer with the borough council, and Elizabeth Ellen (née
Matthews); he had a brother, Ronald Matthews Howarth (born in 1920), who also studied
mathematics at Cambridge and became Managing Director of Bristol Aerojet Ltd. Leslie
was educated at Accrington Grammar School, from where he moved to the University of
Manchester to study mathematics. He was particularly interested in applied mathematics, perhaps partly because of the stimulus of Sydney Goldstein, and gained his degree in mathematics
doi:10.1098/rsbm.2009.0013
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This publication is © 2009 The Royal Society
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Biographical Memoirs
in 1931. From Manchester, Leslie moved to Gonville and Caius College in Cambridge, studied
for Part II of the Mathematical Tripos and gained the BA degree in 1933. Thereafter he became
a research student under the guidance of Goldstein, which was a very fortunate development
for Howarth and for theoretical fluid dynamics; he graduated with the PhD degree in 1936.
His talents had been recognized in 1935 by the award of the Smith’s Prize. A number of fine
papers emerged from this period (including (1–4)*). Thus was the mould set for Howarth’s
future career, which will be discussed below.
In 1934, while he was still a research student, Leslie Howarth and Eva Priestley were married,
a happy marriage which lasted for more than 60 years until Leslie died. Two children were born
to them, Peter David in 1944 and Michael John in 1948. Peter became a member of the Royal
Air Force, retiring as a wing commander, and Michael joined the scientific staff of the Liverpool
Tidal Institute. (Eva Howarth died peacefully some five years after Leslie, in January 2007.)
PROFESSIONAL CAREER
After the award of his PhD degree in 1936, Howarth was elected to the Berry–Ramsey
Research Fellowship at King’s College and was simultaneously appointed as a lecturer in
mathematics in the University of Cambridge. During this period at King’s, Howarth was
a colleague of Alan Turing (FRS 1951), who, in correspondence with his mother, referred
with pleasure to Howarth’s appointment. In 1937–38 Howarth was on leave at the California
Institute of Technology, having the good fortune to work with Theodore von Karman. He
returned to Cambridge, but in 1939 World War II interrupted his career as it did that of many
others, including scientists and mathematicians. From 1939 to 1942 Howarth was recruited to
work for the External Ballistics Department of the Ordnance Board but was then transferred
to the Armament Research Department, in which he served from 1942 to 1945.
After his wartime service Howarth returned to Cambridge, continuing his university lectureship in mathematics but moving from King’s College to St John’s College as a Fellow and
College Lecturer. Here Howarth had Fred (later Sir Fred) Hoyle (FRS 1957) as a colleague
and Abdus Salam (FRS 1959; Nobel laureate 1979) as a student. Here I wish to quote from
a St John’s obituary notice of Abdus Salam by Fred Hoyle: ‘Howarth told me that he had a
man from India who was very good’; later Hoyle writes, ‘What I also heard about Abdus from
Howarth was that he had the embarrassing habit of greeting his teachers in the John’s courts
with a fully fledged Muslim salute, practically going down on the cobble stones with his
knees. It must have taken Leslie, or Peter White I suppose, to inform Abdus that such reverences were not necessary in Cambridge.’
In 1949 Leslie Howarth made a substantial change by leaving Cambridge to join the
University of Bristol as Professor of Applied Mathematics, becoming in 1964 the Henry
Overton Wills Professor of Mathematics and Head of the Department of Mathematics. A large
part of Howarth’s energies was devoted to building up a strong group in applied mathematics and theoretical fluid mechanics, which, because of the great importance of aeronautics in
the UK, was dominant in UK applied mathematics. Staff recruited during his time included
W. Chester from Manchester, P. G. Drazin, D. W. Moore (FRS 1990), D. H. Peregrine,
* Numbers in this form refer to the bibliography at the end of the text.
Leslie Howarth
111
K. Stewartson (FRS 1965), and many others. After Howarth retired in 1976, Bristol continued
to attract staff of high quality in applied mathematics, a tribute to the legacy of Howarth’s
tenure in the Department of Mathematics.
However, Howarth did have an ‘Achilles heel’: a perhaps somewhat rigid approach. In
1964 one of Howarth’s colleagues, Derek Moore, was offered a prestigious senior postdoctoral
fellowship by the US National Academy of Sciences to be held at the Goddard Space Flight
Center, New York. Moore applied to his head of department, Howarth, for unpaid academic
leave to take up this marvellous opportunity. It was denied on the grounds that Moore’s lecturing talents, which were considerable, were needed to teach undergraduates at Bristol. This
was undeniable and one can sympathize with Howarth’s position. However, Moore promptly
resigned. To his credit, Howarth then retracted his refusal, but it was too late. Moore went to
the USA and stayed there for three years, returning to the UK in 1967, not to Bristol but to
Imperial College London.
Another episode at Bristol is of a more humorous kind. Since 1959 an annual Conference
on Applied Mathematics (the British Theoretical Fluid Mechanics Colloquium, or BTMC)
was held in succession at different UK universities. In 1961 it was the turn of Bristol to act as
host; Howarth took on the role of chairman and chose Moore as treasurer. They went along to
the local bank, which happened to be Moore’s bank, to set up a special account for the conference. They saw the manager and this was done. On leaving the bank, Howarth observed to
Moore that the manager seemed rather unfriendly, even ‘frosty’ in his attitude, even though
the request was granted and the account opened. Moore did not tell him the reason: some days
earlier Moore had been interviewed by the same manager, who had refused Moore a loan to
buy an expensive motorbike. Imagine the manager’s concern at seeing Moore appear again,
this time with support of a senior colleague! It is unclear whether Leslie Howarth ever learned
of the reason for that ‘frostiness’. Needless to say, under Howarth’s leadership the conference
was a great success, adding to the strength of the concept of a yearly BTMC.
Leslie Howarth was very conscientious in attending to his university duties, serving on
many university committees and acting as Dean of the Faculty of Science from 1957 to 1960.
The impact of decisions of research councils was often of great concern; I recollect one occasion, when I visited Bristol to give a seminar, at which time Howarth was very agitated by
a decision by the Science Research Council to cut back on studentships for MSc courses, an
excellent example of which existed in applied mathematics at Bristol.
In addition to his university duties, Howarth was for many years an adviser to the government, or its agencies. In particular he had strong associations with the Aeronautical Research
Council (ARC), an advisory body of the Ministry of Defence with a history dating back to
1909. Sadly, as many scientists and engineers felt, it was abolished as a ‘quango’ (quasiautonomous non-governmental organization) in the 1980s. Other prominent members of the
ARC at various times included Sydney Goldstein, G. I. Taylor FRS, G. Temple FRS, E. F. Relf
FRS, A. Fage FRS, Sir Arnold Hall FRS, H. B. Squire FRS, Sir James Lighthill FRS and G. K.
Batchelor FRS. Howarth also served on the Board of the Cabinet Office that was concerned
with promotion of scientific civil servants on special merit, a scheme that led to the promotion
of several who later became Fellows of the Royal Society, one example being M. G. Hall. In
all his duties of administration and in advising government agencies, Howarth was meticulous
in his preparations for meetings and was always ready with penetrating remarks and questions,
as I know from experience of serving on the Fluid Motion Sub-Committee of the ARC, where
I observed Howarth’s perceptiveness and insight into scientific and mathematical questions.
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RESEARCH UP TO 1938
Leslie Howarth’s earliest work was in the theoretical study of the so-called boundary layers on wings of aircraft. This concept arose in 1904 out of pioneering and truly innovative
work of Ludwig Prandtl (ForMemRS 1928) in Göttingen, Germany (Prandtl 1904). Prandtl
was aware of the importance of viscosity in causing the drag or resistance that impeded an
aircraft’s flight; he recognized that, although viscosity is unimportant far from an aircraft if
the Reynolds number (speed multiplied by characteristic size divided by kinematic viscosity)
is high, there must be a thin layer near to the body and wings of the aircraft within which
viscosity is truly vital. This is the ‘Grenzschicht’, or boundary layer. At first this concept was
evaluated in Germany by Blasius (1908) and others, but gradually the idea permeated to workers in other countries, including the UK. Research problems were then pursued in the 1920s
and 1930s. Complications became clear as this work progressed: (i) flow can be either laminar
(smooth) or turbulent (random or chaotic, but with certain possible structures), as had long
been known (see Reynolds 1883); (ii) the boundary layer might break away from the solid
surface, a phenomenon that came to be known as ‘separation’, the possibility of which was
one of the main reasons for studying boundary layers on bodies.
Now that powerful computers are available, it may be difficult for some of us to put ourselves into the frame of computation in the 1930s, when Howarth made such great advances
and put himself at the forefront of advances in the numerical study of the nonlinear differential
equations of the boundary layer. Looming ahead, of course, was the possibility, later realized,
of conflict with Germany and a second World War. Howarth’s greatest work was done in the
1930s, ironically on the topic that had originated with Prandtl in Göttingen; such is the international nature of science. We turn now to a description of that work.
Howarth’s first paper (1) was published in Reports and Memoranda of the ARC and concerned the prototype problem of the flow around a cylinder placed normal to a stream. In this
situation, as explained above, the flow ‘far’ from the cylinder behaved as though it were inviscid,
as though there were no viscosity or friction between neighbouring fluid elements, provided that
the Reynolds number was high. What, then, was the nature of the flow near to the cylindrical
body? This was the subject of Howarth’s work in this and later papers. In (1) Howarth showed
how to calculate the steady behaviour of the boundary layer for the region near to the front stagnation point (or point of zero velocity), confirming calculations by Hiemenz (1911). Moreover,
he used a method to obtain the details of the boundary-layer flow by means of an expansion in
terms of distance from the front stagnation point; this involved the calculation of the solutions
of a succession of nonlinear ordinary differential equations. When Howarth applied this to a circular cylinder, following Hiemenz, he obtained solutions of those equations improving substantially on Hiemenz’s earlier calculations. It was found that the point at which the flow reversed
direction near to the surface (the separation point) occurred at about 82° or 83° from the front
stagnation point, in good agreement with Hiemenz’s experimental observations.
Moreover, in paper (1) he compared the series method with several other approximate
methods, doing a great service to the community thereby.
Paper (2) concerned the determination of the lift for flow around a thin elliptic cylinder at
an angle of incidence according to the formula L = KρV, where L is the lift, K is the circulation, ρ is the fluid density and V is the typical velocity. Howarth determined the circulation,
which is the crucial unknown in the formula, for cases of laminar flow, turbulent flow and
laminar/turbulent flow with a prescribed transition point. In this way the lift was predicted.
Leslie Howarth
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This work was later extended by Wild (1949) to laminar flow on a swept cylinder at an
angle of incidence, for a situation in which the maximum lift coefficient (a non-dimensional
number) was 0.47. Thus Howarth’s work was extended by others to three dimensions, a topic
in which he became interested later.
In paper (3) Howarth turned his attention to unsteady flows, particularly to the growth
with time of a laminar boundary layer when the motion was created impulsively from rest. He
discussed qualitative arguments for the development of circulation for an elliptic cylinder at
incidence (for example, with the major axis at 7° to the stream), where there is a formula for
the development of the circulation K: dK/dt = 2(U 2 − V 2), where U 2 and V 2 are the squares
of the inviscid velocities at separation on the lower and upper surfaces, respectively. Leslie
Howarth’s colleagues, Goldstein & Rosenhead (1936), were stimulated to develop this concept
further by rational calculation to calculate the time required before separation took place.
In paper (4) Howarth used an approximate (integral) method due to Buri to calculate a point
of separation for steady flow past a circular cylinder with turbulent flow in the boundary layer,
the pressure distribution being given by observations of Fage & Falkner (1931). Calculation
indicated a position of the point of separation in good agreement with observation, but there
were indications that relatively small changes in the pressure distribution could produce big
changes in the position of separation.
Paper (5) discussed the velocity and temperature distributions for turbulent flow, using an
approximation for the turbulent (Reynolds) stresses as given by the so-called vorticity-transfer
theory of Prandtl. Good agreement was found with observation, but some empiricism was
involved.
We turn now to one of Howarth’s most famous papers (6), which arose from collaboration
with T. von Karman during a visit to Caltech. Some years earlier Taylor (1935) had put forward a theory of isotropic turbulence and had evaluated many implications. Paper (6) developed Taylor’s ideas further from a mathematical viewpoint, especially in terms of correlations
between two velocity components at two different points. Such double correlation coefficients
form a tensor; Karman and Howarth showed that there are strong relationships between different terms of the tensor in terms of a single scalar function, f(r), a significant result. Results
were also given for correlations of spatial derivatives of velocity components, in which they
confirmed Taylor’s formulae (Taylor 1935). Triple correlations consisting of three velocity
components were considered, two at one point and one at another. In this case the third-order
tensor had terms dependent on one scalar function only, h(r), a result similar to that for the
second-order tensor (of double correlations). A most remarkable result now followed: from the
equations of motion for an incompressible fluid, Karman and Howarth obtained an equation
for the propagation of the correlation function f(r), a partial differential equation of first order
in time, t, and of second order in radial distance between the two points, r, but one in which
the unknown triple correlation function, h(r), appeared. The appearance of both functions is a
consequence of the nonlinearity of the equations of motion, and shows that double and triple
correlations are related, as also would be higher correlations. The relationship between f(r)
and h(r) is the famous Karman–Howarth relation, an enduring fixed point in the difficult field
of turbulence.
If h(r) is ignored (as a type of ‘closure’), solutions can be found for all time when a given
initial condition is specified; this was done by the authors and comparison was made with
observations of the decay of turbulence. However, at small values of r, the triple correlation
may be related to the Reynolds stresses, which are instrumental in generating vorticity by the
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stretching of vortex lines (see Taylor (1937) in connection with another paper of Karman), so
that the omission of h(r) may lead to errors in predictions of the decay of turbulence. One can
say that a fundamental difficulty in treating turbulence mathematically is the occurrence of
both f(r) and h(r) in the Karman–Howarth relation, so that a single differential equation cannot
be obtained for a correlation coefficient, thus emphasizing the importance (albeit negative) of
this relation for turbulence theory.
A second really memorable paper was (8), also published in 1938. As is clear from earlier
discussions of boundary layers (1–5), there was much concern in the 1930s with the development of a good scheme for calculation of the boundary layer. Following Hiemenz, Howarth
had made significant progress in the calculation of a laminar flow when it starts at a stagnation
point, at which the flow is at rest. However, other cases beckoned, particularly where a comparison with experiment could be made. Schubauer (1935) had made experiments on boundary-layer flow on an elliptic cylinder of fineness ratio 2.96:1; he had measured the pressure
distribution around the cylinder and had found the position of the separation point. Numerous
workers had attempted to compare their results with Schubauer’s, but with limited success.
Separately Karman & Millikan (1934) had developed an approximate method, which Millikan
had applied to Schubauer’s case but with only moderate agreement. One prototype problem,
to which Karman and Millikan had applied their method, was that of a velocity (outside the
boundary layer) of the form U = a − bx, such as would be produced by a flat plate placed
edgeways on to an incident stream and with an adverse pressure gradient varying linearly
with distance x from the leading edge. This produced a prototype boundary-layer problem,
which Howarth treated by an excellent scheme of a both computational and mathematical
nature, but not unlike that which he had used in (1). In the prototype case Howarth expanded
the solution of the equations in powers of x; the coefficients were functions of the distance
normal to the plate. Thus, he found a set of ordinary differential equations and solved them
successively, each depending on its predecessors in the sequence. A solution was calculated by
numerical methods for seven functions in the sequence, and from those calculations Howarth
was enabled to estimate the position of separation for a = b = 1 to be at x = 0.1, a value that
confirmed (by his accurate method) the earlier calculations by less satisfactory methods. Thus,
Howarth’s work started to give a degree of certainty to the matter of separation of flow in the
presence of an adverse pressure gradient, as indicated by the negative sign in U = a − bx.
In part II of the paper, Leslie Howarth used this fundamental calculation to devise a scheme
for more general cases, in which the velocity distribution was approximated as a function
of x by a polygon with a finite number of sides. Then the fundamental calculation was used
to evaluate flow development in each of these regions, with a suitable matching condition,
namely that the ‘momentum integral’ is to be conserved.
This led Howarth to a value of x for separation in Schubauer’s experiment of 1.925 compared with the observation of 1.99. However, Howarth rightly pointed out certain problems
associated with experimental/theoretical comparisons, but even so the comparison is a good
one, which did much in 1938 to give confidence in our understanding.
In (9) Howarth calculated the flow and temperature distributions in plane and axisymmetric
turbulent jets, and found moderate agreement for velocity with theory and with experiments
of Tollmien (1926) and Förthmann (1934), but less satisfactory agreement on the temperature
distribution.
The last paper of the 1930s (10) concerned the secondary flow in straight pipes, as brought
about by turbulent stresses (the Reynolds stresses).
Leslie Howarth
115
WORLD WAR II, 1939–45
I applied to the Ministry of Defence for advice about Leslie Howarth’s work in the period
1939–45 when, with many others, Howarth was recruited into scientific service for the government, but unfortunately nothing could be found in the files. However, Howarth himself
provided an account of that period, as follows:
Originally appointed to the External Ballistics Department, Ordnance Board, and subsequently
transferred to the Armament Research Department.
Concerned mainly with both the aerodynamical and dynamical aspects of external ballistics,
including many theoretical investigations of the stability and yawing motions of new and novel
designs of projectile and of pressure distributions over the surface of projectiles, as well as the
design and subsequent analysis of experimental trials. As examples of such problems may be
mentioned:(a) Determination of the motion of a spinning projectile with an eccentric distribution of mass
(with the object of specifying acceptable manufacturing tolerances).
(b) Design of a method employing the use of characteristics and Crocco’s stream function for
obtaining the pressure distribution over the surface of a pointed projectile when the shock wave is
attached at the tip, the curvature of the shock wave and the consequent effects of vorticity being
determined.
(c) Examination, on the basis of intelligence data, of ranges and accuracy to be expected of
the German V2 rockets prior to their use in action. Also problems of stability, control, surface
temperature and audibility.
(d) Preparation of tables of the Standard Ballistic Atmosphere.
Other duties included secretaryships of the Ballistic Air Resistance Committee and the
Scientific Equipment Committee.
Topics (a) and (b) are discussed in (17), which was edited by Howarth; in chapter XIII of
this book W. F. Cope dealt with these topics in detail. On p. 736 Cope remarked, ‘Howarth
has analysed the case where the mass distribution is eccentric and his conclusions have been
verified at the N.P.L.’. Plate 12, which is placed opposite p. 736, shows photographs of the
ballistic range at the NPL (National Physical Laboratory) and of the measuring apparatus, and
is presumably the range to which Howarth referred when he wrote of ‘design and subsequent
analysis of experimental trials’.
Topic (c) refers to the V2 research and development programme based at Peenemünde, and
to the subsequent use of the V2 rockets to target London and elsewhere.
This experience in his wartime service of compressible flow, that is to say a flow in which
the density can vary from place to place and from time to time, influenced Howarth’s postwar
research work (11, 12), as we shall see.
RESEARCH AFTER WORLD WAR II
In the late 1940s, because of the evolution of supersonic flight, a topic of great practical and
theoretical importance was that of knowing how a boundary layer would be affected by a shock
wave when it impinged on it from a supersonic free stream. Typically, Howarth recognized
the importance of this evolution and considered how best to make progress with the problem.
Although the problem was later resolved by Lighthill (1953a, b), many others contributed to
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the understanding that stimulated Lighthill, including Howarth in an important paper (11). In
that work, Leslie Howarth conceived of a supersonic stream neighbouring a subsonic stream,
with a small disturbance in the supersonic stream impinging on the subsonic stream. His
important result was that the disturbance would propagate as a pressure pulse upstream in
the subsonic flow, a phenomenon of significance that was later verified more completely by
Lighthill; it was he who related the disturbance problem to that of the propagation of small
disturbances in a boundary layer, namely the famous Tollmien–Schlichting waves, which are
a possible precursor of turbulence.
In (12) Howarth (together with Illingworth (1949) independently) derived a transformation,
which related a boundary layer in compressible flow to that in the incompressible case. This
transformation proved to be of great significance because it enabled the calculation of some
cases of compressible flow to be derived from corresponding incompressible cases of flow. At
a time when digital computing was still in its infancy, this was of notable value.
At this point Leslie Howarth returned to studies of incompressible boundary-layer flow:
another development in aeronautics in the postwar period was the occurrence of swept-back
wings, which led to a study of boundary layers in three dimensions. This was in contrast with
the research situation in the 1930s, when the simplicity of two dimensions was paramount
and stimulated much research, including Howarth’s. However, we have already indicated how
Wild (1949) built on Howarth’s studies to make an extension to flow on a swept cylinder,
conceived as an embryonic swept wing. Thus, in the 1950s Howarth turned to three-dimensional boundary layers from several points of view. In (13) and (20) he turned to the so-called
Rayleigh problem of impulsive motion for a flat plate, but one that was of semi-infinite or
quarter-infinite type, a generalization of the work of Goldstein & Rosenhead (1936). It had its
importance in boundary layers of the role of edge effects, which is just one aspect of threedimensionality.
One of the crucial problems that needed to be addressed was that of the formulation of a
general set of equations for three-dimensional boundary layers, namely those for boundary
layers on a general curved surface in a general stream of fluid. Howarth achieved this important rationalization in (14). A prototype problem was that of the boundary layer on a rotating
sphere (15). The situation of great interest there, and one that intrigued Howarth, was the fact
that the flow near to the ‘poles’ was closely approximated by that on a rotating disk; flow was
then directed by centrifugal action towards the equator, at which the boundary layers collided
from the two sides. This therefore shows Howarth’s perception in opening interest in another
fundamental problem in fluid motion, the idea of colliding boundary layers. The collision of
the boundary layers at the equator was studied by Stewartson (1957) in a very fine development of Howarth’s work, and some experimental comparisons arose from the work of Kobashi
(1957).
In two dimensions the flow near to a stagnation point is directed towards that point and then
is directed outwards along the solid surface. However, in three dimensions (16) the situation
is more complicated and more interesting; the flow velocity component parallel to the surface
may be of two types. If both are positive with a flow wholly away from the stagnation point,
Howarth referred to it as a nodal point of attachment, but if one is positive and one is negative,
he referred to it as a saddle point of attachment. In (16) Howarth set out the principles that
are outlined above and calculated the flows near to a nodal stagnation point. This analysis and
computation by Howarth for the nodal case led to the paper by Davey (1961), who calculated
the flow near to a saddle point of attachment.
Leslie Howarth
117
In (18) Leslie Howarth assisted G. I. Taylor by solving a boundary-layer problem associated with ‘water bells’, a rather fascinating study of ‘G. I. Taylor type’, and one that illustrated
Howarth’s interests in all things fluid-mechanical.
TEXTBOOKS, 1938–59
In 1938 Howarth was a leading contributor to the timely volumes (7), which were edited by
Goldstein; later, in 1953, he edited and wrote significant parts of their successor, which was on
gas dynamics and ‘high speed flow’ (17). This was followed in 1959 by his masterly account
on ‘laminar boundary layers’ in Handbuch der Physik (19).
LATER LIFE
After 1960, although I can find no further papers, Leslie Howarth was still active in encouraging others’ research, as I know from his encouragement towards me. In addition he took a
lively interest in research activities discussed at the meetings of the ARC and its committees,
as I observed as a junior participant; he also attended the Cabinet Office committee concerned
with special promotions of talented government scientists. Inevitably, given his conscientious
approach, he also was very concerned with university affairs. Howarth retired in 1976 but did
not, I believe, maintain a very close association with the university. However, I did sometimes
consult him about scientific affairs, especially ones connected with the Royal Society, and
found him always most helpful.
He and his wife, Eva, lived in Henleaze, a suburb of Bristol, until they moved later to a
residential home in Essex, so as to be closer to their son, Peter. Leslie Howard died there in
September 2001, followed by Eva in January 2007.
HONOURS
1935 Smith’s Prize, University of Cambridge
1950 Elected FRS (It is interesting to note that his distinguished supporters were G. I.
Taylor, S. Goldstein, G. Temple, L. Bairstow, A. Fage, E. F. Relf and H. Jeffreys.)
1951 Adams Prize, University of Cambridge
1955 Appointed OBE
ACKNOWLEDGEMENTS
I wish particularly to thank Leslie Howarth’s son, Peter (Wing Commander P. D. Howarth, RAF (retired)), for his
great help given in correspondence, and Leslie’s widow, Eva, who advised Peter during that correspondence. I wish
also to record here the great help that Eva gave to Leslie in computing on the mechanical calculators of the 1930s.
The obituary notice by the late Philip Drazin and John Shepherdson FBA, which was published in The Independent
on 26 October 2001, was both fascinating to read and of value to me.
I am indebted to Professor Herbert Huppert FRS, Professorial Fellow of King’s College, Cambridge, for help that
he gave me in obtaining items from the archives of King’s College, my gratitude extending also to the Archivist. In a
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similar way I wish to thank Dr David Stuart, Fellow of St John’s College, Cambridge, together with the Librarian of
St John’s, for the items shown to me from the college records.
I am indebted to Sir Roy Anderson FRS, former Chief Scientific Advisor at the Ministry of Defence, and his
colleague Mr Nassim Baiou for their help in stimulating a search of the Ministry of Defence files of research for the
1940s.
The frontispiece photograph was taken by Godfrey Argent and is reproduced with permission.
REFERENCES TO OTHER AUTHORS
Blasius, H. 1908 Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. Phys. 56, 1–37.
Davey, A. 1961 Boundary-layer flow at a saddle point of attachment. J. Fluid Mech. 10, 593–610.
Fage, A. & Falkner, V. M. 1931 Further experiments on the flow round a circular cylinder. Rep. Memo. Aeronaut.
Res. Coun. Lond. no. 1369.
Förthmann, E. 1934 Über turbulente Strahlausbreitung. Ing.-Arch. 5, 52–54.
Goldstein, S. & Rosenhead, L. 1936 Boundary-layer growth. Proc. Camb. Phil. Soc. 32, 392–401.
Hiemenz, K. 1911 Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsström eingetauchten geraden
Kreiszylinder. Dinglers J. 326, 321–324, 344–348, 357–362, 372–376, 391–393, 407–410.
Illingworth, C. R. 1949 Steady flow in the laminar boundary of a gas. Proc. R. Soc. A 199, 533–558.
Karman, T. von & Millikan, C. B. 1934 On the theory of laminar boundary layers involving separation. Rep. Nat.
Adv. Comm. Aero., Wash. no. 504.
Kobashi, Y. 1957 Measurements of boundary layer of a rotating sphere. J. Sci. Hiroshima Univ. A 20, 149–156.
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120

Leslie Howarth OBE. 23 May 1911

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