Chapter_1.pdf

Editor’s Note

These are a collection of draft files of reference lists, assembled roughly in

order of the chapters of the book. The dates on the draft files range from 1996

to 1999, suggesting the author completed the major part of literature review,

which began about 1986, during those years. I added a few references at

the end (under ”Additional References”) which I found with the manuscript

and which are cited therein. Many entries include the author’s notes on

the reference or other items to check. Numbers of draft chapter sections

have been removed. An unknown number are sources the author checked but

decided not to include or cite in the book. No effort has been made to identify

these or place the entire list of several thousand entries in alphabetical order.

The interested reader is encouraged to use a digital search by name or term

of interest.

– K. Coles

Chapter 1: Introduction

ABELL, W. 1934 William Froude. Transactions of the Institution of

Naval Architects

, 243–252, 1 plate (discussion, 253–256).

ABBOTT, D.E. and KLINE, S.J. 1960 Simple methods for classifica-

tion and construction of similarity solutions of partial differential equations.

Dept. Mech. Eng., Stanford Univ., Rep. MD-6.

AMES, W.F. 1965

Nonlinear Partial Differential Equations in Engi-

neering

. Vol. I. Academic Press.

AMES, W.F. 1972

Nonlinear Partial Differential Equations in Engi-

neering

. Vol. II. Academic Press.

BACK, L.H. 1968 Conservation equations of a viscous, heat-conduct-

ing fluid in curvilinear orthogonal coordinates. Jet Propulsion Lab., Cali-

fornia Inst. Technology, Tech. Rep. 32-1332.

BARENBLATT, G.I. and ZEL’DOVICH, Y.B. 1972 Self-similar so-

lutions as intermediate asymptotics. Ann. Rev. Fluid Mech.

, 285–312.

BARENBLATT, G.I. 1979

Similarity, Self-similarity, and Interme-

diate Asymptotics

. Consultants Bureau.

BETZ, A. 1931 Die v. Karmansche

Ahnlichkeits ̈uberlegung f ̈ur turbu-

lente Vorg ̈ange in physikalischer Auffassung. Zeitschr. angew. Math. Mech.

, 397.

BIRD, R.B. and WIEST, J.M. 1995 Constitutive equations for poly-

meric liquids. Ann. Rev. Fluid Mech.

, 169–193.

BLUMAN, G.W. and COLE, J.D. 1969 The general similarity solu-

tion of the heat equation. J. Mathematics and Mechanics

, 1025–1042.

BLUMAN, G.W. and COLE, J.D. 1974

Similarity Methods for Dif-

ferential Equations

. Applied Mathematical Sciences, Vol. 13, Springer-

Verlag.

BOUSSINESQ, J. 1903

Theorie Analytique de la Chaleur

. Gauthier-

Villars, Paris, Vol. 2, 34th Lesson, 154–176.

BRIDGMAN, P.W. 1992

Dimensionless Analysis

. Yale Univ. Press.

BUCKINGHAM, E. 1914 On physically similar systems; illustrations

of the use of dimensional equations. Phys. Rev. (2)

, 345–376.

BUSSE, F.H. 1978 Non-linear properties of thermal convection. Rep.

Prog. Phys.

, 1929–1967.

CANTWELL, B.J. 1978 Similarity transformations for the two-di-

mensional, unsteady, stream-function equation. J. Fluid Mech.

, 257–271.

CAUCHY, A.-L. 1828 Sur les ́equations qui experiment; les condi-

tions d’ ́equilibre ou les lois du mouvement des fluides. In

Exercices de

Mathematiques

, Vol. 3, Chez de Bure Fr`eres, Libraires du Roi et de la Bib-

lioth ́eque du Roi, Paris, 128–146.

CHANDRASEKHAR, S. 1961

Hydrodynamic and Hydromagnetic Sta-

bility

. Oxford Univ. Press.

COHEN, A. 1931

An Introduction to the Lie Theory of One-Parameter

Groups

. Stechert, New York (reprint of 1911 edition).

DAVIS, R.T. and GHIA, U. 1973 The use of optimal coordinates in

the solution of viscous flow problems. Dept. Aerospace Eng., Univ. Cincin-

nati, Rep. No. AFL 73-8-4.

DAVIS, R.T. and ROUT, R.K. 1979 Calculation of optimal coordi-

nates for two-dimensional incompressible flow. Dept. Aerospace Engineering

and Applied Mechanics, Cincinnati Univ., Final Rep. AFL-79-7-47.

FOURIER, J.B. 1822

Th ́eorie Analytique de la Chaleur

. Gauthier-

Villars, Paris (translated by A. Freeman as

The Analytical Theory of Heat

Cambridge University Press, 1878).

GERSTEN, K. 1989 Die Bedeutung der Prandtlschen Grenzschicht-

theorie nach 85 Jahren. Zeitschr. Flugwiss. Weltraumforsch.

, 209-218.

GIBBINGS, J.C. 1982 The use of dimensional analysis in aerodynam-

ics: an historical note. Aeron. J.

, 176–178.

GOLDSTEIN, S. (ed.) 1938

Modern Developments in Fluid Dynam-

ics

. Vol. 1. Oxford Univ. Press (reprinted, Dover, 1965).

GOLDSTEIN, S. 1969 Fluid mechanics in the first half of this cen-

tury. Ann. Rev. Fluid Mech.

, 1–28.

GRAY, D.D. and GIORGINI, A. 1976 The validity of the Boussinesq

approximation for liquids and gases. Int’l. J. Heat Mass Transf.

, 545–551.

HANSEN, A.G. 1964

Similarity Analyses of Boundary Value Prob-

lems in Engineering

. Prentice-Hall.

HELMHOLTZ, H. 1873 Ueber ein Theorem, geometrisch ̈ahnliche Be-

wegungen fl ̈ussiger K ̈orper betreffend, nebst Anwendung auf das Problem,

Luftballons zu lenken. Monatsberichte der Konigl. Akademie der Wis-

senschaften zu Berlin, 26 Juni, 501-514 (also Wissenschaftiliche Abhand-

lungen, Vol. 1, 158–171, Barth, Leipzig, 1882).

HORNE, W.C. and KARAMCHETI, K. 1988 Extrema principles of

entropy production and energy dissipation in fluid mechanics. AIAA Paper

88-3830.

HOWARTH, L. (ed.) 1953

Modern Developments in Fluid Dynamics:

High Speed Flow

. Oxford Univ. Press.

JEFFREY, D.J. and SHERWOOD, J.D. 1980 Streamline patterns

and eddies in low-Reynolds-number flow. J. Fluid Mech.

, 315–334.

JEFFREYS, H. 1930 The instability of a compressible fluid heated

below. Proc. Cambridge Philosophical Society

, 170–172.

KAPLUN, S. 1954 The role of coordinate systems in boundary-layer

theory. Zeitschr. angew. Math. Physik

, 111–135.

KESTIN, J. and WAKEHAM, W.A. 1988

Transport Properties of

Fluids

. Thermal Conductivity, Viscosity, and Diffusion Coefficient. Hemi-

sphere.

KEVORKIAN, J. and COLE, J.D. 1981

Perturbation Methods in Ap-

plied Mechanics

. Springer-Verlag (esp. 332-370 on subcharacteristics).

KLINE, S.J. 1965

Similitude and Approximation Theory

. McGraw-

Hill.

KOLMOGOROV, A. 1941 The local structure of turbulence in in-

compressible viscous fluid for very large Reynolds’ numbers. C. R. (Dok-

lady) de l’Acad. des Sci. de l’URSS

, 151–155 (reprinted in

Turbulence:

Classic Papers on Statistical Theory

(S.K. Friedlander and L. Topper, eds.),

Interscience, 151–155, 1961).

LAGERSTROM, P.A. 1964 Laminar flow theory. In

High Speed Aero-

dynamics and Jet Propulsion

, Vol. 4,

Theory of Laminar Flows

(F.K.

Moore, ed.). Princeton University Press, 20–285 (esp. 20–46 on equations

of motion).

LAGERSTROM, P.A. and CASTEN, R.G. 1972 Basic concepts un-

derlying singular perturbation techniques. SIAM Review

, 63–120.

LAMB, H. 1932

Hydrodynamics

(6th edition), Cambridge University

Press; reprinted Dover, 1945.

LANGHAAR, H.L. 1951

Dimensional Analysis and Theory of Mod-

els

. Wiley, New York.

LOITSYANSKII, L.G. 1966

Mechanics of Liquids and Gases

(En-

glish translation of second Russian edition), Pergamon.

MA, P.K.H. and HUI, W.H. 1990 Similarity solutions of the two-

dimensional unsteady boundary-layer equations. J. Fluid Mech.

216

, 537–

559.

MACAGNO, E.O. 1971 Historico-critical review of dimensional anal-

ysis. J. Franklin Inst.

292

, 391–402.

MAGNUS, W., OBERHETTINGER, F. and SONI, R.P. 1966

For-

mulas and Theorems for the Special Functions of Mathematical Physics

Springer-Verlag (esp. 472–492 on coordinate systems).

MALKUS, W.V.R. 1964 Boussinesq equations. In Geophysical Fluid

Dynamics, Notes on the 1964 Summer Program, Course Lectures and Sem-

inars, Woods Hole Oceanographic Institution, Vol. 1, 1–12 (U.S. NTIS, PB

186 314).

MALKUS, W.V.R. 1969 A scaling and expansion of equations of mo-

tion to yield the Boussinesq equations. In Geophysical Fluid Dynamics,

Course Lectures and Abstracts of Seminars, Woods Hole Oceanographic In-

stitution, Vol. 1, 23–28.

MALLINSON, G.D. and KENWRIGHT, D.N. 1992 Application of

dual stream functions to the visualisation of three dimensional fluid motion.

In Proc. 11th Australasian Fluid Mechanics Conf., Univ. Tasmania, Vol. 1,

483–486.

MAXWELL, J.C. 1860 Illustrations of the dynamical theory of gases.

Phil. Mag.

, 9- ;

, 21- ; also Scientific Papers, Vol. 1, 377–409, 1890,

reprinted Dover, 1952.

MERRIFIELD, C.W. 1870 Experiments recently proposed on the re-

sistance of ships. Trans. Institution of Naval Architects

, 80–93.

Com-

ments on work of Froude. Ref in Goldstein, p 18. See also 39th Report of

the British Association, Exeter, 1869, 43–47.

MEYER, H.E. 1953 The method of characteristics. In

Modern De-

velopments in Fluid Dynamics

High Speed Flow

(L. Howarth, ed.), Vol. 1,

Oxford Univ. Press, 71–104.

MIHALJAN, J.M. 1962 A rigorous exposition of the Boussinesq ap-

proximations applicable to a thin layer of fluid. Astrophysical J.

136

, 1126–

1133.

von MISES, R. 1958

Mathematical Theory of Compressible Fluid Flow

Academic Press.

MORAN, M.J. 1967 A unification of dimensional and similarity anal-

ysis via group theory. Ph. D. thesis, Dept. Mech. Eng., Univ. Wisconsin.

MORGAN, A.J.A. 1952 The reduction by one of the number of inde-

pendent variables in some systems of partial differential equations. Quart.

J. Math. (2)

, 250–259.

MORSE, P.M. and FESHBACH, H. 1953

Methods of Theoretical Phy-

sics. Part I

. McGraw-Hill.

MORTON, B.R. 1971 The choice of conservation equations for plume

models.

J. Geophys. Research

, 7409–7416.

NAVIER, C.L.M.H. 1823 M ́emoires sur les lois du mouvement des

fluides. M ́emoires de l’Academie Royale des Sciences de l’Institut de France,

Paris

, 389–440.

OBERBECK, A. 1879 Ueber die W ̈armeleitung der Fl ̈ussigkeiten bei

Ber ̈ucksichtigung der Str ̈omungen infolge von Temperaturdifferenzen. An-

nalen der Physik und Chemie, Neue Folge

, 271–292.

OBERBECK, A. 1888

Ueber die Bewegungserscheinungen der Atmo-

sphaere. Sitzungberichte der K ̈oniglich Preussischen Akademie der Wis-

senschaften zu Berlin, 383–395, 1129–1138 (in English as “On the phe-

nomena of motion in the atmosphere,” in

The Mechanics of the Earth’s

Atmosphere

, Smithsonian Miscellaneous Collections No. 843, Smithsonian

Institution, 1891, 176–197).

OLVER, P.J. 1986

Applications of Lie Groups to Differential Equa-

tions

. Springer-Verlag.

OVSIANNIKOV, L.V. 1982

Group Analysis of Differential Equations

Academic Press.

PERRY, A.E. and FAIRLIE, B.D. 1973 Critical points in flow pat-

terns. Adv. in Geophysics

18B

, 299–315.

PHILLIPS, O.M. 1972 The entrainment interface. J. Fluid Mech.

97–118.

POISSON, M. 1831 Sur les ́equations g ́en ́erales de l’ ́equilibre et du

mouvement des corps solides ́elastiques et des fluides. VII. Calcul des pres-

sions dans les fluides en mouvement; ́equations diff ́erentielles de ce mouve-

ment. Journal de l’

Ecole Polytechnique

, 139–174.

PRANDTL, L. 1905

Uber Fl ̈ussigkeitsbewegung bei sehr kleiner Rei-

bung. In

Verhandlungen des III Internationalen Mathematiker-Kongresses

Teubner, Leipzig, 484-491; reprinted in

Vier Abhandlungen zur Hydrody-

namik und Aerodynamik

, Kaiser Wilhelm-Instituts f ̈ur Str ̈omungsforschung,

G ̈ottingen, 1927, 1–8 (in English as “Motion of fluids with very little viscos-

ity,” NACA TM 452, 1928).

PRANDTL, L. 1932 Herstellung einwandfreier Luftstr ̈ome (Windkan-

̈ale) Handbuch der Experimentalphysik, Vol. 4, Part 2, Hydro- und Aerody-

namik (L. Schiller, ed.), Akademische Verlagsgesellschaft, 65–106.

REYNOLDS, O. 1898 Flow of water shown by colour bands. Nature

, 467–468.

ROSENHEAD, L. (ed.) 1963

Laminar Boundary Layers

. Oxford Univ.

Press (reprinted, Dover, 1988).

ROSHKO, A. 1992 Uses of flow visualization in research. In

Recent

Advances in Experimental Fluid Mechanics

(F.G. Zhuang, ed.), Interna-

tional Academic Publishers, 3–11.

ROTT, N. 1985 Jacob Ackeret and the history of the Mach number.

Ann. Rev. Fluid Mech.

, 1–9.

SAINT-VENANT, B. 1843 Note a joindre au memoire sur la dy-

namique des fluides. Comptes Rendus Hebdomadaires des S ́eances de l’Aca-

d ́emie des Sciences, Paris

, 1240–1243.

SCHLICHTING, H. 1960 Some developments in boundary layer re-

search in the past thirty years. J. Roy. Aeron. Soc.

, 64–79.

SCHLICHTING, H. 1975 An account of the scientific life of Ludwig

Prandtl. In

Flow Separation

, AGARD CP 168, Paper 1.

SEDOV, L.I. 1959

Similarity and Dimensional Methods in Mechan-

ics

. Academic Press (QC/20.7/D55/S42).

SESHADRI, R. and NA, T.Y. 1985

Group Invariance in Engineering

Boundary Value Problems

. Springer-Verlag.

SPIEGEL, E.A. and VERONIS, G. 1960 On the Boussinesq approx-

imation for a compressible fluid. Astrophysical J.

131

, 442–447.

STEFAN, M.J. 1862

Uber die Bewegung fl ̈ussiger K ̈orper. Sitzungs-

berichte der Kaiserlichen Akademie der Wissenschaften, Wien, Mathematisch-

naturwissenschaftliche Classe, II Abteilung

, 8–31, 495–520.

STEWART, R.W. 1956 Irrotational motion associated with free tur-

bulent flows. J. Fluid Mech.

, 593–606.

TANI, I. 1977 History of boundary-layer theory. Ann. Rev. Fluid

Mech.

, 87–111.

TAYLOR, G.I. 1958 Flow induced by jets. J. Aero/Space Sci.

464–465.

TRITTON, D.J. 1977

Physical Fluid Dynamics

. Van Nostrand Rein-

hold

(second edition?)

VAN DYKE, M. 1974 Analysis and improvement of perturbation se-

ries. Q. J. Mech. Appl. Math.

, 423–450.

VAN DYKE, M. 1975

Perturbation Methods in Fluid Mechanics

, Par-

abolic Press.

WALLACE, J.M. and FOSS, J.F. 1995 The measurement of vorticity

in turbulent flows. Ann. Rev. Fluid Mech.

, 469–514.

WEBER, M. 1930 Das allgemeine

Ahnlichkeitsprinzip der Physik und

sein Zusammenhang mit der Dimensionslehre und der Modellwissenschaft.

Jahrbuch der Schiffbautechnischen Gessellschaft

, 274–354.

WEYL, H. 1949 Shock waves in arbitrary fluids. Comm. Pure Appl.

Math.

, 103–122.

WILCZYNSKI, E.J. 1900 An application of group theory to hydro-

dynamics. Trans. American Math. Soc.

, 339–352.

ZIEREP, J. 1971

Similarity Laws and Modeling

. Marcel Dekker.

Chapter 2: Pipe Flow

General References

ALLEN, J. 1970 The life and work of Osborne Reynolds. In

Osborne

Reynolds and Engineering Science Today

(D.M. McDowell and J.D. Jackson,

eds.), Manchester Univ. Press, 1–82.

BARR, G. 1931

A Monograph of Viscometry

. Oxford Univ. Press.

Want Ch. 2, pp 9–47 and title page. p. 10 describes Poiseuille’s work.

BERMAN, J. and MOCKROS, L.F. 1984 Flow in a rotating non-

aligned straight pipe. J. Fluid Mech.

144

, 297–310.

BINGHAM, E.C. 1922

Fluidity and Plasticity

. McGraw-Hill.

BLASIUS, H. 1913

BREUER, K.S. 1985

BROCKMAN, M.R. 1956

BUCKINGHAM, E. 1914 On physically similar systems: illustrations

of the use of dimensional equations. Physical Review (2)

, 345–376.

BUCKINGHAM, E. 1914 Physically similar systems. Journal of the

Washington Academy of Sciences

, 347–353.

BUCKINGHAM, E. 1915 The principle of similitude. Nature

396–397.

Remarks on Rayleigh.

BUCKINGHAM, E. 1915 Model experiments and the forms of em-

pirical equations. Transactions, American Society of Mechanical Engineers

, 263–292 (discussion, 292–296).