Chapter_4.pdf

thesis by WHAN, Carnegie Inst. Technology, about 1958.

WIDNALL, S.E. 1984 Growth of turbulent spots in plane Poiseuille

flow. In

Turbulence and Chaotic Phenomena in Fluids

(T. Tatsumi, ed.),

Elsevier, 93–98.

Chapter 4: The Boundary Layer

Boundary layers

Major surveys and theory

ASTIN, P. and WILKS, G. 1996 Jet profile solutions of the Falkner-

Skan equation. Zeitschr. angew. Math. Phys.

, 790–798.

BAIRSTOW, L. 1925 Skin friction. J. Royal Aeron. Soc.

, 3–14

(discussion 15–23).

BANKS, W.H.H. and DRAZIN, P.G. 1973 Perturbation methods in

boundary-layer theory. J. Fluid Mech.

, 763–775.

Falkner-Skan solutions

near turning point at

∗

BIRKHOFF, G. 1950

Hydrodynamics

. Princeton University Press.

BLASIUS, H. 1908 Grenzschichten in Fl ̈ussiskeiten mit kleiner Rei-

bung. Zeitschr. Math. Phys.

, 1–37 (in English as “The boundary layers

in fluids with little friction,” NASA TM 1256, 1950).

BOTTA, E.F.F., HUT, F.J., and VELDMAN, A.E.P. 1986 The role

of periodic solutions in the Falkner-Skan problem for

λ >

0. J. Engineer-

ing Mathematics

, 81–93.

Multiple solutions; can be periodic or satisfy

′

(

∞

) = 1

. Branching for

= 1

...

. Good summary, emphasizing re-

striction

< f

′

. Algorithm is extrapolation type; see Burlisch and Stoer

(

). Study of extrema for

= 4

. Page 84 cites exponential behavior for

→∞

; see Coppel, Hartman. Also resemblance of oscillating and periodic

solutions. See figure 9. Note plot of

′′

(0)

against

BRAUNER, C.M., LAINE, C., and NICOLAENKO, B. 1982 Further

solutions of the Falkner-Skan equation for

−

1 and

= 0. Mathematika

, 231-248.

Case

−

′′

(0) =

−

0863757

. Asymptotic behavior for

−

1988

... < β <

is algebraic (cf node) except for two extremal solutions

by Hartree and Stewartson. Figure 1 shows seven curves for

β <

−

, with

profiles.

126

BRODIE, P. and BANKS, W.H.H. 1986 Further properties of the

Falkner-Skan equation. Acta Mechanica

, 205–211.

Case of large

including eigenfunctions.

BROWN, S.N. 1966 A differential equation occurring in boundary-

layer theory. Mathematika

, 140–146.

See for

′′′

′′

= 1

BROWN, S.N. 1966 Hartree’s solutions of the Falkner-Skan equation.

AIAA J.

, 2215–2216.

Speculative argument about condition of exponential

decay at infinity.

BROWN, S.N. and STEWARTSON, K. 1965 On similarity solutions

of the boundary-layer equations with algebraic decay. J. Fluid Mech.

673–687.

BROWN, S.N. and STEWARTSON, K. 1966 On the reversed flow

solutions of the Falkner-Skan equation. Mathematika

, 1–6.

Limit

→

−

. Mixing layer is limit of

′′

(0)

∼ −

(

−

)

→

. See for

′′′

′′

= 1

CARDELL, G. 1997 Falkner-Skan table. (private communication)

CEBECI, T. and Keller, H.B. 1971 Shooting and parallel shooting

methods for solving the Falkner-Skan boundary-layer equation. J. Comp.

Phys.

, 289–300.

More Stewartson solutions.

CHEN, K.K. 1969 On two-dimensional laminar wakes and jets. J.

Fluid Mech.

, 163–172.

Falkner-Skan flows without wall. One limit gives

plane jet. See Wygnanski and Fiedler. Claims

−

is plane jet.

CHEN, K.K. and LIBBY, P.A. 1968 Boundary layers with small de-

partures from the Falkner-Skan profile. J. Fluid Mech.

, 273–282.

Relax-

ation to FS solution in downstream direction for upper branch.

CHRISTIAN, J.W., HANKEY, W.L., and PETTY, J.S. 1970 Similar

solutions of the attached and separated compressible laminar boundary layer

with heat transfer and pressure gradient. Aerospace Research Laboratories,

U.S. Air Force, Rep. ARL 70–0023.

CLAUSER 1954

COLES, D. 1955 The law of the wall in turbulent shear flow. In

Jahre Grenzschichtforschung

(H. G ̈ortler and W. Tollmien, eds.), Vieweg,

Braunschweig, 153–163.

COLES, D. 1956 The law of the wake in the turbulent boundary layer.

J. Fluid Mech.

, 191–226. 7.47

COLES, D. 1968 The young person’s guide to the data. In

Computa-

tion of Turbulent Boundary Layers

, Proc. 1968 AFOSR-IFP-Stanford Conf.,

Vol. II (D. Coles and E. Hirst, eds.), 1–45. 7.47

COLES, D. 1969 On the need for better experiments. In

Proc. 1968

AFOSR-IFP-Stanford Conference on Computation of Turbulent Boundary

127

Layers,

Vol. I (S.J. Kline, M.V. Morkovin, and D.J. Cockrell, eds.), Stanford

Univ., 434–436.

COPPEL, W.A. 1960 On a differential equation of boundary-layer

theory. Phil. Trans. Royal Society London

A253

, 101–136.

Grand survey.

Arbitrary constant boundary conditions on

f,f

′

′′

. Asymptotic form for

→ ∞

. See p. 133+ for plane stagnation-point flow. Says Weyl (1942)

notes that Blasius equation can be reduced to first order; see Punnis for

simple pole.

CRAVEN, A.H. and PELETIER, L.A. 1972a On the uniqueness of

solutions of the Falkner-Skan equation. Mathematica

, 129–133.

Solution

with

< f

′

is unique for

< β <

CRAVEN, A.H. and PELETIER, L.A. 1972b Reverse flow solutions

of the Falkner-Skan equation for

λ >

1. Mathematica

, 135–138.

Any

Solutions with

′

(0)

somewhere argued for

β >

. Figure 1 shows 0,

1, 2 reversals for

= 1

(cf Pesenson for

= 5

). Also

= 1

but not

= 1

. For

β >

, any solution, including these, approaches

′

= 1

exponentially.

DANBERG, J.E. and FANSLER, K.S. 1974 Additional two-dimensional

wake and jet-like flows. AIAA J.

, 1432–1433 (also BRL Rep. No. 1727,

1974).

Falkner-Skan equation with moving wall. Includes free shear layer

and backward boundary layers with algebraic decay.

DEAN, R.B. 1976 A single formula for the complete velocity profile

in a turbulent boundary layer. Trans. ASME (J. Fluids Eng.)

98I

, 723–726

(discussion 726–727). 7.47

ERDELYI, A., MAGNUS, W., OBERHETTINGER, F., and TRICOMI,

F.G. (eds.) 1953

Higher Transcendental Functions,

McGraw-Hill, Vol. 2,

Chapter 8.

EVANS, H.L. 1968

Laminar Boundary-layer Theory

. Addison-Wesley.

Attributes poor analysis for

→∞

to Mangler (?) Wrong for

−∞

< β <

FALKNER, V.M. and SKAN, S.W. 1931 Solutions of the boundary-

layer equations. Phil. Mag. (7)

, 865–896 (preliminary version as “Some

approximate solutions of the boundary layer equations,” Aeronautical Re-

search Council, Great Britain, R&M 1314, 1930).

FINLEY, KHOO, and CHIN 1966

FORBRICH, C.A. Jr. 1973 Improved solutions to the Falkner-Skan

boundary layer equation. Frank J. Seiler Research Lab., USAF Academy,

Rep. SLR-TR-73-0016 (short summary, same title, in AIAA J.

, 1306–

1307, 1982).

See Hartree for uniqueness condition on upper branch,

β <

Fit of

′′

(0)

to parabola in

on p. 11. Min =

−

1988377

. Has Smith node,

saddle figure.

128

FORBRICH, C.A. Jr. 1982 Improved solutions to the Falkner-Skan

boundary layer equation. AIAA J.

, 1306–1307.

Shooting method, a la

Keller. Priority? See fig. 2. Solutions like Smith. Air force report gives

tables, curve fit for

′′

(0)

against

that may be useful for Thwaites method.

FRAENKEL, L.E. 1962 Laminar flow in symmetrical channels with

slightly curved walls. Proc. Roy. Soc. London

267A

, 119–138.

Sink flow;

infinitely many solutions.

GILBARG, D. and PAOLUCCI, D. 1953 The structure of shock waves

in the continuum theory of fluids. J. Rational Mechanics and Analysis

617–642.

GOLDSTEIN, S. 1939 A note on the boundary layer equations. Proc.

Cambr. Phil. Soc.

, 338–340.

“Backward boundary layer”.

GOLDSTEIN, S. 1965 On backward boundary layers and flow in con-

verging passages. J. Fluid Mech.

, 33–45.

Useful on exponential depen-

dence of free-stream velocity when

= 2

. Also wedge vs cone. Good on

similarity.

GRANVILLE, P.S. 1975 A modified law of the wake for turbulent

shear flows. Naval Ship Research and Development Center, Rep. 4639.

GRANVILLE, P.S. 1976 A modified law of the wake for turbulent

shear layers. Trans. ASME (J. Fluids Eng.)

98I

, 578–580. 7.47

Polynomial

for wake function. No clear definition of delta. Also “A modified law of

the wake for turbulent shear flows,” Naval Ship Res. Dev. Center, Bethesda,

Rep. 4639.

HAMEL, G. 1916 Spiralf ̈ormige Bewegungen z ̈aher Fl ̈ussigkeiten. Jahr-

esbericht der deutschen Mathematiker-Vereinigung

, 34–60.

Sink flow.

HARTMAN, P. 1964

Ordinary Differential Equations

. Wiley.

Ab-

stract and text have formula for exponential behavior at infinity for

β >

For

β <

, only one integral is exponential; others are algebraic.

HARTMAN, P. 1964 On the asymptotic behavior of solutions of a

differential equation in boundary layer theory. Zeitschr. angew. Math. Mech.

, 123–128.

Exponential approach to free stream for Falkner-Skan equation.

HARTMAN, P. 1972 On the existence of similar solutions of some

boundary layer problems. SIAM J. Mathematical Analysis

, 120–147.

HARTREE, D.R. 1937 On an equation occurring in Falkner and Skan’s

approximate treatment of the equations of the boundary layer. Proc. Cam-

bridge Phil. Soc.

, 223–239.

Uniqueness for

β <

from most rapid ap-

proach. (

′′

(0)

) is parabola. Weyl method in eq. 16.

HASTINGS, S.P. 1972 Reversed flow solutions of the Falkner-Skan

equation. SIAM J. Appl. Math.

, 329–334.

Here

β <

and

→

Exponential.

129

HASTINGS, S.P. and TROY, W. 1985 Oscillatory solutions of the

Falkner-Skan equation. Proc. Roy. Soc. London

A397

, 415–418.

For

β <

−

, branching and overshoot in profiles. For

β >

, periodic solutions exist.

For

β >

, an infinite number. See Oskam, Laine, Libby, Troy.

HASTINGS, S.P. and TROY, W.C. 1987 Oscillating solutions of the

Falkner-Skan equation for negative

. SIAM J. Math. Anal.

, 422–429.

These seem to be wake solutions,

′′

(0) = 0

. There is another paper for

β >

. Misuses Evans for

β <

. Here

β <

−

. Partly wake or jet.

Strongly oscillating solutions exist.

HASTINGS, S.P. and TROY, W.C. 1988 Oscillating solutions of the

Falkner-Skan equation for positive

. J. Differential Equations

, 123–144.

Periodic solutions for

≥

HATTA, N., KOKADO, J., and YABUSHITA, S. 1985 On the accu-

rate numerical solution of Blasius equation for laminar boundary layer along

a flat plate. Faculty of Engineering, Kyoto Univ., Memoires

, 18–25.

Bla-

sius problem only.

HEIDEL, J.W. 1973 A third order differential equation arising in fluid

mechanics. Zeitschr. angew. Math. Mech.

, 167–170.

May have other

solutions than Glauert’s for wall jet.

HINZE, J.O. 1959

Turbulence

. McGraw-Hill. 7.47

HOWARTH, L. 1935 Steady flow in the boundary layer near the sur-

face of a cylinder in a stream. Aeron. Res. Committee, R&M 1632.

Plane

stagnation-point flow.

HUDIMOTO, B. 1948 Approximate solution of the laminar boundary

layer problem. The Journal of the Society of Aeronautical Science of Nippon

, 279–282.

Like Thwaites.

IGLISH, R. 1954 Elementarer Beweis f ̈ur die Eindeutigkeit der Str ̈om-

ung in der laminaren Grenzschicht zur Potentialstr ̈omung

∼

mit

≥

0 bei Absaugen und Ausblasen. Zeitschrift f ̈ur angewandte Mathe-

matik und Mechanik

, 441–443.

See refs for other papers by Iglish. For

β >

, solution is unique if there is no reverse flow and

< f

′

JEFFERY, G.B. 1915 The two-dimensional steady motion of a vis-

cous fluid. Phil. Mag. (6)

, 455–465.

Sink flow.

KATAGIRI, M. 1969 On a numerical calculation of laminar boundary

layer flows. Bull. Yamagata Univ. (Eng.)

, 511–523.

Develops Weyl’s

method. See for difficulties.

KATAGIRI, M. 1986 On accurate numerical solutions of Falkner-Skan

equation. In

Proc. Symposium on Mechanics for Space Flight

, Inst. of Space

and Astron. Science, Rep. SP 4, 65–70.

10-place accuracy. Applies Weyl’s

method. Most precise data for

−

1988

< β <

130

KENNEDY, E.D. 1964 Wake-like solutions of the laminar boundary-

layer equations. AIAA J.

, 225–231.

Solution with

(0) =

′′

(0) = 0

but

′

(0)

= 0

. Limiting solution for

→

is mixing layer; boundary layer is

blown off surface. See Wygnanski and Fiedler. Mixing layer found as limit

of wake-jet version of F-S equation.

KLAMKIN, M.S. 1962 On the transformation of a class of boundary

value problems into initial value problems for ordinary differential equations.

SIAM Review

, 43–47.

Toepfer +. Claims T ̈opfer method for any

KUNTZMANN, J. 1948 Note concernant l’ ́equation de Blasius. Ad-

dendum, p. 123–127, to “Les m ́ethodes scientifiques de la couche limite

laminaire,” by A. OUDART, Publications Scientifiques et Techniques du

Minist`ere de l’Air, No. 213.

LAINE, C. and REINHART, L. 1984 Further numerical methods for

the Falkner-Skan equations: shooting and continuation techniques. Interna-

tional Journal for Numerical Methods in Fluids

, 833–852.

Seven branches

for

β <

−

. Nice introduction. For

β <

−

1988

, all possible solutions are

of overshoot type. Details near

−

. Special shooting method. Profiles

for

−

but no numbers.

LEWKOWICZ, A.K. 1982 An improved universal wake function for

turbulent boundary layers and some of its consequences. Z. Flugwiss. Wel-

traumforsch.

, 261–266.

LIBBY, P.A. and CHEN, K.K. 1968 Application of quasi-linearization

to an eigenvalue problem arising in boundary-layer theory. J. Computational

Physics

, 356–362.

Relaxation problems for F-S flows. Eigenvalues of F-S

equation.

LIBBY, P.A. and FOX, H. 1963 Some perturbation solutions in lam-

inar boundary-layer theory. J. Fluid Mech.

, 433–449.

LIBBY, P.A. and LIU, T.M. 1967 Further solutions of the Falkner-

Skan equation. AIAA J.

, 1040–1042.

Wall-jet-like solutions of Falkner-

Skan equation. No clue about where tabulated solutions might be found. First

report of new solutions for

β <

LIEPMANN, H.W. and SKINNER, G.T. 1954 Shearing-stress mea-

surments by use of a heated element. NACA TN 3268.

LUDWIEG, H. 1949 Ein Ger ̈at zur Messung der Wandschubspannung

turbulenter Reibungsschichten. Ing.-Arch.

, 207–218 (in English as “In-

strument for measuring the wall shearing stress of turbulent boundary lay-

ers,” NACA TM 1284, 1950).

LUDWIEG, H. and TILLMANN, W. 1949 Untersuchungen ̈uber die

Wandschubspannung in turbulenten Reibungsschichten. Ing.-Arch.

288–299 (in English as “Investigations of the wall-shearing stress in tur-

131

bulent boundary layers,” NACA TM 1285, 1950).

MANGLER, W. 1943 Die “ ̈ahnlichen” L ̈osungen der Prandtlschen

Grenzschichtgleichungen. Zeitschr. angew. Math. Mech.

, 241–251.

In-

cludes comments on exponential free stream and sink flow. Four classes of

solution. Cites Goldstein 1939. Geometric interpretation of F-S flows.

MEKSYN, D. 1959 Sur la position des singularit ́es dans les solutions

de l’ ́equation de la couche limite. C. R. Acad. Sci. Paris

248

, 2286–2287.

Radius of Blasius series is fixed by ring of three poles. See Meksyn’s book.

MILLS, R.H. 1938 A note on some accelerated boundary layer veloc-

ity profiles. J. Aeron. Sci.

, 325–327.

Nearly sink flow. Also

−

goes

to plane jet.

MILLS, R.D. 1968 The steady laminar incompressible boundary-layer

problem as an integral equation in Crocco variables: investigation of the

similarity flows. Aeron. Res. Council, Gt. Britain, R&M No. 3515.

MILLSAPS, K. 1984 Karl Pohlhausen, as I remember him. Ann. Rev.

Fluid Mech.

, 1–10.

Cites Anderson’s translation of P’s 1921 paper.

MILLSAPS, K. and POHLHAUSEN, K. 1953 Thermal distributions

in Jeffery-Hamel flows between nonparallel plane walls. J. Aeron. Sci.

187–196.

Sink flow.

von MISES, R. and FRIEDRICHS, K.O. 1941

Fluid Dynamics

. Brown

University Press; reprinted, Springer-Verlag, 1971.

Sink flow.

MOSES, H.L. 1964 (cited in 7D)

MOULDEN, T.H. 1979 Comments on an exact solution of the Falkner-

Skan equation. Zeitschr. angew. Math. Mech.

, 289–295.

Case

−

See Yang and Chien. Suction at wall.

NAPOLITANO, L.G. 1959 The Blasius equation with three-point bound-

ary conditions. Quart. Appl. Math.

, 397–408.

Weak mixing layer with

variations. Expansion parameter is

(

−

NICKEL, K. 1973 Prandtl’s boundary-layer theory from the view-

point of a mathematician. Ann. Rev. Fluid Mech.

, 405–428.

OSKAM, B. and VELDMAN, A.E.P. 1982 Branching of the Falkner-

Skan solutions for

less than zero. J. Eng. Math.

, 295–308.

Good review.

See Libby and Liu. Profiles for up to 5 branches for

−

. Figures 5, 6

are intriguing. Here

β <

′

(

∞

) = 1

−

. Multiple solutions. Remarks

about

−

′′

(0) =

−

086381

. Envelope. Mixing layer at origin.

OSTROWSKI, A. 1948 Sur le rayon de convergence de la s ́erie de

Blasius. Comptes Rendus de l’Acad ́emie des Sciences

227

, 580–582.

R <

for

′′′

y y

′

= 0

(0) =

′

(0) = 0

′′

(0) = 1

PERRY, A.E. and CHONG, M.S. 1994 Topology of flow patterns in

vortex motions and turbulence. Appl. Sci. Res.

, 357–374.

132

PERRY, A.E. and FAIRLIE, B.D. 1974 Critical points in flow pat-

terns.

Advances in Geophysics

18B

, Academic Press, 299–315.

PERRY, A.E., MARUSIC, I., and LI, J.D. 1994 Wall turbulence clo-

sure based on classical similarity laws and the attached eddy hypothesis.

Phys. Fluids

, No. 2, Part 2, 1024–1035.

PIERCY, N.A.V. and PRESTON, J.H. 1936 A simple solution of the

flat plate problem of skin friction and heat transfer. Phil. Mag.

, 995–

1005.

Weyl method. Ref in Katagiri.

POHLHAUSEN, K. 1921 Zur n ̈aherungsweisen Integration der Dif-

ferentialgleichung der laminaren Grenzschicht. ZaMM

, 252–268; also Abh.

Aerodyn. Inst. Techn. Hochschule Aachen

, Springer, Berlin, 20–36 (in En-

glish as “The approximate integration of the differential equation for the

laminar boundary layer,” translated by R.C. Anderson, Dept. Aerosp. Eng.,

Univ. Florida, 1965).

ZaMM not checked. Sink flow in closed form.

POHLHAUSEN, K. 1965 The approximate integration of the differ-

ential equation for the laminar boundary layer. Translation by R.C. Ander-

son, Dept. Aerosp. Eng., Univ. Florida.

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

n ̈ale). In Handbuch der Experimentalphysik, Bd. IV, Teil 2, Hydro- und

Aerodynamik, 63–106 (in English as “Attaining a steady air stream in wind

tunnels,” NACA TM 726, 1933).

PUNNIS, B. 1956 Zur Differentialgleichung der Plattengrenzschicht

von Blasius. Arch. Math.

, 165–171.

Three poles on a circle.

−

∗

−

, but

√

∞

νx

PUNNIS, B. 1956 Zur Differentialgleichung der Plattengrenzschicht

von Blasius. Z. angew. Math. Mech., Sonderheft, S26.

Radius of convergence

for series.

RADBILL, J.R. 1964 Application of quasilinearization to boundary-

layer equations. AIAA J.

, 1860–1862.

Weyl method but does not cite

Weyl.

RASMUSSEN, H. 1970 Note on the equation

′′′

′′

−

′

2

= 0.

Zeitschr. f. angew. Math. u. Mech.

, 497–498.

Cf wall jet. See for ref to

Coppel on Falkner-Skan equation.

RICHARDSON, S. 1973 On Blasius’s equation governing flow in the

boundary layer on a flat plate. Proc. Cambridge Philos. Soc.

, 179–184.

Has recurrence relation for coefficients in Blasius series. Weyl gave radius

of convergence and found

= 0

4696

, with

462

< a <

499

. See p 180;

three simple poles on circle (Punnis, Meksyn).

ROSENHEAD, L. 1940 The steady two-dimensional radial flow of

133

viscous fluid between two inclined plane walls. Proc. Roy. Soc. London

175A

, 436–467.

Sink flow. Most exhaustive paper.

ROSENHEAD, L. (ed.) 1963

Laminar Boundary Layers

. Clarendon

Press, Oxford, 687 pp.

SANDHAM, N.D. 1991 An alternative formulation of the outer law of

the turbulent boundary layer. Institut f ̈ur Theoretische Str ̈omungsmechanik,

DLR G ̈ottingen, Rep. IB 221-91 A 10.

SHANKS, D. 1953 The Blasius and Weyl constants in boundary layer

theory. Phys. Rev.

, 377, Abstract U11.

Gives Blasius bounds as

328228

328230

; Weyl constant as

12735

. First corresponds to

46959951

46960022

SHANKS, D. 1954 Non-linear transformation of divergent and slowly

convergent sequences. Ph. D. thesis, Dept. Mathematics, Univ. Maryland.

SHANKS, D. 1955 Non-linear transformations of divergent and slowly

convergent sequences. J. Math. Phys.

, 1–42 (same as Ph.D. thesis, Dept.

Mathematics, Univ. Maryland, 1954).

P 16, eq. (63), refers to Abstract U11

in Phys Rev

(2), p 377, 1953.

SMITH, A.M.O. 1954 Improved solutions of the Falkner-Skan boundary-

layer equation. Fairchild Fund Paper (Inst. Aeron. Sci.) No. FF-10.

Tabu-

lated solutions for

from -0.1988 to 2. Variables used make

′′

(0) = 0

46960

for Blasius solution. Classic paper. Shooting method?

SORIA, J., SONDERGAARD, R., CANTWELL, B., CHONG, M.S.,

and PERRY, A.E. 1994 A study of the fine-scale motions of incompress-

ible time-developing mixing layers. Phys. Fluids

, No. 2, Part 2, 871–884.

STEIGER, M.H. and CHEN, K. 1965 Further similarity solutions of

two-dimensional wakes and jets. AIAA J.

, 528–530.

STEINHEUER, J. 1968 Similar solutions for the laminar wall jet in a

decelerating outer flow. AIAA J.

, 2198–2200.

Type of Falkner-Skan flow.

Approaches Glauert wall jet if

→−

′′

(0) =

∞

STEWARTSON, K. 1954 Further solutions of the Falkner-Skan equa-

tion. Proc. Cambr. Philos. Soc.

, 454–465. [17.22]

Further to Hartree.

Second-branch solutions for

−

1988

< β <

. No solution for

β >

. Con-

jecture about mixing layer as limit. Mentions flows for

−

< β <

with

free streamlines? First paper on lower branch. If

β <

−

1988

...

, condition

′

|≤

everywhere cannot be satisfied. Hartree noted “most rapid approach”

on upper branch, consistent with node. Mentions

′

(

∞

) =

−

STEWARTSON, K. 1964 Falkner-Skan equation for wakes. AIAA

, 1327–1328.

Symmetric profile, with improved estimate for centerline

velocity. Comments on work by Kennedy, AIAA J.

SWINNERTON-DYER, H.P.F. and SPARROW, C.T. 1995 The Falkner-

Skan equation. I. The creation of strange invariant sets. Journal of Differ-

134

ential Equations

119

, 336–394.

TAGHAVI, H. and WAZZAN, A.R. 1974 Spatial stability of some

Falkner-Skan profiles with reversed flow. Phys. Fluids

, 2181-2183.

Orr-

Sommerfeld equation on Stewartson’s branch.

TANI, I. 1955 On the solution of the laminar boundary layer equa-

tions. In

50 Jahre Grenzschichtforschung

(H. G ̈ortler and W. Tollmien,

eds.), Vieweg and Sohn, 193–200.

TANI, I. and MOTOHASHI, T. 1985 Non-equilibrium behavior of

turbulent boundary layer flows. I. Method of analysis. II. Results of analysis.

Proc. Japan Acad.

, Ser. B, 333–340.

THWAITES, B. 1949 Approximate calculation of the laminar bound-

ary layer. Aeron. Quart.

, 245–280.

See Tani, Ann Rev Fluid Mech, for

similar earlier papers by Walz, Hudimoto, Tani.

THWAITES, B. 1955 On two solutions of the boundary-layer equa-

tions. In

50 Jahre Grenzschichtforschung

(H. G ̈ortler and W. Tollmien,

eds.), Vieweg, 210–215.

OPFER, K. 1912 Bemerkung zu dem Aufsatz von H. Blasius “Gren-

zschichten in Fl ̈ussigkeiten mit kleiner Reibung.” Zeitschr. f ̈ur Math. und

Phys.

, 397–398.

TOWNSEND, A.A. 1976

The Structure of Turbulent Shear Flow

(2nd

ed.). Cambridge Univ. Press.

TROY, W.C. 1979 Non-monotonic solutions of the Falkner-Skan bound-

ary layer equation. Quart. Appl. Math.

, 157–167.

β <

. Oscillating

solutions relevant for

→ −∞

. Phase plane. Formula for exponential

behavior at infinity. Study Fig. 2, p. 161. Looks backwards.

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

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

, 423–450.

Alternating signs imply singu-

larity on negative real axis. See p 426, 433, for Blasius problem.

WERLE, M.J. and DAVIS, R.T. 1970 Self-similar solutions to the

second-order incompressible boundary-layer equations. J. Fluid Mech.

343–360.

Considers free-stream vorticity, surface curvature.

WEYL, H. 1941 Concerning the differential equations of some bound-

ary layer problems. Proc. Nat’l. Acad. Sci.

, 578–583.

WEYL, H. 1942 Concerning the differential equations of some bound-

ary layer problems. II. Proc. Nat’l. Acad. Sci.

, 100–102.

WEYL, H. 1942 On the differential equations of the simplest boundary-

layer problems. Annals Math.

, 381–407.

Falkner-Skan equation. Discus-

sion for

= 0

. Proof of existence but not uniqueness of solutions with

exponential approach to free-stream velocity.

135

WIEGHARDT, K. 1947 The roughness-tunnel of the Kaiser-Wilhem-

Institut f ̈ur Str ̈omungsforschung at G ̈ottingen. Reports and Translation No.

946, M.A.P. V ̈olkenrode, AVA Monographs, Section 3.3 of D

Model Test

Technique, II, Test Installations (R. Seiferth, ed.), 23–28.

YANG, H.T. and CHIEN, L.C. 1975 Analytical solutions of the Falkner-

Skan equation when

−

1 and

= 0. SIAM J. Appl. Math.

, 558–569.

Case

−

, usual boundary conditions. Quotes

−

198838

...

from

Goldstein. See Nickel, ARFM. Wedge angle is

−

. See Mills, Case 3. Also

Thwaites, 50 Jahre. See figure 2.

Boundary layer on smooth wall at constant pressure

Major surveys or theory

AFZAL, N. 1996 Turbulent boundary layer on a moving continuous

plate. Fluid Dynamics Research

, 181–194.

ALFREDSSON, P.H. and JOHANSSON, A.V. 1989 Turbulence ex-

periments — instrumentation and processing of data. In

Advances in Tur-

bulence 2

(H.-H. Fernholz and H.E. Fiedler, eds.), Springer-Verlag, 230–243.

Survey.

BANDYOPADHYAY, P.R. 1986 Review — Mean flow in turbulent

boundary layers disturbed to alter skin friction. Trans. ASME (J. Fluids

Eng.)

108

, 127–140.

BANDYOPADHYAY, P.R. 1991 Comments on Reynolds number ef-

fects in wall-bounded shear layers. AIAA Paper 91-0231.

BARRY, M.D.J. and ROSS, M.A.S. 1970 The flat plate boundary

layer. Part 2. The effect of increasing thickness on stability. J. Fluid Mech.

, 813–818.

BARTENWERFER, M. and BECHERT, D.W. 1987 Die viskose Str ̈om-

ung ̈uber Oberfl ̈achen mit L ̈angsrippen. Deutsche Forschungs- und Versuch-

sanstalt f ̈ur Luft- und Raumfahrt, Rep. DFVLR-FB 87–21.

Translation is

ESA-TT-1091; see N88-30067 (24 p 3370)

BECHERT, D.W., BRUSE, M., HAGE, W., and MEYER, R. 1997

Biological surfaces and their technological application—Laboratory and flight

experiments on drag reduction and separation control. AIAA Paper 97–

1960.

BELL, D.M. and FERZIGER, J.H. 1993 Turbulent boundary layer

DNS with passive scalars. In

Near-Wall Turbulent Flows

(R. M. C. So,

136

C. G. Speziale, and B. E. Launder, eds.), Elsevier, 327–336.

Velocity*,

temperature*, figure 2. Reynolds stresses*, figure 3.

BERKOOZ, G., ELEZGARAY, J., HOLMES, P., LUMLEY, J., and

POJE, A. 1993 The proper orthogonal decomposition, wavelets and modal

approaches to the dynamics of coherent structures. In

Eddy Structure Iden-

tification in Free Turbulent Shear Flows

(J.P. Bonnet and M.N. Glauser,

eds.), Kluwer, 295–309.

BISSET, D.K. and ANTONIA, R.A. 1991 Mean velocity and Reynolds

shear stress in a turbulent boundary layer at low Reynolds numbers. Aeron.

, 244–247.

Calculate

from

plus Granville. Shearing stress*, figures

3, 5.

BISSET, D.K., HUNT, J.C.R., CAI, X., and ROGERS, M.M. 1998

Interfaces at the outer boundaries of turbulent motions. In

Annual Research

Briefs 1998,

Center for Turbulence Research, NASA Ames Research Center

and Stanford University, 125–135.

BLACK, T.J. 1968 A new model of the shear stress mechanism in

wall turbulence. AIAA Paper 68-42.

BRADSHAW, P. 1965 The effect of wind-tunnel screens on nominally

two-dimensional boundary layers. J. Fluid Mech.

, 679–687, 1 plate.

Extended version of J Roy Aeron Soc

, 198, 1964.

BRADSHAW, P. 1973 Effects of streamline curvature on turbulent

flow. AGARDograph No. 169.

BRADSHAW, P. 1994 Turbulence: the chief outstanding difficulty of

our subject. Exp. in Fluids

, 203–216.

See p. 206 for Van Driest. No

figures!

BRADSHAW, P. 1996 Turbulent boundary layers. In

Research Trends

in Fluid Dynamics

(J.L. Lumley et al., eds.), AIP Press, 31–42.

BRADSHAW, P. and HUANG, G.P. 1995 The law of the wall in tur-

bulent flow. Proc. Roy. Soc. London

A451

, 165–188.

See p. 169 for analog

log law/inertial range. See p. 176 for Van Driest. See p. 178 for power

series*, figure 5.

BRADSHAW, P. and LANGER, C.A. 1995 Nonuniversality of sub-

layer streaks in turbulent flow. Phys. Fluids

, 2435–2438.

BRADSHAW, P., HUNT, J. C. R., JIMENEZ, J., KLINE, S. J., AND

SPEZIALE, C.G.

1987 Coherent structure. Appendix, Proc. Summer

Program, Center for Turbulence Research, NASA Ames Research Center

and Stanford University, 311–330.

BUSHNELL, D.M. 1992 Aircraft drag reduction. In

Skin Friction

Drag Reduction,

AGARD Rep. 786, Paper 3.

137

CAI, X., STEYN, D.G., and GARTSHORE, I.S. 1993 The velocity

profile in the near-wall region of the atmospheric boundary layer: a large

eddy simulation. In

Near-Wall Turbulent Flows

(R.M.C. So, C.G. Speziale,

and B.E. Launder, eds.), Elsevier, 337–346.

CHACIN, J.M., CANTWELL, B.J., and KLINE, S.J. 1996 Study of

turbulent boundary layer structure using the invariants of the velocity gra-

dient tensor. Experimental Thermal and Fluid Science

, 308–317.

CHOI, K.-S. 1993 Turbulence structure revisited; results and impli-

cations from riblets research. In

Near-Wall Turbulent Flows

(R.M.C. So,

C.G. Speziale, and B.E. Launder, eds.), Elsevier, 699–707.

CHONG, M.S., SORIA, J., PERRY, A.E., CHACIN, J., NA, Y., and

CANTWELL, B.J. 1996 In

Proceedings of the Summer Program 1996,

Center for Turbulence Research, NASA Ames Research Center and Stanford

Univ., 383–404.

CHONG, M.S., SORIA, J., PERRY, A.E., CHACIN, J., CANTWELL,

B.J., and NA, Y. 1998 Turbulence structures of wall-bounded shear flows

found using DNS data. J. Fluid Mech.

357

, 225–247.

CIRAY, C. 1988 Environmental effects on transition and boundary

layer characteristics. In

Boundary Layer Simulation and Control in Wind

Tunnels

, AGARD Advisory Rep. No. 224, Section 4.8, 356–408.

CLAUSER, F.H. 1956 The turbulent boundary layer. Advances in

Applied Mechanics

, 1–51.

COANTIC, M. 1965 Remarques sur la structure de la turbulence `a

proximit ́e d’une parci. C.R. Acad. Sci. Paris

260

, 2981–2984.

Power series.

COUSTOLS, E. and SAVILL, A.M. 1992 Turbulent skin-friction drag

reduction by active and passive means. Part 1. Part 2. In

Skin Friction

Drag Reduction,

AGARD Rep. 786, Paper 8.

de ANGELIS, V., LOMBARDI, P., and BANERJEE, S. 1997 Direct

numerical simulation of turbulent flow over a wavy wall. Phys. Fluids

2429–2442.

DICKINSON, J. 1964 Some observations on skin friction measure-

ments. Journal de Mecanique

, 119–140.

DRYDEN, H.L. 1937 Recent developments of the theory of turbu-

lence. Trans. ASME

, A105–A108.

Nice survey.

DRYDEN, H.L. 1955 Fifty years of boundary-layer theory and exper-

iment. Science

121

, 375–380.

DUSSAUGE, J.P., SMITH, R.W., SMITS, A.J., FERNHOLZ, H., FIN-

LEY, P.J., and SPINA, E.F. 1996 Turbulent boundary layers in subsonic

and supersonic flow. AGARDograph 335.

138

FALCO, R.E. 1991 A coherent structure model of the turbulent bound-

ary layer and its ability to predict Reynolds number dependence. Phil.

Trans. Roy. Soc. London

336A

, 103–129.

FALCO, R.E. 1993 Predictions of the Reynolds number dependence

of the turbulent boundary layer using a new structural model. In

Near-

Wall Turbulent Flows

(R.M.C. So, C.G. Speziale, and B.E. Launder, eds.),

Elsevier, 23–32.

FERNHOLZ, H. 1969 Geschwindigkeitsprofile, Temperaturprofile und

halbempirische Gesetze in kompressiblen turbulenten Grenzschichten bei

konstantem Druck. Ing.-Arch.

, 311–328.

FERNHOLZ, H.H. 1971 Ein halbempirisches Gesetz f ̈ur die Wandrei-

bung in kompressiblen turbulenten Grenzschichten bei isothermer und adi-

abater Wand. Zeitschr. angew. Math. Mech.

, T146–T147.

Looks like

Van Driest.

FERNHOLZ, H.H. and FINLEY, P.J. 1996 The incompressible zero-

pressure-gradient turbulent boundary layer: an assessment of the data.

Progr. Aerospace Sci.

, 245–311.

FIEDLER, H.E. and FERNHOLZ, H.-H. 1990 On management and

control of turbulent shear flows. Progr. Aerospace Sci.

, 305–387.

Base

drag*, figures 24–26.

GAD-EL-HAK, M. and BANDYOPADHYAY, P.R. 1994 Reynolds

number effects in wall-bounded turbulent flows. Applied Mechanics Reviews

, 307–365.

GAD-EL-HAK, M. and BANDYOPADHYAY, P.R. 1995 Field versus

laboratory turbulent boundary layers. AIAA J.

, 361–364.

GALBRAITH, R.A. McD. and HEAD, M.R. 1975 Body viscosity and

mixing length from measured boundary layer developments. Aeron. Quart.

, 133–154.

Profiles. Late entry in 1968 Stanford contest.

GALBRAITH, R.A. McD., SJOLANDER, S., and HEAD, M.R. 1977

Mixing length in the wall region of turbulent boundary layers. Aeron. Quart.

, 97–110.

GIBSON, M.M. and DAFA’ ALLA, A.A. 1995 Two-equation model

for turbulent wall flow. AIAA J.

, 1514–1518.

GYR, A.

1989 Panel Discussions. In

Structure of Turbulence and

Drag Reduction

(A. Gyr, ed.), Springer-Verlag, 585–610.

HALIM, A. and GHIA, U. 1987 Longitudinal flow along circular cylin-

ders and thick plates, including blunt leading-edge separation. AIAA J.

655–658.

Cylinder or plate with flat nose. Solution of Navier-Stokes equa-

tions at low Re. Effect of Re on length of bubble. Comparison with data of

Lane and Loehrke.

139

HAMILTON, J.M. and KIM, J. 1993 On streak spacing in wall-bounded

turbulent flows. In

Annual Research Briefs 1993

, Center for Turbulence Re-

search, Stanford University and NASA Ames Research Center, 249–257.

HAMILTON, J.M., KIM, J., and WALEFFE, F. 1992 Regeneration

of near-wall turbulence structures. In Center for Turbulence Research,

An-

nual Research Briefs 1992

, NASA and Stanford Univ., 303–315.

HARITONIDIS, J.H. 1989 A model for near-wall turbulence. Phys.

Fluids

, 302–306.

HE, J., KAZAKIA, J.Y., and WALKER, J.D.A. 1995 An asymptotic

two-layer model for supersonic turbulent boundary layers. J. Fluid Mech.

295

, 159–198.

HONAMI, S. and SIMON, T.W. 1981 Boundary layer with stream-

wise curvature. In

Proc. 1980-81 AFOSR-HTTM-Stanford Conference on

Complex Turbulent Flows,

Stanford Univ., Vol. 1, 94–110.

HUANG, P.G. and COLEMAN, G.N. 1994 Van Driest transforma-

tion and compressible wall-bounded flows. AIAA J.

, 2110–2113.

HUANG, P.G., BRADSHAW, P., and COAKLEY, T.J. 1993 Skin

friction and velocity profile family for compressible turbulent boundary lay-

ers. AIAA J.

, 1600–1604.

HUFFMAN, G.D. and BRADSHAW, P. 1972 A note on von Kar-

man’s constant in low Reynolds number turbulent flows. J. Fluid Mech.

45–60.

HUNT, J.C.R. 1990 Developments in computational modelling of tur-

bulent flows. In

Numerical Simulation of Unsteady Flows and Transition to

Turbulence

(O. Pironneau et al., eds.), Cambridge Univ. Press, 2–76.

HUNT, J.R.C. and FERNHOLZ, H. 1975 Wind-tunnel simulation of

the atmospheric boundary layer: a report on Euromech 50. J. Fluid Mech.

, 543–559.

KARLSSON, R.I., TINOCO, H., and SVENSON, U. 1991 An im-

proved form of the near-wall

−

model based on new experimental data.

Preprints, Eighth Symposium on Turbulent Shear Flows,

Munich, Vol. 2,

Paper 26-3.

KAWAHARA, G., AYUKAWA, K., and OCHI, J. 1993 On the origin

of streaky structures in wall-bounded turbulent flows. In

Near-Wall Turbu-

lent Flows

(R.M.C. So, C.G. Speziale, and B.E. Launder, eds.), Elsevier,

403–412.

KLINE, S.J. 1966 Some remarks on turbulent shear flows. In

Ther-

modynamics and Fluid Mechanics Convention 1966,

Proc. Inst’n. Mech.

Engrs.

180

, Part 3J, 222–244.

140

KLINE, S.J. 1978 The role of visualization in the study of the struc-

ture of the turbulent boundary layer. In Proc. AFOSR/Lehigh Workshop,

Coherent Structure of Turbulent Boundary Layers

, 1–26.

General survey.

Some useful retrospective remarks on work at Stanford and elsewhere. Very

cautious about referring to sublayer streakes as vortices.

KLINE, S.J. 1989 Turbulent boundary layers: progress, status, and

challenges. In

Structure of Turbulence and Drag Reduction

(A. Gyr, ed.),

Springer-Verlag, 3–22.

KLINE, S.J. and ROBINSON, S.K. 1990 Quasi-coherent structures

in the turbulent boundary layer. Part I. Status report on a community-wide

summary of the data. In

Near-wall Turbulence

(S.J. Kline and N.H. Afgan,

eds.), 1988 Zoran Zaric Memorial Conf., Hemisphere, 200–217.

KRAFT, E.M. 1988 Boundary layer manipulation. In

Boundary Layer

Simulation and Control in Wind Tunnels

, AGARD, Adv. Rep. No. 224, 409–

446.

LANDAHL, M.T. 1967 A wave-guide model for turbulent shear flow.

J. Fluid Mech.

, 441–459.

LANDWEBER, L. 1953 The frictional resistance of flat plates in zero

pressure gradient. Trans. Soc. Naval Architects and Marine Engineers

5–21 (discussion, 21–32).

Figure 4 shows

constant for Nikuradse’s data.

LAUFER, J. 1972 Recent developments in turbulent boundary layer

research. In

Istituto Nazionale di Alta Matematica, Symposia Mathematica

, 299–313.

LI, J.D. and PERRY, A.E. 1989 Shear stress profiles in zero-pressure-

gradient turbulent boundary layers. In

Proc. Tenth Australasian Fluid Me-

chanics Conference

, Univ. Melbourne, Vol. 1, 7.9–7.12.

Corner in profile.

LIN, C.-L., McWILLIAMS, J.C., MOENG, C.-H., and SULLIVAN, P.P.

1996 Coherent structures and dynamics in a neutrally stratified planetary

boundary layer flow. Phys. Fluids

, 2626–2639.

LUND, T.S. 1993 Large eddy simulation of a boundary layer with

concave streamwise curvature. Center for Turbulence Research, NASA

Ames Research Center and Stanford University, Annual Research Briefs–

1993, 91–99.

LUO, J. and LAKSHMINARAYANA, B. 1997 Analysis of streamline

curvature effects on wall-bounded turbulent flows. AIAA J.

, 1273–1279.

MATHEWS, D.C. and CHILDS, M.E. 1970 Use of Coles’ universal

wake function for compressible turbulent boundary layers. J. Aircraft

137–140.

MOHR, E. 1939 Die laminare Str ̈omung l ̈angs der Platte und damit

verwandte Fl ̈ussigkeitsbewegungen. Deutsche Mathematik

, 477–513.

Ref

141

in Nikuradse, laminar boundary layer, 1942.

MOIN, P. and SPALART, P.R. 1987 Contributions of numerical sim-

ulation data bases to the physics, modeling, and measurement of turbulence.

NASA Tech. Memo. 100022.

NAGAOSA, R. 1999 Direct numerical simulation of vortex structures

and turbulent scalar transfer across a free surface in a fully developed tur-

bulence. Phys. Fluids

, 1581–1595.

Intriguing paper.

NARASIMHA, R. 1993 The statistical dynamics of turbulence. Na-

tional Aeronautical Laboratory, Bangalore, Project Document DU 9301.

NARASIMHA, R. 1995 Turbulence: waves or events? Current Sci-

ence

, 33–38.

NARASIMHA, R. 1996 Different approaches to asymptotic expan-

sions in turbulent boundary layers. In

Proc. IUTAM Symposium on Asymp-

totic Methods for Turbulent Shear Flows at High Reynolds Numbers

(K.

Gersten, ed.), Kluwer, 5–16.

OBERLACK, M. 1996 Symmetries in turbulent boundary layer flows.

Annual Research Briefs 1996,

Center for Turbulence Research, NASA

Ames Research Center and Stanford Univ., 183–197.

ORLANDI, P. and JIMENEZ, J. 1994 On the generation of turbulent

wall friction. Phys. Fluids

, 634–641.

PAN, Y. and BANERJEE, S. 1995 A numerical study of free-surface

turbulence in channel flow. Phys. Fluids

, 1649–1664.

PANTON, R.L. 1990 Scaling turbulent wall layers. Trans. ASME

(J. Fluids Eng.)

112

, 425–432.

PANTON, R.L. 1991 The effects of Reynolds number on turbulent

wall layers. In

Preprints, Eighth Symposium on Turbulent Shear Flows

Vol. 2, Technical University of Munich, Paper I-15.

PATEL, V.C. 1973 A unified view of the law of the wall using mixing-

length theory. Aeron. Quart.

, 55–70.

Axisymmetric body. Mixing length

near wall*, figure 2. Velocity*, figures 3, 4, 6.

PEROT, B. and MOIN, P. 1995 Shear-free turbulent boundary lay-

ers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech.

295

, 199–227.

PEROT, B. and MOIN, P. 1995 Shear-free turbulent boundary lay-

ers. Part 2. New concepts for Reynolds stress transport equation modelling

of inhomogeneous flows. J. Fluid Mech.

295

, 229–245.

PERRY, A.E. 1992 A new look at some closure problems of turbulent

boundary layers. California Institute of Technology, GALCIT Rep. No. 92–

142

PERRY, A.E., LI, J.D., and MARUSIC, I. 1988 Novel methods of

modeling wall turbulence. AIAA Paper 88-0219.

PERRY, A.E., MARUSIC, I., and LI, J.D. 1994 Wall turbulence clo-

sure based on classical similarity laws and the attached eddy hypothesis.

Phys. Fluids

, No. 2, Part 2, 1024–1035.

PHILLIPS, W.R.C. and Ratnanather, J.T. 1990 The outer region of

a turbulent boundary layer. Phys. Fluids

, 427–434.

PLATE, E.J. 1971 Aerodynamic characteristics of atmospheric bound-

ary layers. AEC Critical Review Series, U.S. Atomic Energy Commission.

ROBINSON, S.K. 1989 A review of vortex structures and associated

coherent motions in turbulent boundary layers. In

Structure of Turbulence

and Drag Reduction

(A. Gyr, ed.), Springer-Verlag, 23–50.

ROBINSON, S.K., KLINE, S.J., and SPALART, P.R. 1988 Quasi-

coherent structures in the turbulent boundary layer. Part II. Verification

and new information from a numerically simulated flat-plate layer. In

Near-

wall Turbulence

, 1988 Zoran Zaric Memorial Conference (S.J. Kline and N.H.

Afgan, eds.), Hemisphere, 218–247.

ROTTA, J. 1950

Uber die Theorie der turbulenten Grenzschichten.

Mitt. Max-Planck-Institut f ̈ur Str ̈omungsforschung, Nr. 1.

This is NACA

TM 1344. Ing.-Arch. version, 1951, is DTMB Translation No. 242. Defect

variables*, figure 1, equation 6.1. Wall law*, figure 2. Hot-wire data*,

figures 5, 6.

ROTTA, J. 1950 Das in Wandn ̈ahe g ̈ultige Geschwindigkeitsgesetz

turbulenter Str ̈omungen. Ing.-Arch.

, 277–280.

Roughness.

SAVILL, A.M. 1989 Drag reduction by passive devices—a review of

some recent developments. In

Structure of Turbulence and Drag Reduction

(A. Gyr, ed.), Springer-Verlag, 429–465.

SCHLICHTING, H. 1974 Recent progress in boundary-layer research.

AIAA J.

, 427–440.

SHIMA, N., KAWAI, T., OKAMOTO, M., and TSUCHIKARA, R.

1999 Prediction of streamline curvature effects on wall-bounded turbulent

flows. In

Preprints, Turbulence and Shear Flow Phenomena—1

(S. Banerjee

and J.K. Eaton, eds.), Begell House, 221–226.

SMITH, C.R. and WALKER, J.D.A. 1995 Turbulent wall-layer vor-

tices. In

Fluid Vortices

(S.I. Green, ed.), Kluwer, 235–290.

SMITS, A.J. 1990 New developments in understanding supersonic tur-

bulent boundary layers. In

Preprints, Twelfth Turbulence Symposium,

Univ.

Missouri (Rolla), Paper IL4.

SMITS, A.J. and WOOD, D.H. 1985 The response of turbulent bound-

ary layers to sudden perturbations. Ann. Rev. Fluid Mech.

, 321–358.

143

SO, R.M.C., ZHANG, H.S., GATSKI, T.B., and SPEZIALE, C.G. 1994

Logarithmic laws for compressible turbulent boundary layers. AIAA J.

2162–2168.

SPALART, P.J. 1988 Direct simulation of a turbulent layer up to

= 1410. J. Fluid Mech.

187

, 61–98; also NASA Tech. Memo. 89407,

1986.

Mean velocity*, figures 5, 8. Reynolds stresses*, figures 7, 9, 10, 12,

13. Some data tabulated.

Jimenez collection No. 33.

AGARD TBL01.

SREENIVASAN, K.R. 1988 A unified view of the origin and morphol-

ogy of the turbulent boundary layer structure. In

Turbulence Management

and Relaminarisation

(H.W. Liepmann and R. Narasimha, eds.), Springer-

Verlag, 37–61.

Peak stress*, figure 4. Streak spacing*, figure 10.

SREENIVASAN, K.R. 1989 The turbulent boundary layer. In

Fron-

tiers in Experimental Fluid Mechanics

(M.Gad-el-Hak, ed.), Lecture Notes

in Engineering No. 46, Springer-Verlag, 159–209.

Shearing stress*, figure 4.

Spectrum*, figure 14. Peak intensity*, figure 16. Sublayer streaks*, figure

24.

SUKSANGPANOMRUNG, A., DJILALI, N., and MOINAT, P. 1999

Large eddy simulation of separated flow over a bluff plate. In

Preprints,

Turbulence and Shear Flow Phenomena—1

(S. Banerjee and J.K. Eaton,

eds.), Begell House, 1033–1037.

Geometry*, figure 1. Streamline*, figure 2.

Pressure*, figure 3. Velocity*, figure 4.

TAFTI, D.K. and VANKA, S.P. 1991 A numerical study of flow sep-

aration and reattachment on a blunt plate. Phys. Fluids

, 1749–1759.

TAYLOR, G.I. 1932 Note on the distribution of turbulent velocities

in a fluid near a solid wall. Proc. Roy. Soc.

A135

, 678–684, or

The Scientific

Papers of G.I. Taylor

(G.K. Batchelor, ed.), Vol. II, Cambridge Univ. Press,

247–252, 1960.

Argument using eigenfunctions in circular Couette flow to

explain observations by Fage and Townsend. Fluctuations*, figure 2.

TENNEKES, H. 1974 The atmospheric boundary layer. Physics To-

day

TULLIS, S. and POLLARD, A. 1993 A numerical investigation of the

turbulent flow over V and U groove riblets using a viscous wall region model.

Near-Wall Turbulent Flows

(R.M.C. So, C.G. Speziale, and B.E. Launder,

eds.), Elsevier, 761–770.

VAN DYKE, M. 1969 Higher-order boundary-layer theory. Ann. Rev.

Fluid Mech.

, 265–292.

VOKE, P.R., YANG, Z., and SAVILL, A.M. 1996 Large-eddy simu-

lation and modelling of transition following a leading-edge separation bub-

ble. In

Engineering Turbulence Modelling and Experiments 3

(W. Rode and

G. Bergeles, eds.), Elsevier, 601–610.

144

WALKER, D.T., LEIGHTON, R.I., and GARZA-RIOS, L.O. 1996

Shear-free turbulence near a flat free surface. J. Fluid Mech.

320

, 19–51.

WEIGAND, G.G. and WALKER, J.D.A. 1979 A prediction method

for velocity and temperature profiles in a two-dimensional nominally steady

turbulent boundary layer. In

Turbulent Boundary Layers, Forced, Incom-

pressible, Non-reacting

(H.E. Weber, ed.), ASME, 221–235.

WIEGHARDT, K. 1973

Uber den Reibungswiderstand der Platte.

Institute f ̈ur Schiffbau, Univ. Hamburg, Bericht Nr. 291.

WINCKELMANS, G.S. 1995 Some progress in large-eddy simulation

using the 3-D vortex particle method. In

Annual Research Briefs—1995

Center for Turbulence Research, NASA Ames Research Center and Stanford

University, 391–415.

WYGNANSKI, I. 1997 Boundary layer and flow control by periodic

addition of momentum. AIAA Paper 97–2117.

ZAGAROLA, M.V. and SMITS, A.J. 1998 A new mean velocity scal-

ing for turbulent boundary layers. In

Proc. FEDSM’98 1998 ASME Fluids

Engineering Division Summer Meeting,

ASME, Paper FESDM98-4950.

Experimental data

ACARLAR, M.S. and SMITH, C.R. 1984 An experimental study of

hairpin-type vortices as a potential flow structure of turbulent boundary

layers. Dept. Mech. Eng. and Mechanics, Lehigh Univ., Rep. FM-5.

Probably thesis by Acarlar. Mean velocity*, figures 3.36a, 3.37.

AJAGU, C.O. 1984 Surface shear stress characteristics in turbulent

flows. Ph. D. thesis, Aerosp. Sci., Univ. California (San Diego).

Friction

coefficient*, figures 3-6. Moments of pdf for wall shear.

ALFREDSSON, P.H., JOHANSSON, A.V., HARITONIDIS, J.H., and

ECKELMANN, H. 1988 The fluctuating wall-shear stress and the veloc-

ity field in the viscous sublayer. Phys. Fluids

, 1026–1033.

Mean velocity,

figure 2. Reynolds stresses*, figure 2. Tau-u correlation, figure 3.

ALVING, A.E. and SMITS, A.J. 1986 The recovery of a turbulent

boundary layer from longitudinal curvature. AIAA Paper 86-0435.

Geome-

try*, figure 1. Relaxation*, figures 6–11.

ALVING, A.E., WATMUFF, J.H., and SMITS, A.J. 1987 The relax-

ation of a turbulent boundary layer far downstream of a short region of

convex curvature. AIAA Paper 87-0196.

ALVING, A.E., SMITS, A.J., and WATMUFF, J.H. 1990 Turbulent

boundary layer relaxation from convex curvature. J. Fluid Mech.

211

, 529–

556.

Jimenez collection No. 22

. Geometry*, figure 2. Pressure*, figures

145

3, 5. Friction*, figures 4, 6. Velocity*, figure 7. Reynolds stresses*, figures

9–13.

ANDERS, J.B. and WATSON, R.D. 1985 Airfoil large-eddy breakup

devices for turbulent drag reduction. AIAA Paper 85-0520. Also private

communication.

Friction coefficient*, figure 5, implies profiles.

ANDERS, J.B., HEFNER, J.N., and BUSHNELL, D.M. 1984 Perfor-

mance of large-eddy breakup devices at post-transitional Reynolds numbers.

AIAA Paper 84-0345.

Friction coefficient*, figure 5.

ANDREOPOULOS, J., DURST, F., and JOVANOVIC, J. 1984 On

the structure of turbulent boundary layers at different Reynolds numbers. In

Preprints, Fourth Symposium on Turbulent Shear Flows

, Karlsruhe, 2.1–2.7.

Reynolds stresses*, figure 5.

ANDREOPOULOS, J., DURST, F., ZARIC, Z., and JOVANOVIC, J.

1984 Influence of Reynolds number on characteristics of turbulent wall

boundary layers. Exp. Fluids

, 7–16.

Mean velocity*, figure 1. Reynolds

stresses, figure 2. Probability density of

′

ARIE, M. and ROUSE, H. 1956 Experiments on two-dimensional flow

over a normal wall. J. Fluid Mech.

, 129–141.

Cavity flow with splitter

plate in uniform duct; profiles of mean velocity and turbulence intensity.

Mean velocity*, figure 8. Reynolds stresses*, figure 8. Static pressure*,

figure 8. See MS thesis by ARIE at Iowa State.

ARIK, B.E. 1986 Study of boundary layer structure using laser Dop-

pler velocimetry, conditional sampling, and polymer additives. Ph. D. thesis,

Div. Applied Sciences, Harvard Univ.

Student of Abernathy. Free-surface

water table. Velocity*, figures 2.14, 2.15.

ARONSON, D., JOHANSSON, A.V., and LOFDAHL, L. 1997 Shear-

free turbulence near a wall. J. Fluid Mech.

338

, 363–385.

Geometry*, figure

1. Turbulence decay*, figures 4, 5. Reynolds stresses*, figures 9, 10, 12.

ASHKENAS 1960 Some tabulated data, but thesis is missing.

ASHKENAS, H. and RIDDELL, F.R. 1955 Investigation of the tur-

bulent boundary layer on a yawed flat plate. NACA TN 3383.

Unyawed,

mean velocity, figures 17, 18. Growth rate, figures 19–22.

ASHKENAS, H.I., RIDDELL, F.R., and ROTT, N. 1952 An inves-

tigation of the turbulent boundary layer on a flat plate. Graduate School

Aeron. Eng., Cornell Univ., Contract Rep. NAw-6014.

Mean velocity*, fig-

ures 12, 13, 16–23. Growth rate, figures 14, 15. Reynolds stresses*, figures

16–23.

ATLI, V. 1988 Subsonic flow over a two-dimensional obstacle im-

mersed in a turbulent boundary layer on a flat surface. J. Wind Eng. Ind.

Aerodyn.

, 225–239.

Geometry*, figure 5. Velocity*, figures 7, 8.

146

BADRI NARAYANAN, M.A. and MARVIN, J.G. 1978 On the pe-

riod of the coherent structure in boundary layers at large Reynolds num-

bers. In

Coherent Structure of Turbulent Boundary Layers

(C.R. Smith and

D.E. Abbott, eds.), Lehigh Univ., 380–385 (also NASA Tech. Memo. 78477,

1978).

Mean velocity*, figure 3. Friction coefficient*, figure 4, table 1.

BALINT, J.-L., VUKOSLAVCEVIC, P., and WALLACE, J.M. 1987

A study of the vortical structure of the turbulent boundary layer. In

Ad-

vances in Turbulence

(G. Comte-Bellot and J. Mathieu, eds.), Springer-

Verlag, 456–464.

See JFM.

BALINT, J.-L., WALLACE, J.M., and VUKOSLAVCEVIC, P. 1991

The velocity and vorticity vector fields of a turbulent boundary layer. Part 2.

Statistical properties. J. Fluid Mech.

228

, 53–86.

Velocity*, figure 1.

Reynolds stresses*, figure 2. Moments of pdf for velocity, vorticity. En-

ergy balance.

BARLOW, R.S. and JOHNSTON, J.P. 1988 Structure of a turbulent

boundary layer on a concave surface. J. Fluid Mech.

191

, 137–176.

Ge-

ometry*, figure 2. Velocity*, figure 14. Reynolds stresses*, figures 19, 21.

AGARD TBL30.

BECHERT, D.W., BRUSE, M., HAGE, W., van der HOEVEN, J.G.T.,

AND HOPPE, G. 1997 Experiments on drag-reducing surfaces and their

optimization with an adjustable geometry. J. Fluid Mech.

338

, 59–87.

Geometry*, figure 24. Drag reduction*, figures 8, 9, 12, 14, 18, 20.

BELL 1966

BERTELRUD, A. 1977 Flow disturbances associated with Preston

tubes in turbulent boundary layers. FFA (Sweden) Rep. 127.

Preston tube

in pipe flow. Some hot-wire profiles of mean velocity. Useful details, includ-

ing oil flow viz, for flow around Preston tube. Main issue is measurement

of static pressure. Mean velocity*, figure 7. Reynolds stresses*, figure 8.

Pressure disturbance.

BLACKWELDER, R.F. and ECKELMANN, H. 1979 Streamwise vor-

tices associated with the bursting phenomenon. J. Fluid Mech.

, 577–594.

Preliminary version (same authors) is The spanwise structure of the bursting

phenomenon, in

Structure and Mechanisms of Turbulence I

, Lecture Notes

in Physics No. 75, Springer-Verlag, 190–204, 1977.

Eckelmann’s channel.

Several pairs of hot films in

configuration on wall, with

and

−

probes at

= 15

(problem with interference; were some of these data repu-

diated at Lehigh?). Careful analysis of data. Relevant for sublayer model.

Data support model of counter-rotating vortices.

BLACKWELDER, R. and KAPLAN, R. 1976 On the wall structure

of the turbulent boundary layer. J. Fluid Mech.

, 89–112, 1 plate; early

147

version is Intermittent structure in turbulent boundary layers, in

Turbulent

Shear Flows

, AGARD CP 93, 1971, Paper 5 (same authors).

Condition is

high

-fluctuation level at

= 15

. Low coherence in spanwise direction.

Conditioned profiles of mean velocity. Momentum excess outside sublayer.

Large double peak in

′

. Independence of threshold value*, figure 16.

BLACKWELDER, R.F. and HARITONIDIS, J.H. 1983 Scaling of

the bursting frequency in turbulent boundary layers. J. Fluid Mech.

132

87–103.

Mean velocity*, figure 2. Reynolds stresses*, figure 3.

BRADSHAW, P. 1967 Irrotational fluctuations near a turbulent bound-

ary layer. J. Fluid Mech.

, 209–230.

Fluctuation level*, figures 1, 2.

BRADSHAW, P. and FERRISS, D.H. 1967 The effect of initial con-

ditions on the development of turbulent boundary layers. National Physical

Laboratory, NPL Aero. Rep. 1223.

Relaxation*, figures 2, 6.

BROWN, G.L. and THOMAS, A.S.W. 1977 Large structure in a tur-

bulent boundary layer. Phys. Fluids

, No. 10, Part II, S243–S251.

Cor-

relations.

BROWNE, L.W.B.. CHAN, W.K., and ANTONIA, R.A. 1986 A

thick viscous sublayer test facility. In

Proc. Ninth Australasian Fluid Me-

chanics Conference

, Auckland, 524–528.

Velocity*, figure 5, Reynolds stresses*,

figure 6.

BRUSE, M., BECHERT, D.W., van der HOEVEN, J.G.T., HAGE, W.

and HOPPE, G. 1993 Experiments with conventional and with novel ad-

justable drag-reducing surfaces. In

Near-Wall Turbulent Flows

(R.M.C. So,

C.G. Speziale, and B.E. Launder, eds.), Elsevier, 719–738.

BULL, M.K. 1967 Wall-pressure fluctuations associated with subsonic

turbulent boundary layer flow. J. Fluid Mech.

, 719–754 (see also BULL,

M.K., WILBY, J.F., and BLACKMAN, D.R., Wall pressure fluctuations in

boundary layer flow and response of simple structures to random pressure

fields, Dept. Aeron. Astron., Univ. Southampton, A.A.S.U. Rep. No. 243,

1963).

Mean velocity*, figures 5, 6, 13, 14. Friction coefficient*, figure 15.

Reynolds stresses*, figure 17. Space-time correlations for wall pressure.

BUTLER, S.F.J., MOY, B.A., and POUND, T.N. 1967 A moving-

belt rig for ground simulation in low-speed wind tunnels. Aeron. Research

Council, Great Britain, R&M No. 3451.

Mean velocity*, figures 4–7.

CARDOSO, A.H., GRAF, W.H., and GUST, G. 1989 Uniform flow

in a smooth open channel. J. Hydraulic Research

, 603–616.

Velocity*,

figures 2, 3.

CHAMBERS, F.W. 1982 Preliminary measurements of a synthetic

turbulent boundary layer. Lockheed-Georgia Co., Rep. LG82RR0009.

Mean

velocity*, figures 6a, 7a, 8a, 9a, 12, 15. Growth rate, figure 17. Friction

148

coefficient, figures 22, 23.

CHAMBERS, F.W. 1985 Synthetically generated turbulent bound-

ary layer development and structure. AIAA J.

, 1987–1993.

Mean veloc-

ity*, figures 5, 6, 11. Growth rate*, figure 7. Friction coefficient*, figures

8, 10. Reynolds stresses*, figure 11.

CHANG, S.-I. and BLACKWELDER, R.F. 1990 Modification of large

eddies in turbulent boundary layers. J. Fluid Mech.

213

, 419–442.

Mean

velocity*, figure 2. Reynolds stresses*, figures 4, 5, 8. See thesis by CHANG.

CHARNAY, G., MATHIEU, J., and COMTE-BELLOT, G. 1976 Re-

sponse of a turbulent boundary layer to random fluctuations in the external

stream. Phys. Fluids

, 1261–1272.

Reynolds stresses*, figure 2. Inter-

mittency*, figure 12. Energy balance.

CHEN, C.-H.P. and BLACKWELDER, R.F. 1978 Large-scale mo-

tion in a turbulent boundary layer: a study using temperature contamina-

tion. J. Fluid Mech.

, 1–31 (see also Ph.D. thesis by CHEN, same title,

Dept. Aerosp. Eng., Univ. Southern California, 1975).

Mean velocity*,

figures 3, 4. RMS temperature*, figure 4. Intermittency*, figure 8.

CHEUNG, T.K. and KOSEFF, J.R. 1983 Simultaneous backward-

scatter forward-scatter laser Doppler anemometer measurements in an open

channel flow. DISA Information, No. 28, 3–9.

Mean velocity*, figure 4.

Reynolds stresses*, figure 5.

CHIWANGA, S.C. and RAMAPRIAN, B.R. 1993 The effect of con-

vex wall curvature on the large-scale structure of the turbulent boundary

layer. Experimental Thermal and Fluid Science

, 168–176.

CHOI, H. and MOIN, P. 1990 On the space-time characteristics of

wall-pressure fluctuations. Phys. Fluids

, 1450–1460.

Space-time pres-

sure correlation, figure 10. Celerity*, figures 15–19.

CHOI, K.-S. 1988 The wall-pressure fluctuations of modified turbu-

lent boundary layer with riblets. In

Turbulence Management and Relaminar-

isation

(H.W. Liepmann and R. Narasimha, eds.), Springer-Verlag, 149–160.

Mean velocity*, figures 1, 2. Reynolds stresses*, figure 1.

CHOI, K.-S. 1989 Drag reduction mechanisms and near-wall turbu-

lence structure with riblets. In

Structure of Turbulence and Drag Reduction

(A. Gyr, ed.), Springer-Verlag, 553–560.

CORKE, T.C. 1981 A new view on origin, role and manipulation of

large scales in turbulent boundary layers. Ph. D. thesis, Dept. Mech. and

Aerosp. Eng., Illinois Institute of Technology.

Mean velocity*, figures 29,

30, 36, 37. Reynolds stresses*, figures 31, 32, 38, 39. Friction coefficient*,

figure 35. No tables.

CORKE, T.C., GUEZENNEC, Y., and NAGIB, H.M. 1980 Modifi-

149

cation in drag of turbulent boundary layers resulting from manipulation of

large-scale structures. In

Viscous Flow Drag Reduction

(G.R. Hough, ed.),

Prog. Astron. Aeron.

, 128–143.

Mean velocity*, figures 4, 6; see also

figure 10. Reynolds stresses*, figure 4.

COUGHRAN, M.T. 1988 Interdependence of large and small scale

structures in a turbulent boundary layer. Ph. D. thesis, Dept. Mech. Eng.,

Univ. Texas (Austin).

Student of Bogard. Friction*, figure 3.2. Velocity*,

figures 3.3–3.5. Reynolds stress*, figure 3.6. Wake strength*, figure 3.8.

COUSTOLS, E. and COUSTEIX, J. 1986 Reduction of turbulent

skin friction: turbulence moderators. La Recherche A ́erospatiale (English

edition), No. 2, 63–78.

Mean velocity*, figures 19, 20. Reynolds stresses*,

figures 20–24.

COUSTOLS, E., TENAUD, C., and COUSTEIX, J. 1989 Manipula-

tion of turbulent boundary layers in zero-pressure gradient flows: detailed

experiments and modelling. In

Turbulent Shear Flows 6

(J.-C. Andr ́e et al.,

eds.), Springer-Verlag, 164–178.

Reynolds stresses*, figures 3, 4, 5.

de BRAY, B.G. 1969 Some investigations into the spanwise non-uni-

formity of nominally two-dimensional incompressible boundary layers down-

stream of gauze screens.Aeron. Res. Council, R&M 3578.

Argument about

vorticity generation at wire screen. Otherwise only spanwise traverses. Mean

velocity*, figure 9. Intermittency*, figure 9. Lack of two-dimensionality*,

figure 9.

de JONCKHEERE, R.K., CHOU, D.C., WALKER, J., and MILLER,

D.J. 1988 Large-scale turbulence structuring in high Reynolds number

flows. In

Preprints, AIAA/ASME/ SIAM/APS First National Fluid Dy-

namics Congress

, AIAA, Part 1, 368–375 (AIAA Paper 88–3671).

DEGRAAF, D.B. and EATON, J.K. 1999 Reynolds number scaling

of the turbulent boundary layer on a flat plate and on swept and unswept

bumps. Dept. Mech. Eng., Stanford Univ., Rep. No. TSD-118.

Mean

velocity*, figures 4.2–4.4. Wake*, figure 4.6. Reynolds stresses*, figures

4.11–4.26. Bump geometry*, figure 5.2. Flow*, figure 5.7. HW no. LDA*,

figures A.2–A.4.

DHAWAN, S. 1951 Direct measurements of skin friction. Ph.D. The-

sis, California Institute of Technology.

Mean velocity*, figure 12.

DINKELACKER, A., HESSEL, M., MEIER, G.E.A., and SCHEWE, G.

1977 Investigation of pressure fluctuations beneath a turbulent boundary

layer by means of an optical method. Phys. Fluids

, No. 10, Part II, S216–

S224; (see also “Further results on wall pressure fluctuations in turbulent

flow,” same authors, in

Proc. 3rd U.S.-F.R.G. Hydroacoustics Symp

., Vol.

3, 29–38, 1975).

Mean velocity*, figures 5, 6. Reynolds stress*, figure 7.

150

DJENIDI, L. and ANTONIA, R.A. 1993 LDA measurements in low

Reynolds number turbulent boundary layer. Experiments in Fluids

, 280–

288.

DJENIDI, L. and ANTONIA, R.A. 1993 LDA Measurement in a low

Reynolds number turbulent boundary layer. Erratum. Exp. in Fluids

368.

Figures were wrong. Velocity*, figures 1, 2. Shearing stress*, figure 3.

DJILALI, N., GARTSHORE, I.S., and SALCUDEAN, M. 1987 An

experimental and numerical study of the flow around a blunt rectangular

section: a test case for computational methods? In

Preprints, Sixth Sym-

posium on Turbulent Shear Flows

, Toulouse, Paper 19.3.

Mean velocity*,

figure 3. Reynolds stresses*, figure 4. Surface pressure, figure 5.

DUCOFFE, A.L. 1957 I. A report on the final calibration of the low

turbulence wind tunnel including dynamic pressure and angularity surveys

and free tunnel turbulence measurements. II. Turbulence studies behind

square mesh grids. III. Boundary-layer velocity profiles and turbulence stud-

ies on a flat plate in the presence of a zero longitudinal pressure gradient.

Eng. Exp. Sta., Georgia Inst. Tech., Project No. 219 (Contract NOnr-

991(01)).

Mean velocity*, figures 10, 11, 12. Reynolds stress*, figure 14.

DURST, F., JOVANOVIC, J., and KANEVCE, L. 1987 Probability

density distribution in turbulent wall boundary-layer flows. In

Turbulent

Shear Flows 5

(F. Durst et al., eds.), Springer-Verlag, 197–220.

Mean ve-

locity*, figure 2. Reynolds stresses*, figure 3.

DUTTON, R.A. 1957 The accuracy of measurement of turbulent skin

friction by means of surface pitot-tubes and the distribution of skin friction

on a flat plate. Aeron. Res. Council, R&M 3058.

Effect of various trips

using Preston tube. Friction coefficient*, figures 4, 8, 9, 10. No profiles.

Comments on fluctuation terms in Karman momentum-integral equation.

Growth rate*, figures 6, 7

DUTTON, R.A. 1959 The velocity distribution in a turbulent bound-

ary layer on a flat plate. Great Britain, Aeron. Res. Council, CP 453.

Mean

velocity*, figures 6, 7, 8.

ELATA, C. 1961 The dynamics of open channel flow with suspensions

of neutrally buoyant particles. Sc. D. thesis, Civil and Sanitary Eng., MIT.

Friction, figures 16, 17. Mean velocity*, figures 18–20. No tables.

ELENA, M. and LACHARME, J.-P. 1988 Experimental study of a

supersonic turbulent boundary layer using a laser Doppler anemometer.

Journal de Mecanique Theorique et Appliquee

, 175–190.

Velocity*, figure

3. Intermittency*, figure 12.

ELFSTROM, G.M. 1984 An experimental investigation of subsonic

turbulent boundary-layer flow over a wide Reynolds number range up to

151

140 million. Part 1. Flat plate zero pressure gradient. Nat’l. Res. Council,

Canada, Nat’l. Aeron. Estab., Lab. Tech. Rep. LTR-HA-5 x 5/0146.

Compressible but subsonic. Friction coefficient*, figure 28, tables 5, 6. Mean

velocity*, figures 25-27, 34, table 4

EMMERLING, R., MEIER, G.E.A., and DINKELACKER, A. 1973

Investigation of the instantaneous structure of the wall pressure under a tur-

bulent boundary layer flow. In

Noise Mechanisms

, AGARD Conference Pro-

ceedings CP-131, Paper 24.

Mean velocity*, figures 3, 5. Reynolds stress*,

figure 4. See also Dinkelacker, et al.

ERIKSEN, S., SAKBANI, K., and WITTIG, S.L.K. 1984 Laser-Dop-

pler and laser-dual-focus measurements in laminar and fully turbulent bound-

ary layers. In

Heat and Mass Transfer in Rotating Machinery

(D.E. Metzger

and N.H. Afgan, eds.), Hemisphere, 281–292.

Mean velocity*, figures 6, 7,

8. Reynolds stresses*, figure 9.

ERM, L.P. 1988 Low-Reynolds-number turbulent boundary layers.

Ph. D. thesis, Dept. Mech. and Manuf. Eng., Univ. Melbourne.

Mean

velocity, figures 5.2–5.6, 5.10–5.11, 6.1. Reynolds stresses*, figures 6.2, 6.4-

6.22. Energy balance. No tables.

ERM, L.P. and JOUBERT, P.N. 1991 Low-Reynolds-number turbu-

lent boundary layers. J. Fluid Mech.

230

, 1–44.

Velocity*, figures 5, 6, 7,

others. Reynolds stresses, figures 14, 15, 16. Letter to Joubert, 30 August

1993. Cite thesis from p 28.

ERM, L.P. and JOUBERT, P.N. 1992 Turbulent boundary layers at

low Reynolds numbers. In

Proc. 11th Australasian Fluid Mechanics Confer-

ence

, Vol. 2, Univ. Tasmania, 837–840.

Erm versus Spalart. Wake strength*,

figure 1. Reynolds stresses, figure 6.

ERM, L.P., SMITS, A.J., and JOUBERT, P.N. 1987 Low Reynolds

number turbulent boundary layers on a smooth flate surface in a zero pres-

sure gradient. In

Turbulent Shear Flows 5

, (F. Durst et al., eds.), Springer-

Verlag, 186–196.

Mean velocity*, figure 2. Reynolds stresses*, figures 3, 4,

5, 6.

FAVRE, A. 1958 Quelques r ́esultats d’exp ́eriences sur la turbulence

corr ́elations spatio-temporelles spectres. In

S ́eminaire d’A ́erothermique de

la Facult ́e des Sciences de Paris

, Notes Techniques du Minist`ere de l’Air,

No. 73, 15-54.

Space-time correlations*, figures 6a, 6b, 7, 8.

FAVRE, A.J. 1965 Review on space-time correlations in turbulent flu-

ids. Trans. ASME (J. Appl. Mech.

32E

), 241–257.

Space-time correlation*,

figures 1–3, 5.

FAVRE, A. and GAVIGLIO, J. 1960 Turbulence et perturbations dans

la couche limite d’une plaque plane. Groupe Consultatif pour la Recherche

152

et la Realisation Aeronautiques, Rep. 278, for AGARD Boundary Layer

Research Meeting, London.

Reynolds stresses*, figures 2, 23, 25. Lack of

two-dimensionality*, figures 11, 13, 16, 17. Space-time correlations.

FAVRE, A., GAVIGLIO, J., and DUMAS, R. 1955 Couche limite tur-

bulente: Correlations spatio-temporelles doubles, spectres. La Rech. Aero-

nautique, No. 48, 3–14.

Preliminary to JFM.

FAVRE, A.J., GAVIGLIO, J.J., and DUMAS, R. 1957 Space-time

double correlations and spectra in a turbulent boundary layer. J. Fluid

Mech.

, 313-342.

Give profile data. Tunnel now closed circuit. Stream

turbulence 0.0004. Mostly data for boundary layer with external grid tur-

bulence. No cross-flow separation of probes. Mean velocity*, figures 2, 3.

Space-time corrrelations.

FAVRE, A.J., GAVIGLIO, J.J., and DUMAS, R.J. 1957 Further space-

time correlations of velocity in a turbulent boundary layer. J. Fluid Mech.

, 344–356..

FAVRE, A., GAVIGLIO, J., and DUMAS, R. 1958 Couche limite tur-

bulente: corr ́elations spatio-temporelles et spectres de vitesses. ONERA,

Pub. No. 92.

Mean velocity, figures p. 36–39.

FAVRE, A., GAVIGLIO, J., and DUMAS, R. 1962 Correlations spatio-

temporelles en ecoulements turbulents. In

Mecanique de la Turbulence

CNRS, Paris, 419–445.

Time-space correlations*, figures 1, 3, 4, 5.

FAVRE, A., GAVIGLIO, J. and DUMAS, R. 1967 Structure of ve-

locity space-time correlations in a boundary layer. Phys. Fluids

(Kyoto

Suppl.), S138–S145.

Good on celerity. Data filtered, probe separation normal

to wall. Celerity*, figure 7.

FERNHOLZ, H. 1964 Three-dimensional disturbances in a two-dimen-

sional incompressible turbulent boundary layer. Aeronautical Research Coun-

cil, R&M 3368.

3-D effect*, figures 1–7, 9, 10. Flow viz, figures 11–13.

FERNHOLZ, H.H., KRAUSE, E., NOCKEMANN, M., and SCHOBER,

M. 1995 Comparative measurements in the canonical boundary layer at

≤

on the wall of the German-Dutch windtunnel. Phys. Fluids

, 1275–1281.

Friction*, figure 1. Mean velocity*, figure 2.

FINLEY, P.J., KHOO, C.P., and CHIN, J.P. 1966 Velocity measure-

ments in a thin turbulent water layer. La Houille Blanche

, 713–720.

Profiles of mean velocity. Layer reaches free surface? Wake component

smaller than normal. Polynomial for corner in wake function, but

wrong.

FOMINA, N.N. and BUCHINSKAYA, E.K. 1938 Eksperimental’noe

issledovanie dvukhmernogo pogranichnogo sloia. Trudy TsAGI, no. 374.

Mean velocity*, figures 22a, 22b.

FONTAINE, A.A., PETRIE, H.L., and BRUNGART, T.A. 1990 Mod-

153

ification to a turbulent boundary layer due to slot injected drag reducing

polymer solutions. In

Forum on Turbulent Flows—1990

(W.M. Bower et al.,

eds.), ASME, 43–49.

Velocity*, figures 1, 2. Reynolds stresses*, figures 4,

FONTAINE, A.A., PETRIE, H.L., and BRUNGART, T.A. 1992 Ve-

locity profile statistics in a turbulent boundary layer with slot-injected poly-

mer. J. Fluid Mech.

238

, 435–466.

FOSS, J.F., BOHL, D.G., BRAMKAMP, F.D., and KLEWICKI, J.G.

1994 Transverse vorticity measurements in the NASA Ames 80x120 wind

tunnel boundary layer. Center for Turbulence Research, NASA Ames Re-

search Center and Stanford University, Annual Research Briefs–1994, 263–

268.

FRASER, C.J. 1986 The assessment of boundary layer two-dimension-

ality. Aeron. J.

, 41–48.

Boundary layer profiles* implied but not re-

ported. Uneven spanwise variation* of

. Momentum balance, figures 2,

FRASER, C.J. and MILNE, J.S. 1980 Boundary layer development

from transition provoking devices. Int. J. Heat Fluid Flow

, 165–173.

Zero

pressure gradient. Trip wire or wedges from two isolated spheres. Skimpy

profiles of intermittency, mean velocity, turbulence intensity. Thesis by

Fraser, Dundee, 1979. Faired mean velocity and intermittency.

FULACHIER, L., ARZOUMANIAN, E., AND DUMAS, R. 1977 Ex-

perimental investigation of a turbulent field from temperature fluctuations.

Structure and Mechanisms of Turbulence II

, Lecture Notes in Physics

No. 76 (H. Fiedler, ed.), Springer-Verlag, 46–57.

Intermittency in boundary

layer. Intermittency, figure 9.

FURUYA, Y. and OSAKA, H. 1975 The spanwise non-uniformity of

nominally two-dimensional turbulent boundary layer. (First report; charac-

teristics of spanwise velocity distribution.) Bull. JSME

, 664–672.

Non-

uniformities are large. See second report for effect of various mesh screens.

Lack of two-dimensionality, figures 4, 7, 8. Surface friction, figure 6.

FURUYA, Y., NAKAMURA, I., OSAKA, H. and HONDA, H. 1975

The spanwise non-uniformity of nominally two-dimensional turbulent bound-

ary layer. (Second report; wall shear stress and flow field.) Bull. JSME

673–680.

Floating element with effect of non-alignment with surface. Pro-

files of

and

mean velocity, suggesting weak streamwise vorticity. Friction

coefficient. Mean velocity*, figures 9, 10, 14. Lack of two-dimensional flow*,

figure 8. Surface friction*, figures 13, 15.

GAD-el-HAK, M. and HUSSAIN, A.K.M.F. 1986 Coherent structures

in a turbulent boundary layer. Part 1: generation of “artificial” bursts.

154

Phys. Fluids

, 2124–2139.

Mean velocity*, figures 12, 13a. Reynolds

stresses*, figure 13b.

GAUDET, L. 1986 Experimental investigation of the turbulent bound-

ary layer at high Reynolds numbers and a Mach number of 0.8. Aeron. J.

, 83–94.

Follow-on to Winter and Gaudet. Friction coefficient*, figure 3.

Mean velocity*, figure 18.

GAVIGLIO, J. 1958 I. Sur quelques probl`emes de mesures de turbu-

lence, effectu ́ees `a l’aide de l’an ́emom`etre `a fils chauds parcourus par un

courant d’intensit ́e constante. II. Sur les bruits d’origine a ́erodynamique.

Thesis, Univ. d’Aix-Marseille.

Mean velocity*, table 17, figure 36. Reynolds

stresses*, tables 18–22, figures 38, 39. Hot wire is constant current. Also

pipe flow.

GILABERT, R.M. and GAVALDA, J. 1987 Experimental study of

the turbulent boundary layer developed over a wake splitter plate. In

Preprints, Sixth Symposium on Turbulent Shear Flows

, Toulouse, Paper 2.5.

Mean velocity*, figure 2. Reynolds stresses*, figure 3.

GILLIS, J.C. and JOHNSTON, J.P. 1980 Experiments on the turbu-

lent boundary layer over convex walls and its recovery to flat-wall condi-

tions. In

Turbulent Shear Flows 2

(L.J.S. Bradbury et al., eds.), Springer-

Verlag, 116-128.

Mean velocity*, figure 3. Surface friction*, figure 4. Faired

Reynolds stresses.

Stanford case 0233

GILLIS, J.C. and JOHNSTON, J.P. 1983 Turbulent boundary-layer

flow and structure on a convex wall and its redevelopment on a flat wall. J.

Fluid Mech.

135

, 123–153.

Flow turns

◦

, then constant pressure. Is this

thesis by Gillis? See HMT-31, Stanford. Geometry*, figure 6. Velocity*,

figure 8. Reynolds stress*, figures 12, 19. Friction*, figures 17, 21.

GILLIS, J.C., JOHNSTON, J.P., KAYS, W.M., and MOFFAT, R.J.

1980 Turbulent boundary layer on a convex, curved surface. Dept. Mech.

Eng., Stanford Univ., Rep. No. HMT-31.

Geometry*, figure 6. Velocity*,

figure 10. Friction*, figure 11. Reynolds stresses*, figures 15–21, 23–27,

etc. Data are tabulated.

GOOD, M.C. and JOUBERT, P.N. 1968 The form drag of two-dimen-

sional bluff-plates immersed in turbulent boundary layers. J. Fluid Mech.

, 547–582.

Mean velocity*, figures 7, 16. Bubble, figure 16.

GRESKO, L.S. Jr. 1988 Characteristics of wall pressure and near-wall

velocity in a flat plate turbulent boundary layer. M.S. thesis, Dept. Aeron.

and Astron., MIT.

Mean velocity*, figures 3.7, 3.8, 5.2, 5.10, 5.15, 5.16,

5.18, 5.19, 6.1. Reynolds stresses*, figures 3.7, 3.8, 5.2, 5.10, 5.15, 5.16,

5.18, 5.19, 6.2, 6.3.

GUEZENNEC, Y.G. 1985 Documentation of large coherent struc-

155

tures associated with wall events in turbulent boundary layers. Ph. D.

thesis, Illinois Inst. Technology.

Mean velocity*, figures 12–19. Reynolds

stresses*, figures 20-23.

GUEZENNEC, Y.G. and NAGIB, H.M. 1990 Mechanisms leading to

net drag reduction in manipulated turbulent boundary layers. AIAA J.

245–252.

See for intermittency. Faired data for mean velocity, Reynolds

stresses, intermittency.

GUPTA, A.K. 1970 An experimental investigation of the viscous sub-

layer region in a turbulent boundary layer. Ph. D. thesis, Dept. Aerosp.

Eng., Univ. Southern California.

Reynolds stresses*, figure 13.

GUPTA, A.K. and KAPLAN, R.E. 1972 Statistical characteristics of

Reynolds stress in a turbulent boundary layer. Phys. Fluids

, 981–985.

Reynolds stresses*, figures 2–4.

GUPTA, A.K., LAUFER, J., and KAPLAN, R.E. 1971 Spatial struc-

ture in the viscous sublayer. J. Fluid Mech.

, 493–512; see also Gupta and

Kaplan, “Statistical characteristics of Reynolds stress in a turbulent bound-

ary layer”, Phys. Fluids

, 981–985, 1972, and Ph.D. Thesis, An experi-

mental investigation of the viscous sublayer region in a turbulent boundary

layer, Univ. So. Calif., 1970, by A.K. Gupta.

Hot-wire array across flow

very near wall. Mostly data on

by spanwise correlations. Averaging time

should be less than 0.5

δ/U

. PF has mean and moments of

′

, some

data on

′

in sublayer.Streak spacing*, figures 6–8.

GUST, G. 1976 Observations on turbulent-drag reduction in a dilute

suspension of clay in sea-water. J. Fluid Mech.

, 29–47, 2 plates.

Profiles

with drag reduction. Velocity*, figures 4, 6–9.

HAMELIN, J. and ALVING, A.E. 1996 A low-shear turbulent bound-

ary layer. Phys. Fluids

, 789–804.

Standard boundary layer flows onto a

moving wall. Geometry*, figure 1. Wall stress*, figure 3. Velocity*, figures

5, 6. Reynolds stresses*, figures 7, 8, 9.

HANSEN, M. 1928 Die Geschwindigkeitsverteilung in der Grenzschicht

an einer eingetauchten Platte. Zeitschr. angew. Math. Mech.

, 185–199;

also Abh. Aerodyn. Inst. Technischen Hochschule Aachen, Heft 8, 31–

45, 1928 (translated as “Velocity distribution in the boundary layer of a

submerged plate,” NACA TM 585, 1930).

Friction coefficient*, figures 23,

24.Mean velocity*, figure 17.

HARITONIDIS, J.H., GRESKO, L.S., and BREUER, K.S. 1990 Wall

pressure peaks and waves. In

Near-Wall Turbulence

(S.J. Kline and N.H.

Afgan, eds.), 1988 Zoran Zaric Memorial Conf., Hemisphere, 397–417.

Mean

velocity*, figure 1a. Reynolds stresses, figures 1b, 1c.

HARTMANN, U. and DENGEL, P. 1989 On turbulence measure-

156

ments with a split-film probe. In

Advances in Turbulence 2

(H.-H. Fern-

holz and H.E. Fiedler, eds.), Springer-Verlag, 262–266.

Velocity*, Reynolds

stresses*, figure 4.

HEAD, M.R. and BANDYOPADHYAY, P. 1981 New aspects of tur-

bulent boundary-layer structure. J. Fluid Mech.

107

, 297–338.

Structure*,

figures 13, 18, 19. Velocity*, figures 28, 30.

HEAD, M.R. and RECHENBERG, I. 1962 The Preston tube as a

means of measuring skin friction. J. Fluid Mech.

, 1–17.

Comparison of

probe response in pipe and in boundary layer. Lack of two-dimensionality*,

figure 8. Mean velocity*, figure 12.

HEDLEY, T.B. and KEFFER, J.F. 1974 Some turbulent/non-turbu-

lent properties of the outer intermittent region of a boundary layer. J. Fluid

Mech.

, 645–678.

Mean velocity*, figure 1. Intermittency*, figure 6.

Bulge frequency, figure 9. Reynolds stresses*, figures 13, 14, 19. Moments

of pdf. Celerity.

HICKS, J.W. 1976 Laser Doppler anemometer (LDA) and pitot mea-

surements of the flat plate incompressible turbulent boundary layer in two-

dimensional flow with zero pressure gradient. Unpublished research re-

port, GALCIT (for tabulated data see COLLINS, D.J., COLES, D.E., and

HICKS, J.W., Measurements in the turbulent boundary layer at constant

pressure in subsonic and supersonic flow. Part I. Mean flow. Arnold Eng.

Dev. Center, Rep. AEDC-TR-78-21, 1978; also AGARD 223, files 7801S0101-

7801S0106.)

Mean velocity*, figures 16–27, tables 2–8.

HITES, M., NAGIB, H., and WARK, C. 1997 Velocity and wall shear-

stress measurements in high-Reynolds-number turbulent boundary layers.

AIAA Paper 97-1873.

Geometry*, figure 1. Velocity*, figures 3, 4. Reynolds

stresses*, figure 9. Wall law constants*, figures 14, 15. MEMS data, figures

19, 20.

IMAKI, K. 1968 Structure of superlayer in the turbulent boundary

layer. Univ. Tokyo, Bull. Inst. Space Aeron. Sci.

, 348–367 (in Japanese).

Mean velocity*, figures 2, 4, 6, 9. Intermittency*, figures 9, 10.

JOHANSSON, T.G. 1988 An experimental study of the structure of

a flat plate turbulent boundary layer, using laser-Doppler velocimetry. Ph.

D. thesis, Dept. Applied Thermodynamics and Fluid Mechanics, Chalmers

Institute of Technology.

Mean velocity*, figure 5. Reynolds stresses*, figures

7, 8, 10, 11. Moments of pdf, figures 13–16.

JOHANSSON, T.G. and KARLSSON, R.I. 1989 The energy budget

in the near-wall region of a turbulent boundary layer. In

Applications of

Laser Anemometry to Fluid Mechanics, 4th Int’l. Symposium

(R.J. Adrian

et al., eds.), Springer-Verlag, 3–22.

Mean velocity*, figure 3. Reynolds

157