Some Remarks on Turbulent Shear Flows

Hinze J. O. Turbulence 1958 (McGraw-Hill Book Co., New York).

Klebanoff P. S. ‘Characteristics of turbulence in a boundary layer with zero pressure gradient’, N.A.C.A. Rept 1247, 1956.

Van Driest E. R. On turbulent flow near a wall 1955 (Heat Transfer and Fluid Mechanics Institute).

Townsend A. A. Structure of turbulent shear flow 1956 (Cambridge University Press).

Halleen R. M. ‘A literature survey on subsonic free turbulent shear flow’, A.F.O.S.R. tech. Note 5444, 1964 (U.S. Air Force); Report MD-11 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Corrsin S. Kistler A. ‘Free-stream boundaries of turbulent flows’, N.A.C.A. Rept 1244, 1955.

Abernathy F. H. Kronauer R. A. ‘The formation of vortex streets’, J. Fluid Mech. 1962 13.

Browand F. K. ‘An experimental investigation of the instability of an incompressible, separated shear layer’, Report TR 92-4, 1965 (Aeroelastic and Structures Research Laboratory, Massachusetts Inst. of Technology, Cambridge, Mass.).

Hsu H. C. ‘Characteristics of mean flow and turbulence at an abrupt two-dimensional expansion’, Ph.D. Dissertation, 1950 (Department of Mechanics and Hydraulics, State University of Iowa).

Sabin C. M. Kline S. J. ‘An analytical and experimental study of the plane, incompressible, turbulent free shear layer with arbitrary velocity ratio and pressure gradient’, Ph.D. Dissertation, 1963 (Mech. Engng Dept, Stanford University, Stanford, California); J. basic Engng, Trans. Am. Soc. mech. Engrs, 1965 87 (Ser. D, No. 2).

Schraub F. A. Kline S. J. Henry J. Runstadler P. W. Littell A. ‘Use of hydrogen bubbles for quantitative determination of time dependent velocity fields in low speed water flows’, J. basic Engng, Trans. Am. Soc. mech. Engrs 1965 87 (Ser. D, No. 2).

Schraub F. A. Kline S. J. ‘A study of the structure of the turbulent boundary layer with and without longitudinal pressure gradients’, Report MD-12, 1965 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Runstadler P. W. Kline S. J. Reynolds W. C. ‘An investigation of the flow structure of the turbulent boundary layer’, Report MD-8, 1963 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Kline S. J. Runstadler P. W. ‘Some preliminary results of visual studies of the flow model of the wall layers of the turbulent boundary layer’, J. appl. Mech., Trans. Am. Soc. mech. Engrs 1959 26 (Ser. E), 2.

Meyer K. A. Kline S. J. ‘A visual study of the flow model in the later stages of laminar-turbulent transition on a flat plate’, Report MD-7 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Motion Picture Film: Runstadler P. W. Kline S. J. Reynolds W. C. ‘A visual study of the flow structure in the fully developed turbulent boundary layer on a flat plate’ (Available from Engng Soc. Lib., 345 East 47th Street, New York, New York 10017, as film catalogue item R-7).

Ludwieg H. Tillman W. Ing. Arch. 1949 17, 288.

Coles D. ‘The law of the wake in the turbulent boundary layer’, J. Fluid Mech. 1956 1 (Pt 2), 191.

Stratford B. S. ‘An experimental flow with zero skin friction throughout its region of pressure rise’, J. Fluid Mech. 1959 5, 17.

Townsend A. A. ‘Equilibrium layers and wall turbulence’, J. Fluid Mech. 1961 11, 97.

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Bradshaw P. Ferriss D. H. ‘Response of a retarded equilibrium turbulent boundary layer to sudden removal of pressure gradient’, N.P.L. Aero. Rept 1145, 1965; A.R.C. 26758, FM 3577.

Rotta J. Paper presented to Symposium on Fluid Mechanics on Internal Flow; held at General Motors Research Laboratories, September 1965 (to be published by Elsevier Publ. Co., Netherlands).

Schlichting H. Boundary layer theory 4th ed., 1960 (McGraw-Hill Book Co., New York).

Thomson B. G. J. ‘A critical review of existing methods of calculating the turbulent boundary layer’, A.R.C. 26109, FM 3492.

Clauser F. H. ‘Turbulent boundary layers in adverse pressure gradients’, J. aeronaut. Sci. 1954 21, 91.

Clauser F. H. ‘The turbulent boundary layer’, Advances in applied mechanics vol. IV, 1956 (Academic Press, New York).

Head M. R. ‘Entrainment in the turbulent boundary layer’, R & M 3152, 1958 (Aeronaut. Res. Ccl.).

Millikan C. B. ‘A critical discussion of turbulent flows in channels and circular tubes’, Proc. Fifth Int. Cong. Appl. Mech. (Cambridge) 1938, 386 (Instn Mech. Engrs, London).

Einstein H. A. Li H. ‘The viscous sublayer along a smooth boundary’, Proc. Am. Soc. civ. Engrs 1956 82, 945.

Hanratty T. J. ‘Turbulent exchange of mass and momentum with a boundary’, J. Am. Inst. chem. Engrs 1956 2 (No. 3), 359.

Tiederman W. G. Reynolds W. C. ‘Stability of turbulent Poiseuille flow with application to the Malkus theory of turbulence’, Report FM-2, 1965 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Kline S. J. Lisin A. V. Waitman B. A. ‘An experimental investigation of the effect of free stream turbulence on the turbulent boundary layer growth’, N.A.S.A. tech. Note D 368, 1960.

Klebanoff P. S. Diehl Z. ‘Some features of artificially thickened, fully developed turbulent boundary layers with zero pressure gradient’, N.A.C.A. tech. Note 2475, 1951.

Reynolds W. C. ‘Finite amplitude oblique waves in turbulent shear flow’, Paper No. A-6, Fluid Dynamics Division Meeting, November 1965 (Am. Phys. Soc, New York).

Perry A. E. Joubert P. N. ‘Rough-wall boundary layers in adverse pressure gradients’, J. Fluid Mech. 1963 17, 193.

Weighardt K. ‘On the turbulent friction layer for rising pressure’, N.A.C.A. tech. Memo. 1314, 1951.

Sternberg J. ‘The transition from a turbulent to a laminar boundary layer’, U.S. Army Bal. Res. Lab. Rept 906, 1954 (Aberdeen).

Senoo Y. ‘The boundary layer on the end wall of a turbine nozzle cascade’, Gas Turbine Laboratory Rept 35, 1957 (Massachusetts Inst. of Technology, Cambridge, Mass.); also Trans. Am. Soc. mech. Engrs 80, 1711; also Am. Soc. mech. Engrs Paper A-172.

Sergienko A. A. Gretsov V. K. ‘Transition from a turbulent into a laminar boundary layer’, Soviet Phys. (Doklady) 1959 4 (No. 1). (A translation of the Physics Sections of the Proceedings of the Academy of Sciences of the USSR, Russian original volume 124, Nos 1-6, published by the American Institute of Physics, New York.).

Launder B. E. ‘The turbulent boundary layer in a strongly negative pressure gradient’, Gas Turbine Laboratory Rept No. 71, 1963 (Massachusetts Inst. of Technology, Cambridge, Mass.).

Moretti P. M. Kays W. M. ‘Heat transfer through an incompressible turbulent boundary layer with varying free-stream velocity and varying surface temperature’, Report PG-1 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Back L. H. Massier P. F. Gier H. L. ‘Convective heat-transfer in a convergent-divergent nozzle’, Int. J. Heat Mass Transfer 1964 7 (5), 549.

Hall G. W. ‘Application of boundary layer theory to explain some nozzle and venturi flow peculiarities’, Proc. Instn mech. Engrs 1959 173 (No. 36), 837.

Cannon J. ‘Heat transfer from a fluid flowing inside a rotating cylinder’, Ph.D. Dissertation, 1965 (Mech. Engng Dept, Stanford University, Stanford, California).

Briggs D. C. ‘Heat transfer in rotating turbulent pipe flow’, Report TR 45, 1959 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Uzkan T. Reynolds W. C. ‘A turbulent boundary layer on a wall moving at the free-stream velocity’, Report MD-14, 1965 (Thermosciences Division, Mech. Engng Dept, Stanford University, Stanford, California).

Elder J. W. ‘An experimental investigation of turbulent spots and breakdown to turbulence’, J. Fluid Mech. 1960 9 (Pt 2), 235.

Klebanoff P. S. Tidstrom K. D. Sargent L. M. ‘The three-dimensional nature of boundary-layer instability’, J. Fluid Mech. 1962 12 (Pt 1), 1.

Kline S. J. Paper presented to Symposium on Fluid Mechanics on Internal Flow, held at General Motors Research Laboratories, September 1965 (to be published by Elsevier Publ. Co., Netherlands).

Abramovich G. N. ‘The theory of a free jet of a compressible gas’, N.A.C.A. tech. Memo. 1058, 1944.

Abramovich G. N. The theory of turbulent jets 1963 (Massachusetts Inst. of Technology Press, Cambridge, Mass.).

Albertson M. L. Dai Y. B. Jensen R. A. Rouse H. ‘Diffusion of submerged jets’, Trans. Am. Soc. chem. Engrs 1950 115, 639.

Alexander L. G. Baron T. Comings E. W. ‘Transport of momentum, mass and heat in turbulent jets’, University of Illinois Engng Exptl Station Bull. 413, 1953.

Batchelor G. K. ‘Note on free turbulent flows with special reference to two-dimensional wakes’, J. Aerospace Sci. 1950 17 (No. 7), 441.

Betz A. ‘Velocity and pressure distribution behind bodies in an air current’, N.A.C.A. tech. Memo. 268, 1924.

Bhuta P. G. Page R. H. ‘Non-steady two-dimensional laminar and turbulent jet mixing theory’, Proc. Fourth U.S. Natnl Cong. Appl. Mech. 1962 vol. II, 1205.

Billerbeck W. J. Jr. ‘Empirical equation for the wake-spreading limits behind three-dimensional bodies’, J. Aero-Spaces Sci. 1960 27 (No. 8), 640.

Birkhoff G. Zarantonello E. H. ‘Jets, wakes, and cavities’, Appl. Math. and Mech. 1957 2 (Academic Press, New York).

Chapman A. J. Korst H. H. ‘Free jet boundary with consideration of initial boundary layer’, Proc. Second U.S. Natnl Cong. Appl. Mech. 1954 vol. I, 723.

Cooper R. D. Lutzky M. ‘Exploratory investigation of the turbulent wakes behind bluff bodies’, David Taylor Model Basin Rept 963, 1955 (Department of U.S. Navy).

Cordes G. Ing.-Arch. 1937 8 (No. 4).

Corrsin S. ‘Investigation of flow in an axially symmetrical heated jet of air’, N.A.C.A. Wartime Rept W-94, 1943.

Corrsin S. Uberoi M. S. ‘Further experiments on the flow and heat transfer in a heated turbulent air jet’, N.A.C.A. Rept 998, 1950.

Crane L. J. Pack D. C. ‘The laminar and turbulent mixing of jets of compressible fluid—Part I: Flow far from the orifice’, J. Fluid Mech. 1957 2 (5), 449.

Crane L. J. ‘The laminar and turbulent mixing of jets of compressible fluid—Part II: The mixing of two semi-infinite streams’, J. Fluid Mech. 1957 3 (1), 81.

Eichhorn R. Eddy T. L. ‘Some measurements of a wake-boundary layer interaction’, Am. Soc. mech. Engrs Paper 61-Wa-52, 1960.

Ershin S. A. Sakipov Z. B. ‘A study of the initial section of a turbulent jet of compressed gas’, Soviet Phys. (Tech. Phys.) 1959 4 (No. 1), 43.

Eskinaki S. ‘Mixing of wakes in a turbulent shear flow’, N.A.S.A. tech. Note D-83, 1959.

Fage A. Falkner V. M. Proc. R. Soc, Lond. 1935 135 (Ser. A, No. 702).

Forstall W. Jr. Shapiro A. H. ‘Momentum and mass transfer in coaxial gas jets’, J. Appl. Mech., Trans. Am. Soc. mech. Engrs 1950 72, 399.

Förthmann E. ‘Turbulent jet expansion’, N.A.C.A. tech. Memo. 789, 1936.

Ginevski A. S. ‘The turbulent wake and jet in an ambient flow having a stream-wise pressure gradient’, Izv. Akad. Nauk SSSR., Otd. Tekh. Nauk Nekh. i. Mash., No. 2. 1959; also Appl. Mech. Rev. 1962, Item No. 3457.

Goldstein S. ‘On the velocity and temperature distribution in the turbulent wake behind a heat body of revolution’, Proc. Cambridge Phil. Soc. 1938 34, 48.

Goldstein S. Modern developments in fluid dynamics, Vol. II, 1950 (Clarendon Press, Oxford).

Görtler H. Z. angew. Math. Mech. 1942 22 (No. 5), 244.

Grant H. L. ‘The large eddies of turbulent motion’, J. Fluid Mech. 1958 4 (No. 2), 149.

Hall A. A. Hislop G. S. ‘Velocity and temperature distributions in the turbulent wake behind a heated body of revolution’, Proc. Cambridge Phil. Soc. 1938 34, 345.

Hama F. R. ‘The three-dimensional vortex pattern behind a circular cylinder’, J. Aerospace Sci. 1957 24 (No. 2), 156.

Hill P. G. Schaub U. W. Senoo Y. ‘Turbulent wakes in pressure gradients’, J. appl. Mech., Trans. Am. Soc. mech. Engrs 1963 30 (Ser. E).

Hinze J. O. van der Hegge Zijnen B. G. Appl. Sci. Res. 1A, 435.

Hollingdale S. ‘Stability and configuration of wakes produced by solid bodies moving through fluids’, Phil. Mag. 1941 29 (Ser. 7), 209.

Howarth L. ‘Concerning the velocity and temperature distribution in plane and axially symmetrical jets’, Proc. Cambridge Phil. Soc. 1938 34, 185.

Johanneson N. H. ‘The mixing of free axially symmetrical jets of Mach number 1-40’, A.R.C. 1896 7, FM 2409, 1957.

Kuethe A. M. ‘Investigations of the turbulent mixing regions formed by jets’, J. appl. Mech., Trans. Am. Soc. mech. Engrs 1935 57, 87.

Kovasznay L. S. G. ‘Hot-wire investigation of the wake behind cylinders at low Reynolds numbers’, Proc. R. Soc, Lond. 1949 198 (Ser. A), No. A 1053, 174.

Laurence J. C. ‘Intensity, scale, and spectra of turbulence in mixing region of free subsonic jet’, N.A.C.A. tech. Note 3561, 1955.

Lieblein S. Roudebush W. H. ‘Low-speed wake characteristics of two-dimensional cascade and isolated airfoil sections’, N.A.C.A. tech. Rept 3771, 1956.

Liepmann H. W. Laufer J. ‘Investigations of free turbulent mixing’, N.A.C.A. tech. Note 1257, 1947.

Lock R. C. ‘The velocity distribution in the laminar boundary layer between parallel streams’, Quart. J. Mech. Appl. Math. 1951 4.

Maydew R. C. Reed J. F. ‘Turbulent mixing of axisymmetric compressible jets (in the half-jet region) with quiescent air’, Report No. SC-4764, 1963 (Sandia Corp.).

Miller D. R. Comings E. W. ‘Static pressure distribution in the free turbulent jet’, J. Fluid Mech. 1957 3 (No. 1), 1.

Napolitano L. G. ‘Turbulent mixing of two non-reacting gases’, Pibal Rept 323, 1957.

Napolitano L. G. ‘Two-dimensional plane mixing of homogeneous and non-homogeneous streams’, Pibal Rept 400, 1957.

Napolitano L. G. ‘Incompressible mixing of a shear flow with fluid at rest’, J. Aero/Space Sci. 1958 25 (No. 7), 444.

Napolitano L. G. ‘The Blasius equation with three point boundary condition’, Quart. appl. Math. 1958 16 (No. 4), 397.

Napolitano L. G. ‘Critical study of the adequacy of integral methods in plane mixing problems’, A.F.O.S.R. Rept AD 136746, 1960.

Pabst O. Ing.-Arch. 1957 25 (No. 1), 10.

Pai S. I. Fluid dynamics of jets 1959, 96 (D. Van Nostrand, New York).

Reichardt H. V.D.I. ForschHft 1942, 414; 2nd ed., 1951.

Roshko A. ‘On the development of turbulent wakes from vortex streets’, N.A.C.A. Rept 1191, 1954.

Rouse H. Advanced mechanics of fluids 359 (Wiley and Sons, New York).

Ruden V. P. Die NaturWiss 1933 21, 375.

Schaub U. W. ‘The behavior of a wake in an adverse pressure gradient’, Report 62, 1961 (Massachusetts Inst. of Technology, Cambridge, Mass.).

Schlichting H. Ing.-Arch. 1930 1 (No. 5), 537.

Schubauer G. B. Tchen C. M. Turbulent flow 1961, 86 (Princeton Aeronautical Paperbacks, Princeton, New Jersey).

Seban R. A. Back L. H. ‘Velocity and temperature profiles in turbulent boundary layers with tangential injection’, J. Heat Transfer, Trans. Am. Soc. mech. Engrs 1962 84 (Ser. C, No. 1), 45.

Silverstein Abe . N.A.C.A. Rept 651, 1939.

Silverstein A. Katzoff S. ‘Design charts for predicting downwash angles and wake characteristics behind plain and flapped wings’, N.A.C.A. Rept 684, 1939.

Squire H. B. Trouncer J. ‘Round jets in a general stream’, R. & M. Rept 1974, 1944 (Aeronaut. Res. Council).

Steiger M. H. Bloom M. H. ‘Velocities in two-dimensional asymmetric wakes’, A.F.O.S.R. Rept 1085, 1961.

Steiger M. H. Bloom M. H. ‘Three-dimensional viscous wakes’, A.F.O.S.R. Rept 1580, 1961.

Streeter V. L. Handbook of fluid dynamics 1959, 10 (McGraw-Hill Book Co., New York).

Swain L. M. ‘On the turbulent wake behind a body of revolution’, Proc. R. Soc, Lond. 1929 125 (Ser. A, No. 799), 647.

Szablewski W. ‘The diffusion of a hot air jet in motion’, N.A.C.A. tech. Memo. 1288, 1950.

Szablewski W. ‘Contributions to the theory of the spreading of a free jet issuing from a nozzle’, N.A.C.A. tech. Memo. 1311, 1951.

Szablewski W. Ing.-Arch. 1952 20 (No. 2), 73.

Szablewski W. Ing.-Arch. 1957 25 (No. 1), 10.

Taylor G. I. ‘The transport of vorticity and heat through a fluid in turbulent motion’, Proc. R. Soc. Lond. 1932 135 (Ser. A), 635.

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Tollmien W. Ing.-Arch. 1933 4 (No. 1).

Tomotika S. ‘Application of the modified vorticity transport theory to the turbulent spreading of a jet’, Proc. R. Soc, Lond. 1938 165, 65.

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Townsend A. A. ‘Measurements in the turbulent wake of a cylinder’, Proc. R. Soc, Lond. 1947 190 (Ser. A), 551.

Townsend A. A. ‘The fully developed wake of a circular cylinder’, Austral. J. Sci. 1949 (Ser. A, Phys. Sci.), 451.

Townsend A. A. ‘Energy distributions and intermittency in established turbulent wakes’, Proc. R. Soc, Lond. 1949 197 (Ser. A), 124.

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Yakovlevskii O. V. ‘On thickness of the turbulent mixing zone at the boundary of two gas flow with different speed and density’, Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk 1958 10, 153.

Vulis L. A. Terekhina N. N. ‘Propagation of a turbulent gas jet in a medium with a different density’, Soviet Phys. (Techn. Phys.) 1957 1 (No. 6), 1249.

Yen K. T. ‘On the indeterminateness of the boundary conditions for the mixing of two parallel streams’, J. appl. Mech., Trans. Am. Soc. mech. Engrs 1960 27 (Ser. E, No. 3), 390.

Johnston J. P. ‘Three-dimensional turbulent boundary layer’, Tech. Rept No. 39, 1954 and Sc.D. Thesis (Gas Turbine Laboratory, Massachusetts Inst. of Technology, Cambridge, Mass.).

Landahl M. T. ‘A wave-guide model for turbulent shear flow’, N.A.S.A. Contractor Rept CR-317, 1963.

Betchov R. Criminale W. O. ‘Oscillations of a turbulent flow’, J. Phys. Fluids 1964 7, 12.

Mellor G. L. Gibson D. M. ‘Equilibrium turbulent boundary layers’, FLD 13, 1963 (Department of Aerospace and Mechanical Sciences, Princeton University, Princeton, New Jersey).

Mellor G. L. ‘The effects of pressure gradients on turbulent flow near a smooth wall’, FLD 14, 1964 (Department of Aerospace and Mechanical Sciences, Princton University, Princeton, New Jersey).

Herring H. J. Norbury J. F. ‘Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients’, FLD 15 (Department of Aerospace and Mechanical Sciences, Princeton University, Princeton, New Jersey).