Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T07:44:55.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental evidence for the existence of the ‘mesolayer’ in turbulent systems

Published online by Cambridge University Press:  20 April 2006

Robert R. Long  and
Tien-Chay Chen
Robert R. Long
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
Tien-Chay Chen
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper is a study of experimental data in the light of new theories of turbulence recently developed by the first author for a number of problems including flow in a pipe, boundary layer at zero incidence, atmospheric boundary layer, turbulent convection and distribution of energy in wavenumber space in decaying, isotropic turbulence. In each of these, a basic element is a ‘mesolayer’ or ‘mesoregion’ in physical space or wavenumber space which is absent in earlier theories and which intrudes between the inner and outer regions preventing the overlap assumed in the derivation of the classical results, e.g. the logarithmic profile in shear flow. The new and old theories differ both in principle and in the final results: the new ideas replace rather than modify or extend the older ones.

The main purpose of this paper is to bring together accumulated evidence concerning the mesolayer theories. We believe that this evidence provides overwhelming support for the existence of the mesolayer and for its pervasive importance in problems of turbulence.Editorial footnote. Although the referees were not persuaded that the claims for the ‘new theories of turbulence’, made by the authors in the abstract and elsewhere in this paper, are justified, we think that publication in the Journal may serve a useful purpose. The authors have assembled a large body of data for various turbulent flow systems. These data should enable readers to test different aspects of the ‘classical’ and ‘new’ theories for themselves and should stimulate thought about the foundations of the classical ideas and about extensions of these ideas, as well as about the validity of the new theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 19 - 59
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. & Ferreira, R. T. S. 1979 Higher order moments in turbulent thermal convection. 2nd Symp., Turbulent Shear Flows, Imperial College. 12$1–12$6.Google Scholar
Afzal, N. 1976 Millikan's argument at moderately large Reynolds number. Phys. Fluids 19, 600–602.Google Scholar
Afzal, N. & Yajnik, K. 1973 Analysis of turbulent pipe and channel flows at moderately large Reynolds numbers. J. Fluid Mech. 61, 23–31.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Bullock, K. J., Cooper, R. E. & Abernathy, F. H. 1978 Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow. J. Fluid Mech. 88, 585–608.Google Scholar
Bush, W. B. & Fendell, F. E. 1972 Asymptotic analysis of turbulent channel and boundary-layer flow. J. Fluid Mech. 56, 657–681.Google Scholar
Bush, W. B. & Fendell, F. E. 1973 Asymptotic analysis of turbulent channel flow for mean turbulent energy closures. Phys. Fluids 16, 1189–1197.Google Scholar
Bush, W. B. & Fendell, F. E. 1974 Asymptotic analysis of turbulent channel flow for mixing length theory. SIAM, J. Appl. Math. 26, 314–427.Google Scholar
Businger, J. A., Wyngaard, J. C., Isumi, Y. & Bradley, E. F. 1971 Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28, 181–189.Google Scholar
Caldwell, D. R., Van Atta, C. W. & Holland, K. N. 1972 A laboratory study of the turbulent Ekman layer. Geophys. Fluid Dynamics 3, 125–160.Google Scholar
Chen, C. H. & Blackwelder, R. F. 1978 Large-scale motion in a turbulent boundary layer: A study using temperature contamination. J. Fluid Mech. 89, 1–31.Google Scholar
Chern, C. S. & Long, R. R. 1980 A new theory of turbulent thermal convection over heated surfaces. (Unpublished manuscript.)
Csanady, G. T. 1967 On the resistance law of a turbulent Ekman layer. J. Atmos. Sci. 24, 407–471.Google Scholar
Deardorff, J. W. & Willis, G. F. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675–704.Google Scholar
Falco, R. E. 1974 Some comments on turbulent boundary layer structure inferred from the movements of a passive contaminant. A.I.A.A. Paper no. 74–99.Google Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, S124–132.Google Scholar
Falco, R. E. 1978 An experimental study of Reynolds stress producing motions in the outer part of turbulent boundary layers, Part I. The shape, scale, evolution and Reynolds number dependence. (Unpublished manuscript.)
Fendell, F. E. 1972 Singular perturbation and turbulent shear layers near walls. J. Astro. Sci. 20, 129–165.Google Scholar
Ferreira, R. T. D. 1978 Unsteady turbulent thermal convection. Ph.D. thesis, Dept. Mech. Engng., University of Illinois.
Fbitsch, W. 1928 Einfluss der Wandrauhigkeit auf die turbulente Geschwindigkeit-Verteilung in Rinnen. Z. angew. Math. Mech. 8, 199–216.Google Scholar
Gill, A. E. 1967 The turbulent Ekman layer. (Unpublished manuscript.)
Globe, S. & Dropkin, D. 1959 Natural convection heat transfers in liquids confined by two horizontal plates and heated from below. J. Heat Transfer 81, 24–28.Google Scholar
Gupta, A. K. & Kaplan, R. E. 1972 Statistical characteristics of Reynolds stress in a turbulent boundary layer. Phys. Fluids 15, 981–895.Google Scholar
Gupta, A. K., Laufer, J. & Kaplan, R. E. 1971 Spatial structure in the viscous sublayer. J. Fluid Mech. 50, 493–512.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hishida, M. & Nagono, Y. 1979 Structure of turbulent velocity and temperature fluctuation in fully developed pipe flow. J. Heat Transfer 101, 15–22.Google Scholar
Hopfinger, E. J. & Toly, J.-A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155–175.Google Scholar
Howroyd, G. C. & Slawson, P. R. 1975 The characteristics of a laboratory produced turbulent Ekman layer. Boundary Layer Met. 8, 201–219.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.Google Scholar
Izakson, A. 1937 Formula for the velocity distribution near a wall. Zh. Eksper. Teor. Fiz. 7, 919–924.Google Scholar
Kármán, T. von 1930 Mechanische Ähnlichkeit und Turbulenz. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 58–76.Google Scholar
Klebanoff, R. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. TN 3178.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layer. J. Fluid Mech. 30, 741–772.Google Scholar
Korneyev, A. L. & Sedov, L. I. 1976 Theory of isotropic turbulence and its comparison with experimental data. Fluid Mechanics, Soviet Research 5, No. 5, 37–48.Google Scholar
Kreider, J. F. 1973 A Laboratory Study of the Turbulent Ekman Layer. Ph.D. Thesis, College of Engineering, University of Colorado, Boulder.
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. Nat. Advis. Comm. Aeronautics, Rep. No. 1174.Google Scholar
Laufer, J. 1975 New trends in experimental turbulence research. Ann. Rev. Fluid Mech. 7, 307–326.Google Scholar
Lawn, C. J. 1971 The determination of the rate of dissipation in turbulent pipe flow. J. Fluid Mech. 48, 477–505.Google Scholar
Long, R. R. 1976 Relation between Nusselt number and Bayleigh number in turbulent thermal convection. J. Fluid Mech. 73, 445–451.Google Scholar
Long, R. R. 1978a The decay of turbulence. Tech. Rep. No. 13 (Series C). The Johns Hopkins University.
Long, R. R. 1978b Theory of turbulence in a homogeneous fluid induced by an oscillating grid. Phys. Fluids 21, 1887–1888.Google Scholar
Long, R. R. 1980a A new theory of turbulent flow in a pipe. (Unpublished manuscript.)
Long, R. R. 1980b A new theory of the turbulent boundary layer in zero pressure gradient. (Unpublished manuscript.)
Long, R. R. 1980c A new theory of the neutral planetary boundary layer. (Unpublished manuscript.)
Long, R. R. 1980d On the energy spectrum at higher wave numbers. (Unpublished manuscript.)
Ludwieg, H. & Tillmann, W. 1950 Investigations of the wall shearing stress in turbulent boundary layers. N.A.C.A. TM 1285.Google Scholar
Lund, K. O. & Bush, W. B. 1980 Asymptotic analysis of plane turbulent Couette-Poiseuille flows. J. Fluid Mech. 96, 81–104.Google Scholar
Malkus, W. V. R. 1979 Turbulent velocity profiles from stability criteria. J. Fluid Mech. 90, 401–414.Google Scholar
McDougall, T. J. 1979 Measurements of turbulence in a zero-mean shear mixed layer. J. Fluid Mech. 94, 409–431.Google Scholar
Millikan, C. B. 1938 A critical discussion of turbulent flows in channels and circular tubes. Proc. 5th Int. Cong. Appl. Mech., Cambridge (USA.).Google Scholar
Mitchell, J. E. & Hanratty, T. J. 1966 A study of turbulence at a wall using an electrochemical wall shear-stress meter. J. Fluid Mech. 26, 199–221.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics. I. Mechanics of Turbulence. Massachusetts Institute of Technology Press.
Nychas, S. G., Hershey, H. S. & Brodkey, M. P. 1973 A visual study of turbulent shear flow. J. Fluid Mech. 61, 513–540.Google Scholar
Nikuradse, J. 1932 Gesetzmässigkeiten der turbulenten Strömung in glatten Rohren. Forsch. Arbeiten Ing.-Wesen, No. 356.Google Scholar
Perry, A. E. & Abell, C. J. 1975 Scaling laws for pipe flow turbulence. J. Fluid Mech. 67, 257–271.Google Scholar
Perry, A. E. & Abell, C. J. 1977 Asymptotic similarity of turbulence structure in smooth-and-rough-walled pipes. J. Fluid Mech. 79, 785–791.Google Scholar
Plate, E. J. 1971 Aerodynamic Characteristics of the Atmospheric Boundary Layers. U.S. Atomic Engng Comm.
Peandtl, L. 1925 Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. angew. Math. Mech. 5, No. 2, 136–139.Google Scholar
Prandtl, L. 1932 Zur turbulenten Strömung in Röhren und läns Platten. Ergebn. Aerodyn. Versuchsanst., Göttingen 4, 18–29.Google Scholar
Rao, K., Narahari, Narasimha, R. & Narayanan, M. A. B. 1971 The ‘bursting’ phenomenon in a turbulent boundary layer. J. Fluid Mech. 48, 339–352.Google Scholar
Rotta, J. C. 1962 Turbulent boundary layers in incompressible flow. Progress in Aeronautical Sciences 2, 1–220.Google Scholar
Schildknecht, M., Miller, J. A. & Meir, G. E. A. 1979 The influence of suction on the structure of turbulence in fully developed pipe flow. J. Fluid Mech. 90, 67–107.Google Scholar
Smith, D. W. & Walker, J. H. 1959 Skin-friction measurements in incompressible flow. NASA Rep. R-26.
Somerscales, E. F. C. & Gazda, I. W. 1969 Thermal convection in high Prandtl number liquids at high Rayleigh numbers. Int. Heat and Mass Transfer 12, 1491–1511.Google Scholar
Tennekes, H. 1968 Outline of a second-order theory of turbulent pipe flow. A.I.A.A. J. 6, 1735–1740.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. Massachusetts Institute of Technology Press.
Theodorsen, T. 1955 The structure of turbulence. 50 Jahre Grenzschichtforschung (ed. H. Görtler & W. Tollmien). Braunschweig: Vieweg und Sohn.
Theodorsen, T. 1962 The structure of turbulence. In Fluid Dynamics and Applied Mathematics (ed. J. B. Diaz & S. I. Pai). Gordon and Breach.
Thomas, N. H. & Hancock, D. E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82, 481–496.Google Scholar
Thomas, D. B. & Townsend, A. A. 1957 Turbulent convection over a heated horizontal surface. J. Fluid Mech. 2, 473–492.Google Scholar
Thompson, S. M. & Turner, J. S. 1975 Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67, 349–368.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tritton, D. J. 1967 Some new correlation measurements in a turbulent boundary layer. J. Fluid Mech. 28, 439–462.Google Scholar
Ueda, H. & Mizushina, T. 1977 Turbulence structure in the inner part of the wall region in a fully developed turbulent tube flow. Proc. 5th Biennial Symp. on Turb., Univ. Missouri, Rolla.Google Scholar
Uzkan, T. & Reynolds, W. C. 1967 A shear-free turbulent boundary layer. J. Fluid Mech. 28, 803–821.Google Scholar
Wieghardt, K. 1969 Computation of turbulent boundary layer. Proc. 1968 AFOSR-IFP Stanford Conf., vol. 2 (ed. D. E. Coles & E. A. Hirst).
Yajnik, K. S. 1970 Asymptotic theory of turbulent shear flows. J. Fluid Mech. 42, 411–427Google Scholar