Abstract
Many experimental studies emphasize the importance of periodic recognizable flow patterns for the transport process in turbulent flow. In this paper a model is formulated for the large scale part of the turbulent motion. The experimental observation that the structures in the outer region run in phase with the bursting cycle in the wall layer forms the basis of the model. The wall layer, where viscous stresses are important and the outer region where the inviscid approximation holds, are treated separately. The small scale part of the turbulent motion, which is assumed to be important in localized regions only (bursts regions), couples the wall region and the outer region.
The mean wall shear stress calculated with this model agrees reasonably well with the empirical formulae for the friction coefficient even for the more complex case of the transpired boundary layer. The main conclusion of the model calculations is that the transport of momentum can be very well explained in terms of turbulent structures. The model clearly illustrates how momentum is transported in three stages: (i) Thin elongated layers near the wall slow down as the result of viscous forces. (ii) The retarded fluid-is ejected in localized regions or bursts. (iii) The large scale motion in the outer region takes over the transport.
In this paper special attention will be given to the function of the longitudinal vortices in the wall layer. In turns out that they hardly influence the turbulent exchange, but that they are very important for the creation of locally unstable regions. It is believed that the strength of the longitudinal vortices is influenced by the large scale structures in the outer region. By this mechanism the large scales in the outer region can influence the burst frequency.
In a discussion some ideas are presented about what this can mean for special flow phenomena as: drag reduction by polymer solutions or along compliant walls and rapid shear stress change along curved walls.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Acton, E., (1976). The modelling of large eddies in a two-dimensional shear layer, J. Fluid Mech., 76, 561.
Bark, F.H., (1975). On the wave structure of the wall region of a turbulent boundary layer, J. Fluid Mech., 70, 229.
Beljaars, A.C.M., (1979). A model for turbulent exchange in boundary layers, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, Netherlands.
Beljaars, A.C.M., Krishna Prasad, K. and Vries, D.A. de, (1980). A structural model for turbulent exchange in boundary layers, submitted to J. Fluid Mech.
Blackwelder, R.F. and Eckelmann, H., (1979). Streamwise vortices associated with the bursting phenomenon, J. Fluid Mech., 24, 577.
Blackwelder, R.F., and Kaplan, R.E., (1972). The intermittent structure of the wall region of a turbulent boundary layer, Univ. S. Calif. Rep. USCAE, 1-22.
Blackwelder, R.F., and Kaplan, R.E., (1976). On the wall structure of turbulent boundary layers, J. Fluid Mech., 76, 89.
Blackwelder, R.F., and Kovasznay, L.S.G., (1972). Time scales and correlation in a turbulent boundary layer, Phys. Fluids, 15, 1545.
Bradshaw, P., (1973). Effects of streamline curvature on turbulent flow. AGARDograph No. 169.
Bradshaw, P., (1973). The strategy of calculation methods for complex turbulent flows, Imperial College Aero report 73-05.
Brodkey, R.S., Wallace, J.M., and Eckelmann, H., (1974). Some Properties of Truncated Turbulence Signals in Bounded Shear Flows. J. Fluid Mech., 63, 209.
Brown, G.L., and Roshko, A., (1974). On density effects in turbulent mixing layers, J. Fluid Mech., 64, 775.
Brown, G.L., and Thomas, A.S.W., (1977). Large structures in a turbulent boundary layer, Phys. Fluids, 20, S243.
Bushnell, O.M., J.N. Hefner and R.L. Ash, (1977). Compliant wall drag reduction for turbulent boundary layers. Phys. Fluids, 20, S31.
Cebeci, T., and Smith, A.M.O., (1974). Analysis of turbulent boundary layers, Academic Press, New York.
Corino, E.R., and Brodkey, R.S., (1969). A visual investigation in the wall region of turbulent flow, J. Fluid, Mech., 37, 1.
Deardorff, J.W., (1970). A numerical study of three-dimensional turbulent channel flow at large Reynolds number, J. Fluid Mech., 41, 453.
Eckelmann, H., (1974). The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow, J. Fluid Mech., 65, 439
Einstein, H.A., and Li, H., (1956). The viscous sublayer along a smooth boundary, J. Engng. Mech. Div. Am. Soc. Civ. Engrs., 82 (EM2), 945.
Falco, R.E., (1977). Coherent motion in the outer region of turbulent boundary layers, Phys. Fluids, 20, S124.
Fendell, F.E., (1972). Singular perturbation and turbulent shear flow near walls, J. Astronautical Sc., 20, 129.
Fortuna, G. and Hanratty, T.J., (1972). The influence of drag-reducing polymers on turbulence in the viscous sublayer, J. Fluid Mech., 53, 575.
Hanratty, T.J., (1956). Turbulent exchange of mass and momentum with a boundary, A.I.Ch.E.Je, 2, 359.
Hinze, J.O., (1975). Turbulence, McGrawhill, New York, 2nd ed.
Johnston, J.P., (1972). The Suppression of shear-layer turbulence in rotating systems. ARARD Conf. Proc. 93.
Kim, H.T., Kline, S.J., and Reynolds, W.C., (1971). The production of turbulence near a smooth wall in a turbulent boundary layer, J. Fluid Mech., 50, 133.
Kim, J. & Moin, P., (1979). Large eddy simulation of turbulent channel flow — Illiac IV Calculation, AGARD Symposium on Turbulent Boundary Layer-Experiment, Theory, and Modelling.
Kline, S.J., (1968). Discussion, Proc. of AFOSR-IFP-Stanford Conf. on computation of Turbulent Boundary Layers. Ed: S.J. Kline et al., Vol. 1 p. 527.
Kline, S.J., Reynolds, W.C., Schraub, F.A. and Rundstadler, P.W., (1967). The structure of turbulent boundary layers. J. Fluid Mech., 30, 741.
Kovasznay, L.S.G., Kibens, V., and Blackwelder, R.F., (1970). Large scale motion in the intermittent region of a turbulent boundary layer, J. Fluid Mech., 41, 283.
Landahl, M.T., (1965). A wave-guide model for turbulent shear flow, NASA, CR-317.
Landahl, M.T., (1967). A wave-guide model for turbulent shear flow, J. Fluid Mech., 29, 441.
Landahl, M.T., (1975). Wave breakdown and turbulence, SIAM, J. Appl. Mech., 28, 735.
Laufer, J., and Badri Narayanan, M.A., (1971). The mean period of the production mechanism in a boundary layer, Phys. Fluids, 14, 182.
Mager, A., (1964). Three-dimensional laminar boundary layers in “Theory of Laminar flows”, Ed. F.K. Moore, Princeton University Press.
Mellor, G.L., (1972). The large Reynolds number asymptotic theory of turbulent boundary layers. Int. J. Engng. Sci., 10, 851.
Mizushina, T., and Usui, H., (1977). Reduction of eddy diffusion for momentum and heat in viscoleastic fluid flow in a circular tube. Phys. Fluids, 20, S100.
Nychas, S.G., Hershey, H.C., and Brodkey, R.S., (1973). A visual study of turbulent flow, J. Fluid Mech., 61, 513.
Offen, G.R., and Kline, S.J., (1974). Combined dye-streak and hydrogen bubble visual observations of a turbulent boundary layer, J. Fluid Mech., 62, 223.
Offen, G.R., and Kline, S.J., (1975). A proposed model of the bursting process in turbulent boundary layers, J. Fluid Mech., 70, 209.
Orszag, S.A., (1978). Prediction of compliant wall drag reduction-Part II, Cambridge Hydrodynamics Report 11.
Praturi, A.K., and Brodkey, R.S., (1978). A stereoscopic visual study of coherent structures in turbulent shear flow, J. Fluid Mech., 89, 251.
Rajagopalan, S., and Antonia, R.A., (1979). Some properties of the large structures in a fully developed turbulent duct flow, Phys. Fluids, 22, 614.
Ramapriyan, B.R. and B.G. Shivaprasad, (1977). Mean flow measurements in turbulent boundary layers along mildly curved surfaces. AIAA Journal, 15, 189.
Ramapriyan, B.R., and B.G. Shivaprasad, (1978). The structure of turbulent boundary layers along mildly curved surfaces, J. Fluid Mech., 76, 561.
Schumann, U. (1975). Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli, J. Comp. Phys., 18, 376.
Senda, M., Susuki, K. and Sats, T., (1979). Turbulence structure related to the heat transfer in a turbulent boundary layer with injection, 2nd symposium on Turbulent Shear Flows, London, 1979.
Shen, S.F., (1964). Stability of laminar flows, in: Theory of laminar flows, edited by F.K. Moore, Princeton Univ. Press, New Jersey.
Shubert, G., and Corcos, G.M., (1967). The dynamics of turbulence near a wall according to a linear model, J. Fluid Mech., 29, 113.
Sternberg, J., (1962). A theory for the viscous sublayer of a turbulent flow, J. Fluid Mech., 13, 241.
Sternberg, J., (1968). Discussion, Proc. of AFOSR-IFP-Stanford Conf. on computations of turbulent boundary layers. Ed: S.J. Kline et al., Vol. 1, p. 411.
Stuart, J.T., (1965). The production of intense shear layers by vortex stretching and convection, AGARD Rep. 514.
Tennekes, H., and Lumley, J.L., (1974). A first course in turbulence, MIT Press, Cambridge.
Virk, P.S., (1975). Drag reduction fundamentals, AICHE J., 21, 625.
Willmarth, W.W., (1975). Structure of turbulence in boundary layers, Adv. App. Mech., vol. 15, p. 159., Academic Press.
Willmarth, W.W., and Woodridge, G.E., (1962). Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer, J. Fluid Mech., 14, 187.
Witting, H., (1958). Ober den Einfluss der Strömlinien-Krümmung auf die stabilität Laminarer Strömingen, Arch. Rat. Mech. Anal., 2, No. 3, 243.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Beljaars, A.C.M., Krishna Prasad, K. (1981). A model for periodic structures in turbulent boundary layers. In: Jimenez, J. (eds) The Role of Coherent Structures in Modelling Turbulence and Mixing. Lecture Notes in Physics, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10289-2_23
Download citation
DOI: https://doi.org/10.1007/3-540-10289-2_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10289-2
Online ISBN: 978-3-540-38425-0
eBook Packages: Springer Book Archive