Abstract
The Karhunen—Loève procedure is used to analyze two turbulent channel flow simulations. In both instances this reveals the presence of propagating plane wave structures in the turbulent flows. These waves appear to play an essential role in the local production of turbulence via bursting or sweeping events. The envelope of the propagating modes propagates with a speed which is equal to the mean velocity at the locus of maximal average Reynolds stress. Despite marked differences between the two flows similar results are obtained from each simulation. This is suggestive of the existence of universal or near universal features in the turbulent boundary layer. An analogy with critical layer mechanisms of transitional flows is discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Armbruster, D., Guckenheimer, J., and Holmes, P. (1988). Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry. Phys. D, 29, 257.
Aubry, N., Holmes, P., Lumley, J.L., and Stone, E.J. (1988). The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech., 192, 115.
Ball, K.S., Sirovich, L., and Keefe, L.R. (1991). Dynamical eigenfunction decomposition of turbulent channel flow. Internat. J. Numer. Methods Fluids, 12, 585.
Bayly, B.J., Orszag, S.A., and Herbert, T. (1988). Instability mechanisms in shear-flow transition. Ann. Rev. Fluid Mech., 20, 359.
Dean, R.B. (1978). Reynolds number dependents of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Engrg., 100, 215.
Eckelmann, H. (1974). The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech., 65, 439.
Handler, R.A., Hendricks, E.W., and Leighton, R.I. (1989). Low Reynolds number calculation of turbulent channel flow: A general discussion. NRL Memorandum Report 6410.
Herbert, T. (1988). Secondary instability of boundary layers. Ann. Rev. Fluid Mech., 20, 487.
Kim, J., Moin, P., and Moser, R. (1987). Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech., 177, 133.
Kline, S.J., Reynolds, W.C., Schaub, F.A., and Rundstadler, P.W. (1967). The structure of turbulent boundary layers. J. Fluid Mech., 30, 741.
Kreplin, H., and Eckelmann, H. (1979). Behavior of the three fluctuation velocity components in the wall region of a turbulent channel flow. Phys. Fluids, 22, 1233.
Loève, M. M. (1955). Probability Theory. van Nostrand, Princeton, NJ.
Lumley, J.L. (1967). The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (A.M. Yaglom and V.I. Tatarski, eds.), pp. 166–178. Nauka, Moscow.
Lumley, J.L. (1970). Stochastic Tools in Turbulence. Academic Press, New York.
Lumley, J.L. (1981). Coherent structures in turbulence. In Transition and Turbulence (R.E. Meyer, ed.), pp. 215–242. Academic Press, New York.
Marcus, P.S. (1984). Simulation of Taylor-Couette flow. Part I: Numerical methods and comparison with experiment. J. Fluid Mech., 146, 45.
Orszag, S.A., and Kells, L.C. (1980). Transition to turbulence in plane Poiseuille and Couette flow. J. Fluid Mech., 96, 159.
Panton, R.L. (1991). Scaling turbulent wall layers, J. Fluids Engrg., 112, 425.
Patel, V.C., and Head, M.R. (1969). Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J. Fluid Mech., 38, 181.
Perry, A.E., and Chong, M.S. (1982). On the mechanism of wall turbulence. J. Fluid Mech., 119, 173.
Praturi, A.K., and Brodkey, R.S. (1978). A steroscopic visual study of coherent structures in turbulent shear flow. J. Fluid Mech., 89, 251.
Sirovich, L. (1987). Turbulence and the dynamics of coherent structures, Part I: Coherent structures, Part II: Symmetries and transformations, Part III: Dynamics and scaling. Quart. Appl. Math., XLV (3), 561–590.
Sirovich, L. (1989). Chaotic dynamics of coherent structures. Phys. D, 37, 126.
Sirovich, L. (1991). Analysis of turbulent flows by means of the empirical eigenfunction. Fluid Dynamics Res. (in press).
Sirovich, L., and Rodriguez, J.D. (1987). Coherent structures and chaos: A model problem. Phys. Lett. A, 120, 211.
Sirovich, L., Ball, K.S., and Keefe, L.R. (1990). Plane waves and structures in turbulent channel flow. Phys. Fluids A, 2(12), 2217.
Sreenivasan, K.R. (1988). A unified view of the origin and morphology of the turbulent boundary layer structure. In Turbulence Management and Relaminarization (H.W. Liepmann and R. Narasimha, eds.), pp. 37–61. Springer-Verlag, New York.
Stone, E., and Holmes, P. (1989). Noise induced intermittency in a model of a turbulent boundary layer. Phys. D, 37, 20.
Tennekes, H., and Lumley, J.L. (1972). A First Course in Turbulence. MIT Press, Cambridge, MA.
Townsend, A.A. (1966). The flow in a turbulent boundary layer after a change in surface roughness. J. Fluid Mech., 26, 255.
Willmarth, W.W. (1975a). Structure of turbulence in boundary layers. Adv. Appl. Mech., 15, 159.
Willmarth, W.W. (1975b). Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech., 7, 13.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.
We gratefully acknowledge support provided by DARPA-URI under Contract Number N00014-86-K0754. The use of the Pittsburgh Supercomputing Center is also acknowledged.
Rights and permissions
About this article
Cite this article
Sirovich, L., Ball, K.S. & Handler, R.A. Propagating structures in wall-bounded turbulent flows. Theoret. Comput. Fluid Dynamics 2, 307–317 (1991). https://doi.org/10.1007/BF00271470
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00271470