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Evolution of three-dimensional coherent structures in a flat-plate boundary layer

  • Dietmar Rempfer (a1) and Hermann F. Fasel (a2)
Abstract

Using a data base generated by a numerical simulation, the three-dimensional coherent structures of a transitional, spatially evolving boundary layer are determined and their spatio-temporal behaviour is investigated in detail. The coherent structures are calculated by the proper orthogonal decomposition method (POD), which leads to an expansion of the flow field variables into Karhunen-Loéve eigenfunctions. It is shown that the dynamical coherent structures of the flat-plate boundary layer can be described by pairs of eigenfunctions that contain complete information on the spatial evolution of the structures. It is further demonstrated that first-order coherent structures determined by POD correspond to structures that are observed in experiments. In the region of the boundary layer where the spike signals of transition occur, higher-order coherent structures also play an essential role. By considering these higher-order structures as well as their dynamical behaviour in time, a compact description of the flow phenomena in the boundary layer can be obtained. The description of the events occurring at the spike stages of the transitional boundary layer shows, from a coherent structures point of view, striking similarities to the bursting event of fully turbulent boundary layers.

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Aubry, N., Guyonnet, R. & Lima, R.1991Spatiotemporal analysis of complex signals: theory and applications. J. Statist. Phys.64, 683739.

Aubry, N., Guyonnet, R. & Lima, R.1992Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions. J. Nonlin. Sci.2, 183215.

Aubry, N., Holmes, P., Lumley, J. L. & Stone, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115173.

Bakewell, H.P. & Lumley, J. L.1967Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids A 10, 18801889.

Ball, K.S., Sirovich, L. & Keefe, L. R.1991Dynamical eigenfunction decomposition of turbulent channel flow. Intl J. Num. Meth. Fluids12, 585604.

Blackwelder, R. F.1983Analogies between transitional and turbulent boundary layers. Phys. Fluids A 26, (10), 28072815.

Breuer, K.S. & Sirovich, L.1991The use of the Karhunen-Loéve procedure for the calculation of linear eigenfunctions. J. Comput. Phys96, 277296.

Glezer, A., Kadioglu, Z. & Pearlstein, A. J.1989Development of an extended proper orthogonal decomposition and its application to a time-periodically forced plane mixing layer. Phys. Fluids A 1, 13631373.

Kirby, M., Boris, J. & Sirovich, L.1990An eigenfunction analysis of axisymmetric jet flow. J. Comput. Phys.90, 98122.

Klebanoff, P.S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 134.

Kleiser, L & Zang, T.A.1991Numerical simulation of transition in wall-bounded shear flows. Ann. Rev. Fluid Mech.23, 495537.

Landahl, M.T. 1972 Wave mechanics of breakdown. J. Fluid Mech. 56, 775802.

Lorenz, E. N.1963Deterministic nonperiodic flow. J.Atmos. Sci.20, 130141.

Moin, P. & Moser, R. D. 1989 Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471509.

Park, H. & Sirovich, L.1990Turbulent thermal convection in a finite domain: Part II. Numerical results. Phys. Fluids A 2, 16591668.

Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots. J. Fluid Mech. 104, 387405.

Rajaee, M. & Karlsson, S. K. F.1990Shear flow coherent structures via Karhunen-Loéve expansion. Phys. Fluids A 2, 22492251.

Rajaee, M., Karlsson, S. K. F. & Sirovich, L. 1994 Low-dimensional description of free shear flow coherent structures and their dynamical behaviour. J. Fluid Mech. 258, 129.

Robinson, S. K.1991Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech.23, 601639.

Sirovich, L.1987Turbulence and the dynamics of coherent structures. Q. Appl. Maths45, 561590.

Sirovich, L., Ball, K.S. & Handler, K. H.1991Propagating structures in wall-bounded turbulent flows. Theoret. Comput. Fluid Dyn.2, 307317.

Sirovich, L., Ball, K.S. & Keefe, L. R.1990Plane waves and structures in turbulent channel flow. Phys. Fluids A 2, 22172226.

Sirovich, L., Kirby, M. & Winter, M.1990An eigenfunction approach to large scale transitional structures in jet flow. Phys. Fluids A 2, 127136.

Sirovich, L. & Park, H.1990Turbulent thermal convection in a finite domain: Part I. theory. Phys. Fluids A 2, 16491658.

Wallace, J. M. & Hussain, F.1990Coherent structures in turbulent shear flows. Appl. Mech. Rev.43, S203S209.

Williams, D. R., Fasel, H. & Hama, F. R. 1984 Experimental determination of the threedimensional vorticity field in the boundary-layer transition process. J. Fluid Mech. 149, 179203.

Zhou, X. & Sirovich, L.1992Coherence and chaos in a model of a turbulent boundary layer. Phys. Fluids A 4, 28552874.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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