Abstract
The dynamics of infinitely long steamwise rolls in the wall region of a turbulent boundary layer have been described by a ten dimensional representation of Aubry et al. (1988). In this model, the rolls undergo intermittent cross stream dynamics which qualitatively resemble the cyclic bursting event experimentally observed. The explosion phenomenon in this model is due to the presence of a heteroclinic cycle in the phase space, a connection between saddle points, where each saddle represents streamwise rolls. We demonstrate here that the dynamics of streamwise rolls of finite length is also strongly intermittent. This intermittency is still of the heteroclinic type. Streamwise modes, absent in Aubry et al.’s model and included in the present study, participate to the explosion events, corresponding to a streamwise burst in the physical space. A stability analysis of the systems linearized at the fixed points which represent steady rolls is presented in dynamical systems of dimensions as high as 32 and 54 so that bifurcations to intermittency are clearly identified. We show that all non zero streamwise Fourier modes eventually burst, resulting in a streamwise energy cascade during the bursts. Although the explosion of the zero and first non zero streamwise Fourier modes occur through bifurcations of the system linearized about the fixed points (i.e. the rolls), the activation of all higher modes is a result of non linear phenomena.
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References
Adrian, R. J., Moin, P. and Moser R. D. 1987 Stochastic estimation of conditional eddies in turbulent channel flow. In Proceedings of the 1987 Summer Program of Center for Turbulence Research (NASA Ames/Stanford Univ., Stanford, CA 1987 )
Armbruster, D., Guckenheimer, J. and Holmes, P. 1988 Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Physica 29D, 257–282.
Aubry. N. 1987 A dynamical system/coherent structure approach to the fully developed turbulent wall layer. Ph. D. thesis, Cornell University.
Aubry, N., Holmes, P., Lumley, J.L., and Stone, E. 1988 The dynamics of coherent structures in the wall Region of a turbulent boundary layer. J. Fluid Mech. 192, 115–173.
Aubry, N. and Sanghi, S. 1989 Streamwise and spanwise dynamics in the turbulent wall layer. In Forum on chaotic Flow, ed. K.N. Ghia. New York: ASME.
Aubry, N., Lumley, J.L., and Holmes, P. 1990 The effect of drag reduction on the wall region. Theoret. comput. Fluid Dynamics. In press.
Bakewell, P and Lumley, J.L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 10, 1880–1889.
Blackwelder, R. F. and Eckelman, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94 (3), 577–594.
Cantwell, B.J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457–515.
Corino, E.R. and Brodkey, R.S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1–30.
Curry, J. H., Herring, J. R., Loncaric, J. and Orszag, S.A. 1984. Order and disorder in two-and three-dimensional Benard c onvection. J. Fluid Mech. 147, 1–38.
Doedel, E.J. and Kernevez, J.P. 1985 Software for continuation problems in ordinary differential equations with applications. Applied Mathematics Rep. California Institute of Technology.
Foias, C and Temam, R. 1977 Structure of the set of stationary solutions of the Navier Stokes equations. Comm. Pure Appl., 30, 149–164.
Guezennec, Y. G. 1989 Stochastic estimation of coherent structures in turbulent boundary layers. Phys. Fluids A 1 (6), 1054–1060.
Herzog, S. 1986 The large scale structure in the near-wall region of turbulent pipe flow. Ph.D. thesis, Cornell University.
Hogenes, J.H.A. and Hanratty, T. J. 1982 The use of multiple wall probes to identify coherent flow patterns in the viscous wall region. J. Fluid Mech. 95, 655–679.
Jang, P. S., Benney, D. J. and Gran, R. L. 1986 On the origin of streamwise vortices in a turbulent boundary layer. J. Fluid Mech. 169, 109–123.
Jimenez, J. 1987 Bifurcations and bursting in two-dimensional Poiseuille flow. Phys. Fluids 30 (12), 3644–6.
Jimenez, J., Moin, P., Moser, R. and Keefe, L. 1988 Ejection mechanisms in the sublayer of a turbulent channel. Phys. Fluids 31 (6), 1311–3.
Jimenez, J.and Moin, P. 1989 A minimal turbulent channel. American Physical Society/Division of Fluid Mechanics, 42nd annual meeting, DA3. Palo Alto, CA.
Kline, S.J., Reynolds, W.C., Schraub, F.A. and Runstadler, P.W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 74–173.
Kim, J. 1985 Turbulence structures associated with the bursting event. Phys. Fluids 28, 52–58.
Landahl, M. 1975 Wave breakdown and turbulence. SIAM J. Appl. Math. 28 (4), 735–56.
Loève, M. 1955 Probability Theory. Van Nostrand.
Lumley, J.L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. A.M. Yaglom and V.I. Tatarski ), pp. 166–178. Moscow: Nauka.
Moffatt, H.K. 1989 Fixed points of turbulent dynamical systems and suppression of nonlinearity. In Whither Turbulence (ed J L Lumley ), 22–24 March, Cornell University, NY. Springer-Verlag.
Moin, P. and Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.
Moin, P. and Moser, R.D. 1989 Characteristic-eddy decomposition of turbulence in a channel, J. Fluid Mech. 200, 471–509.
Robinson, S.K., Kline, S.J. and Spalart, P.R. 1988 Quasi-coherent structures in the turbulent boundary layer: Part II. Verification and new information from a numerically simulated flat-plate layer. In Near Wall Turbulence, eds. S. J. Kline et al., Washington DC: Hemisphere.
Silnikov, L. P. 1970 A contribution to the problem of the structure of an extended neighbourhood of a rough equilibrium state of saddle-focus type. Math. USSR Sbornik 10, 91–102.
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Rt = 1410. J. Fluid Mech. 187, 61–98.
Temam, R. 1988 Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematical Sciences 68. Springer-Verlag.
Willmarth, W. W. and Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65–92.
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© 1991 Springer Science+Business Media Dordrecht
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Aubry, N., Sanghi, S. (1991). Bifurcations and bursting of streaks in the turbulent wall layer. In: Metais, O., Lesieur, M. (eds) Turbulence and Coherent Structures. Fluid Mechanics and Its Applications, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7904-9_15
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DOI: https://doi.org/10.1007/978-94-015-7904-9_15
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