Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 26
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    He, K. Seddighi, M. and He, S. 2016. DNS study of a pipe flow following a step increase in flow rate. International Journal of Heat and Fluid Flow, Vol. 57, p. 130.


    Alizard, Frédéric 2015. Linear stability of optimal streaks in the log-layer of turbulent channel flows. Physics of Fluids, Vol. 27, Issue. 10, p. 105103.


    Alizard, Frédéric Robinet, Jean-Christophe and Filliard, Guillaume 2015. Sensitivity analysis of optimal transient growth for turbulent boundary layers. European Journal of Mechanics - B/Fluids, Vol. 49, p. 373.


    Ashton, R Viola, F Gallaire, F and Iungo, G V 2015. Effects of incoming wind condition and wind turbine aerodynamics on the hub vortex instability. Journal of Physics: Conference Series, Vol. 625, p. 012033.


    Camarri, Simone 2015. Flow control design inspired by linear stability analysis. Acta Mechanica, Vol. 226, Issue. 4, p. 979.


    Thomas, Vaughan L. Farrell, Brian F. Ioannou, Petros J. and Gayme, Dennice F. 2015. A minimal model of self-sustaining turbulence. Physics of Fluids, Vol. 27, Issue. 10, p. 105104.


    Brandt, Luca 2014. The lift-up effect: The linear mechanism behind transition and turbulence in shear flows. European Journal of Mechanics - B/Fluids, Vol. 47, p. 80.


    Mettot, Clément Sipp, Denis and Bézard, Hervé 2014. Quasi-laminar stability and sensitivity analyses for turbulent flows: Prediction of low-frequency unsteadiness and passive control. Physics of Fluids, Vol. 26, Issue. 4, p. 045112.


    Mettot, Clément Renac, Florent and Sipp, Denis 2014. Computation of eigenvalue sensitivity to base flow modifications in a discrete framework: Application to open-loop control. Journal of Computational Physics, Vol. 269, p. 234.


    Pirozzoli, Sergio 2014. Revisiting the mixing-length hypothesis in the outer part of turbulent wall layers: mean flow and wall friction. Journal of Fluid Mechanics, Vol. 745, p. 378.


    Squire, J. and Bhattacharjee, A. 2014. MAGNETOROTATIONAL INSTABILITY: NONMODAL GROWTH AND THE RELATIONSHIP OF GLOBAL MODES TO THE SHEARING BOX. The Astrophysical Journal, Vol. 797, Issue. 1, p. 67.


    Thomas, Vaughan L. Lieu, Binh K. Jovanović, Mihailo R. Farrell, Brian F. Ioannou, Petros J. and Gayme, Dennice F. 2014. Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow. Physics of Fluids, Vol. 26, Issue. 10, p. 105112.


    Jiménez, Javier 2013. How linear is wall-bounded turbulence?. Physics of Fluids, Vol. 25, Issue. 11, p. 110814.


    Jiménez, Javier 2013. Near-wall turbulence. Physics of Fluids, Vol. 25, Issue. 10, p. 101302.


    McKeon, B. J. Sharma, A. S. and Jacobi, I. 2013. Experimental manipulation of wall turbulence: A systems approach. Physics of Fluids, Vol. 25, Issue. 3, p. 031301.


    Foures, D. P. G. Caulfield, C. P. and Schmid, P. J. 2012. Variational framework for flow optimization using seminorm constraints. Physical Review E, Vol. 86, Issue. 2,


    Duque, C A Baig, M F Lockerby, D A Chernyshenko, S I and Davies, C 2011. Modelling turbulent skin-friction control using linearised Navier-Stokes equations. Journal of Physics: Conference Series, Vol. 318, Issue. 4, p. 042026.


    Hwang, Yongyun and Cossu, Carlo 2010. Self-Sustained Process at Large Scales in Turbulent Channel Flow. Physical Review Letters, Vol. 105, Issue. 4,


    Marusic, I. McKeon, B. J. Monkewitz, P. A. Nagib, H. M. Smits, A. J. and Sreenivasan, K. R. 2010. Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues. Physics of Fluids, Vol. 22, Issue. 6, p. 065103.


    McKeon, Beverley and Sharma, Ati 2010. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.

    ×
  • Journal of Fluid Mechanics, Volume 619
  • January 2009, pp. 79-94

Optimal transient growth and very large–scale structures in turbulent boundary layers

  • CARLO COSSU (a1), GREGORY PUJALS (a1) (a2) and SEBASTIEN DEPARDON (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112008004370
  • Published online: 25 January 2009
Abstract

The optimal energy growth of perturbations sustained by a zero pressure gradient turbulent boundary is computed using the eddy viscosity associated with the turbulent mean flow. It is found that even if all the considered turbulent mean profiles are linearly stable, they support transient energy growths. The most amplified perturbations are streamwise uniform and correspond to streamwise streaks originated by streamwise vortices. For sufficiently large Reynolds numbers two distinct peaks of the optimal growth exist, respectively scaling in inner and outer units. The optimal structures associated with the peak scaling in inner units correspond well with the most probable streaks and vortices observed in the buffer layer, and their moderate energy growth is independent of the Reynolds number. The energy growth associated with the peak scaling in outer units is larger than that of the inner peak and scales linearly with an effective turbulent Reynolds number formed with the maximum eddy viscosity and a modified Rotta–Clauser length based on the momentum thickness. The corresponding optimal perturbations consist of very large–scale structures with a spanwise wavelength of the order of 8δ. The associated optimal streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer, in which they are proportional to the mean flow velocity. These outer streaks protrude far into the near wall region, having still 50% of their maximum amplitude at y+ = 20. The amplification of very large–scale structures appears to be a robust feature of the turbulent boundary layer: optimal perturbations with spanwise wavelengths ranging from 4δ to 15δ can all reach 80% of the overall optimal peak growth.

Copyright
Corresponding author
Email address for correspondence: Carlo.Cossu@ladhyx.polytechnique.fr
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

P. Andersson , M. Berggren & D. Henningson 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134150.

A. Bottaro , H. Souied & B. Galletti 2006 Formation of secondary vortices in a turbulent square-duct flow. AIAA J. 44, 803811.

K. M. Butler & B. F. Farrell 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 16371650.

K. M. Butler & B. F. Farrell 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids 5, 774777.

P. Corbett & A. Bottaro 2000 Optimal perturbations for boundary layers subject to streamwise pressure gradient. Phys. Fluids 12, 120130.

C. Cossu & L. Brandt 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14, L57L60.

T. Ellingsen & E. Palm 1975 Stability of linear flow. Phys. Fluids 18, 487.

B. F. Farrell & P. J. Ioannou 1993 Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys. Fluids 5, 13901400.

B. F. Farrell & P. J. Ioannou 1996 Generalized stability theory. Part I: autonomous operators. Part II: nonautonomous operators. J. Atmos. Sci. 53, 20252053.

B. F. Farrell & P. J. Ioannou 1998 Perturbation structure and spectra in turbulent channel flow. Theoret. Comput. Fluid Dyn. 11, 237250.

J. Fransson , L. Brandt , A. Talamelli & C. Cossu 2004 Experimental and theoretical investigation of the non-modal growth of steady streaks in a flat plate boundary layer. Phys. Fluids 16, 36273638.

J. Fransson , L. Brandt , A. Talamelli & C. Cossu 2005 Experimental study of the stabilisation of Tollmien–Schlichting waves by finite amplitude streaks. Phys. Fluids 17, 054110.

J. Fransson , A. Talamelli , L. Brandt & C. Cossu 2006 Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96, 064501.

S. Hoyas & J. Jiménez 2006 Scaling of the velocity fluctuations in turbulent channels up to reτ = 2003. Phys. Fluids 18, 011702.

O. Kitoh & M. Umeki 2008 Experimental study on large-scale streak structure in the core region of turbulent plane Couette flow. Phys. Fluids 20, 025107.

E. Lauga & C. Cossu 2005 A note on the stability of slip channel flows. Phys. Fluids 17, 088106.

P. A. Monkewitz , K. A. Chauhan & H. M. Nagib 2007 Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101.

J. M. Österlund , A. V. Johansson , H. M. Nagib & M. H. Hites 2000. A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 1.

P. J. Schmid & D. S. Henningson 2001 Stability and Transition in Shear Flows. Springer.

L. N. Trefethen , A. E. Trefethen , S. C. Reddy & T. A. Driscoll 1993 A new direction in hydrodynamic stability: beyond eigenvalues. Science 261, 578584.

F. Waleffe 1995 Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process. Stud. Appl. Math. 95, 319343.

J. A. C. Weideman & S. C. Reddy 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Soft. 26 (4), 465519.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax