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Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence

Published online by Cambridge University Press:  16 January 2024

Diego C.P. Blanco Open the ORCID record for Diego C.P. Blanco [Opens in a new window] ,
Ardeshir Hanifi Open the ORCID record for Ardeshir Hanifi [Opens in a new window] ,
Dan S. Henningson Open the ORCID record for Dan S. Henningson [Opens in a new window]  and
André V.G. Cavalieri Open the ORCID record for André V.G. Cavalieri [Opens in a new window]
Diego C.P. Blanco*
Affiliation:
Divisão de Engenharia Aeroespacial, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil
Ardeshir Hanifi
Affiliation:
KTH Engineering Mechanics, FLOW Turbulence Lab, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden
Dan S. Henningson
Affiliation:
KTH Engineering Mechanics, FLOW Turbulence Lab, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden
André V.G. Cavalieri
Affiliation:
Divisão de Engenharia Aeroespacial, Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil
*
†Email address for correspondence: diegodcpb@ita.br
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Abstract

Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free-stream turbulence are considered in the present work. Within an input–output model, where nonlinear terms of the incompressible Navier–Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric nonlinear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or nonlinear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the nonlinear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.

JFM classification

Boundary Layers: Boundary layer receptivity Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 979 , 25 January 2024 , A31
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Andersson, P., Berggren, M. & Henningson, D.S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.CrossRefGoogle Scholar
Antoni, J. & Schoukens, J. 2009 Optimal settings for measuring frequency response functions with weighted overlapped segment averaging. IEEE Trans. Instrum. Meas. 58 (9), 3276–3287.CrossRefGoogle Scholar
Berlin, S., Wiegel, M. & Henningson, D.S. 1999 Numerical and experimental investigations of oblique boundary layer transition. J. Fluid Mech. 393, 23–57.CrossRefGoogle Scholar
Blanco, D.C., Martini, E., Sasaki, K. & Cavalieri, A.V. 2022 Improved convergence of the spectral proper orthogonal decomposition through time shifting. J. Fluid Mech. 950, A9.CrossRefGoogle Scholar
Borée, J. 2003 Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Exp. Fluids 35 (2), 188–192.CrossRefGoogle Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 80–96.CrossRefGoogle Scholar
Brandt, L., Henningson, D.S. & Ponziani, D. 2002 Weakly nonlinear analysis of boundary layer receptivity to free-stream disturbances. Phys. Fluids 14 (4), 1426–1441.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D.S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Butler, K.M. & Farrell, B.F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A8, 1637–1650.CrossRefGoogle Scholar
Cheung, L.C. & Zaki, T.A. 2014 An exact representation of the nonlinear triad interaction terms in spectral space. J. Fluid Mech. 748, 175–188.CrossRefGoogle Scholar
Chevalier, M., Hæpffner, J., Bewley, T.R. & Henningson, D.S. 2006 State estimation in wall-bounded flow systems. Part 2. Turbulent flows. J. Fluid Mech. 552, 167–187.CrossRefGoogle Scholar
Chevalier, M., Lundbladh, A. & Henningson, D.S. 2007 Simson – a pseudo-spectral solver for incompressible boundary layer flow. Tech. Rep. TRITA-MEK.Google Scholar
Denissen, N.A. & White, E.B. 2008 Roughness-induced bypass transition, revisited. AIAA J. 46 (7), 1874–1877.CrossRefGoogle Scholar
von Deyn, L.H., Forooghi, P., Frohnapfel, B., Schlatter, P., Hanifi, A. & Henningson, D.S. 2020 Direct numerical simulations of bypass transition over distributed roughness. AIAA J. 58 (2), 702–711.CrossRefGoogle Scholar
Dong, M. & Wu, X. 2013 On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances. J. Fluid Mech. 732, 616–659.CrossRefGoogle Scholar
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18 (4), 487–488.CrossRefGoogle Scholar
Farrell, B.F., Ioannou, P.J., Jiménez, J., Constantinou, N.C., Lozano-Durán, A. & Nikolaidis, M.-A. 2016 A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow. J. Fluid Mech. 809, 290–315.CrossRefGoogle Scholar
Fransson, J.H.M., Matsubara, M. & Alfredsson, P.H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.CrossRefGoogle Scholar
Fransson, J.H.M. & Shahinfar, S. 2020 On the effect of free-stream turbulence on boundary-layer transition. J. Fluid Mech. 899, A23.CrossRefGoogle Scholar
Grosch, C.E. & Salwen, H. 1978 The continuous spectrum of the Orr-Sommerfeld equation. Part 1. The spectrum and the eigenfunctions. J. Fluid Mech. 87 (1), 33–54.CrossRefGoogle Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Hæpffner, J., Chevalier, M., Bewley, T.R. & Henningson, D.S. 2005 State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows. J. Fluid Mech. 534, 263–294.CrossRefGoogle Scholar
Jacobs, R.G. & Durbin, P.A. 1998 Shear sheltering and the continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10 (8), 2006–2011.CrossRefGoogle Scholar
Jacobs, R.G. & Durbin, P.A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jovanović, M.R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145–183.CrossRefGoogle Scholar
Karban, U., Martini, E., Cavalieri, A., Lesshafft, L. & Jordan, P. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. J. Fluid Mech. 939, A36.CrossRefGoogle Scholar
Kendall, J. 1998 Experiments on boundary-layer receptivity to freestream turbulence. AIAA Paper 1998-530.CrossRefGoogle Scholar
Klebanoff, P. 1971 Effect of free-stream turbulence on a laminar boundary layer. In Bulletin of the American Physical Society, vol. 16, p. 1323. American Institute of Physics.Google Scholar
Landahl, M.T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243–251.CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.CrossRefGoogle Scholar
Martini, E., Cavalieri, A.V.G., Jordan, P. & Lesshafft, L. 2020 a Accurate frequency domain identification of odes with arbitrary signals. arXiv:1907.04787.Google Scholar
Martini, E., Cavalieri, A.V.G., Jordan, P., Towne, A. & Lesshafft, L. 2020 b Resolvent-based optimal estimation of transitional and turbulent flows. J. Fluid Mech. 900, A2.CrossRefGoogle Scholar
Matsubara, M. & Alfredsson, P.H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.CrossRefGoogle Scholar
McKeon, B.J. & Sharma, A.S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Moffatt, H.K. 2014 Note on the triad interactions of homogeneous turbulence. J. Fluid Mech. 741, R3.CrossRefGoogle Scholar
Morkovin, M.V. 1969 On the many faces of transition. In Viscous Drag Reduction (ed. C.S. Wells), pp. 1–31. Springer.CrossRefGoogle Scholar
Morkovin, M.V. 1985 Bypass transition to turbulence and research desiderata. In Transition in Turbines, pp. 161–204. National Aeronautics and Space Administration.Google Scholar
Morkovin, M.V. 1990 On roughness-induced transition: facts, views, and speculations. In Instability and Transition (ed. M.Y. Hussaini & R.G. Voigt), pp. 281–295. Springer.CrossRefGoogle Scholar
Morkovin, M.V., Reshotko, E. & Herbert, T. 1994 Transition in open flow systems – a reassessment. Bull. Am. Phys. Soc. 39, 1882.Google Scholar
Morra, P., Nogueira, P.A.S., Cavalieri, A.V.G. & Henningson, D.S. 2021 The colour of forcing statistics in resolvent analyses of turbulent channel flows. J. Fluid Mech. 907, A24.CrossRefGoogle Scholar
Nogueira, P.A.S., Morra, P., Martini, E., Cavalieri, A.V.G. & Henningson, D.S. 2021 Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow. J. Fluid Mech. 908, A32.CrossRefGoogle Scholar
Reed, H.L., Saric, W.S. & Arnal, D. 1996 Linear stability theory applied to boundary layers. Annu. Rev. Fluid Mech. 28 (1), 389–428.CrossRefGoogle Scholar
Reshotko, E. 1984 Disturbances in a laminar boundary layer due to distributed surface roughness. In Turbulence and Chaotic Phenomena in Fluids, pp. 39–46. Elsevier.Google Scholar
Reshotko, E. 2001 Transient growth: a factor in bypass transition. Phys. Fluids 13 (5), 1067–1075.CrossRefGoogle Scholar
Rogallo, R.S. 1981 Numerical Experiments in Homogeneous Turbulence, vol. TM-81315. National Aeronautics and Space Administration.Google Scholar
Rosenberg, K. & McKeon, B.J. 2019 Efficient representation of exact coherent states of the Navier–Stokes equations using resolvent analysis. Fluid Dyn. Res. 51 (1), 011401.CrossRefGoogle Scholar
Saric, W.S., Reed, H.L. & Kerschen, E.J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291–319.CrossRefGoogle Scholar
Sasaki, K., Morra, P., Cavalieri, A.V.G., Hanifi, A. & Henningson, D.S. 2020 On the role of actuation for the control of streaky structures in boundary layers. J. Fluid Mech. 883, A34.CrossRefGoogle Scholar
Schlatter, P. 2001 Direct numerical simulation of laminar-turbulent transition in boundary layer subject to free-stream turbulence. Master's thesis, KTH Royal Institute of Technology/ETH Zürich.Google Scholar
Schlatter, P., Stolz, S. & Kleiser, L. 2006 Large-eddy simulation of spatial transition in plane channel flow. J. Turbul. 7, N33.CrossRefGoogle Scholar
Schmid, P.J., Henningson, D.S., Khorrami, M.R. & Malik, M.R. 1993 A study of eigenvalue sensitivity for hydrodynamic stability operators. Theor. Comput. Fluid Dyn. 4 (5), 227–240.CrossRefGoogle Scholar
Schmid, P.J., Reddy, S.C. & Henningson, D.S. 1996 Transition thresholds in boundary layer and channel flows. In Advances in Turbulence VI (ed. S. Gavrilakis, L. Machiels & P.A. Monkewitz), pp. 381–384. Springer.CrossRefGoogle Scholar
Schubauer, G.B. & Skramstad, H.K. 1947 Laminar boundary-layer oscillations and stability of laminar flow. J. Aeronaut. Sci. 14 (2), 69–78.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures part I: coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Stolz, S., Adams, N.A. & Kleiser, L. 2001 An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. Fluids 13 (4), 997–1015.CrossRefGoogle Scholar
Suder, K.L., Obrien, J.E. & Reshotko, E. 1988 Experimental study of bypass transition in a boundary layer. Master's thesis, Lewis Research Center, NASA.Google Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Towne, A., Lozano-Durán, A. & Yang, X. 2020 Resolvent-based estimation of space–time flow statistics. J. Fluid Mech. 883, A17.CrossRefGoogle Scholar
Towne, A., Schmidt, O.T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Webber, J.B.W. 2012 A bi-symmetric log transformation for wide-range data. Meas. Sci. Technol. 24 (2), 027001.CrossRefGoogle Scholar
Welch, P.D. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.CrossRefGoogle Scholar
Westin, K.J.A., Boiko, A.V., Klingmann, B.G.B., Kozlov, V.V. & Alfredsson, P.H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 1. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193–218.CrossRefGoogle Scholar