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Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows

Published online by Cambridge University Press:  12 August 2020

Leandra I. Abreu Open the ORCID record for Leandra I. Abreu [Opens in a new window] ,
André V. G. Cavalieri Open the ORCID record for André V. G. Cavalieri [Opens in a new window] ,
Philipp Schlatter Open the ORCID record for Philipp Schlatter [Opens in a new window] ,
Ricardo Vinuesa Open the ORCID record for Ricardo Vinuesa [Opens in a new window]  and
Dan S. Henningson
Leandra I. Abreu*
Affiliation:
São Paulo State University (UNESP), Campus of São João da Boa Vista, 13876-750SP, Brazil Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900SP, Brazil
André V. G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900SP, Brazil
Philipp Schlatter
Affiliation:
KTH Mechanics, Linné FLOW Centre, StockholmSE-100-44, Sweden
Ricardo Vinuesa
Affiliation:
KTH Mechanics, Linné FLOW Centre, StockholmSE-100-44, Sweden
Dan S. Henningson
Affiliation:
KTH Mechanics, Linné FLOW Centre, StockholmSE-100-44, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers $Re_{\tau } = 180$ and $550$. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.

JFM classification

Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abreu, L. I., Cavalieri, A. V. G. & Wolf, W. R. 2017 Coherent hydrodynamic waves and trailing-edge noise. AIAA Paper 2017-3173. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Andersson, P., Berggren, M. & Henningson, D. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.CrossRefGoogle Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.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
Cavalieri, A. V. G., Jordan, P. & Lesshafft, L. 2019 Wave-packet models for jet dynamics and sound radiation. Appl. Mech. Rev. 71 (2), 020802.CrossRefGoogle Scholar
Del Alamo, J. C. & Jimenez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to $Re_{\theta }=8300$. Intl J. Heat Fluid Flow 47, 57–69.CrossRefGoogle Scholar
El Khoury, G. K., Schlatter, P., Noorani, A., Fischer, P. F., Brethouwer, G. & Johansson, A. V. 2013 Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers. Flow Turbul. Combust. 91 (3), 475–495.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. 1993 Stochastic forcing of the linearized Navier–Stokes equations. Phys. Fluids A 5 (11), 2600–2609.CrossRefGoogle Scholar
Farrell, B. F. & Ioannou, P. J. 2012 Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech. 708, 149–196.CrossRefGoogle Scholar
Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G. 2008 Nek5000: Open Source Spectral Element CFD Solver. Available at: http://nek5000.mcs.anl.gov.Google Scholar
Gupta, A. K., Laufer, J. & Kaplan, R. E. 1971 Spatial structure in the viscous sublayer. J. Fluid Mech. 50 (3), 493–512.CrossRefGoogle Scholar
Hall, P. & Sherwin, S. 2010 Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures. J. Fluid Mech. 661, 178–205.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
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_{\tau }=2003$. Phys. Fluids 18 (1), 011702.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 51–73.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842.CrossRefGoogle Scholar
Jovanović, M. R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145–183.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.CrossRefGoogle 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
Lesshafft, L., Semeraro, O., Jaunet, V., Cavalieri, A. V. G. & Jordan, P. 2019 Resolvent-based modeling of coherent wave packets in a turbulent jet. Phys. Rev. Fluids 4 (6), 063901.CrossRefGoogle Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. A. M. Yaglom & V. I. Tatarsky). Nauka.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence, Applied Mathematics and Mechanics, vol. 12. Academic.Google Scholar
Marusic, I., Baars, W. J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner-outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.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
McKeon, B. J., Sharma, A. S. & Jacobi, I. 2013 Experimental manipulation of wall turbulence: a systems approach. Phys. Fluids 25 (3), 031301.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Morra, P., Sasaki, K., Hanifi, A., Cavalieri, A. V. G. & Henningson, D. 2019 A realizable data-driven approach to delay bypass transition with control theory. arXiv:1902.05049.CrossRefGoogle Scholar
Nogueira, P. A. S., Morra, P., Martini, E., Cavalieri, A. V. G. & Henningson, D. S. 2020 Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow. arXiv:2001.02576.Google Scholar
Picard, C. & Delville, J. 2000 Pressure velocity coupling in a subsonic round jet. Int. J. Heat Fluid Flow 21 (3), 359–364.CrossRefGoogle Scholar
Pickering, E. M., Rigas, G., Sipp, D., Schmidt, O. T. & Colonius, T. 2020 Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets. arXiv:2005.10964.CrossRefGoogle Scholar
Sasaki, K., Morra, P., Cavalieri, A. V. G., Hanifi, A. & Henningson, D. 2019 On the role of actuation for the control of streaky structures in boundary layers. arXiv:1902.04923.CrossRefGoogle Scholar
Schmidt, O. T. & Colonius, T. 2020 Guide to spectral proper orthogonal decomposition. AIAA J. 58 (3), 1023–1033.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.CrossRefGoogle Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Towne, A., Lozano-Durán, A. & Yang, X. 2020 Resolvent-based estimation of space–time flow statistics. J. Fluid Mech. 883.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
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578–584.CrossRefGoogle ScholarPubMed
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar