Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-16T01:55:18.281Z Has data issue: false hasContentIssue false
  • English
  • Français

Composition of resolvents enhanced by random sweeping for large-scale structures in turbulent channel flows

Published online by Cambridge University Press:  07 February 2023

Ting Wu Open the ORCID record for Ting Wu [Opens in a new window]  and
Guowei He Open the ORCID record for Guowei He [Opens in a new window]
Ting Wu
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Guowei He*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: hgw@lnm.imech.ac.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Composite sweeping-enhanced resolvents, referred to as the ${\boldsymbol {R}}_s^2$ model, are proposed to predict the space–time statistics of large-scale structures in turbulent channel flows. This model incorporates two key mechanisms: (i) eddy damping is introduced to represent random sweeping decorrelation caused by nonlinear forcing, leading to a sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$; and (ii) the sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$ is composited into its iterations ${\boldsymbol {R}}_s^2$ to yield non-zero Taylor time microscales. The resulting ${\boldsymbol {R}}_s^2$ model can correctly predict the frequency spectra and two-point cross-spectra of large-scale structures. This model is compared numerically with eddy-viscosity-enhanced resolvent models. The latter are designed to represent energy transfer instead for time decorrelation, and thus underpredict the characteristic decay time scales. The ${\boldsymbol {R}}_s^2$ model correctly yields the characteristic decay time scales in turbulent channel flows.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 956 , 10 February 2023 , A31
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bamieh, B. & Dahleh, M. 2001 Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13, 3258–3269.CrossRefGoogle Scholar
Bossuyt, J., Meneveau, C. & Meyers, J. 2017 Wind farm power fluctuations and spatial sampling of turbulent boundary layers. J. Fluid Mech. 823, 329–344.CrossRefGoogle Scholar
Cess, R.D. 1958 A survey of the literature on heat transfer in turbulent tube flow. Tech. Rep. Report 8-0529-R24. Westinghouse Research.Google Scholar
De Cillis, G., Cherubini, S., Semeraro, O., Leonardi, S. & De Palma, P. 2022 Stability and optimal forcing analysis of a wind turbine wake: comparison with POD. Renew. Energy 181, 765–785.CrossRefGoogle Scholar
Dong, G.D., Li, Z.B., Qin, J.H. & Yang, X.L. 2022 How far the wake of a wind farm can persist for? Theor. Appl. Mech. Lett. 12, 100314.CrossRefGoogle Scholar
Farrell, B.F. & Ioannou, P.J. 1993 Stochastic forcing of the linearized Navier–Stokes equations. Phys. Fluids A 5, 2600–2609.CrossRefGoogle Scholar
Farrell, B.F. & Ioannou, P.J. 1998 Perturbation structure and spectra in turbulent channel flow. Theor. Comput. Fluid Dyn. 11, 237–250.CrossRefGoogle Scholar
Geng, C.H., He, G.W., Wang, Y.S., Xu, C.X., Lozano-Durán, A. & Wallace, J.M. 2015 Taylor's hypothesis in turbulent channel flow considered using a transport equation analysis. Phys. Fluids 27, 025111.CrossRefGoogle Scholar
Gupta, V., Madhusudanan, A., Wan, M.P., Illingworth, S.J. & Juniper, M.P. 2021 Linear-model-based estimation in wall turbulence: improved stochastic forcing and eddy viscosity terms. J. Fluid Mech. 925, A18.CrossRefGoogle Scholar
He, G.W., Jin, G.D. & Yang, Y. 2017 Space–time correlations and dynamic coupling in turbulent flows. Annu. Rev. Fluid Mech. 49, 51–70.CrossRefGoogle Scholar
He, G.W., Wang, M. & Lele, S.K. 2004 On the computation of space–time correlations by large-eddy simulation. Phys. Fluids 16 (11), 3859–3867.CrossRefGoogle Scholar
He, G.W. & Zhang, J.B. 2006 Elliptic model for space–time correlations in turbulent shear flows. Phys. Rev. E 73, 055303(R).CrossRefGoogle ScholarPubMed
Huang, K.Y. & Katul, G.G. 2022 Profiles of high-order moments of longitudinal velocity explained by the random sweeping decorrelation hypothesis. Phys. Rev. Fluids 7 (4), 044603.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 a Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number. J. Fluid Mech. 643, 333–348.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 b Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 51–73.CrossRefGoogle Scholar
Illingworth, S.J., Monty, J.P. & Marusic, I. 2018 Estimating large-scale structures in wall turbulence using linear models. J. Fluid Mech. 842, 146–162.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
Jovanović, M.R. 2021 From bypass transition to flow control and data-driven turbulence modeling: an input–output viewpoint. Annu. Rev. Fluid Mech. 53, 311–345.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.V.G., Lesshafft, L. & Jordan, P. 2022 Self-similar mechanisms in wall turbulence studied using resolvent analysis. J. Fluid Mech. 939, A36.CrossRefGoogle Scholar
Katul, G.G., Banerjee, T., Cava, D., Germano, M. & Porporato, A. 2016 Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis. Phys. Fluids 28 (9), 095104.CrossRefGoogle Scholar
Kim, K.C. & Adrian, R.J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kraichnan, R.H. 1964 Kolmogorov's hypotheses and Eulerian turbulence theory. Phys. Fluids 7, 1723–1734.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_{\tau }\approx 5200$. J. Fluid Mech. 774, 395–415.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, 063901.CrossRefGoogle Scholar
Liu, C. & Gayme, D.F. 2020 An input–output based analysis of convective velocity in turbulent channels. J. Fluid Mech. 888, A32.CrossRefGoogle Scholar
Martini, E., Cavalieri, A.V.G., Jordan, P., Towne, A. & Lesshafft, L. 2020 Resolvent-based optimal estimation of transitional and turbulent flows. J. Fluid Mech. 900, A2.CrossRefGoogle Scholar
McKeon, B.J. 2017 The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. 817, P1.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
McMullen, R.M., Rosenberg, K. & McKeon, B.J. 2020 Interaction of forced Orr–Sommerfeld and Squire modes in a low-order representation of turbulent channel flow. Phys. Rev. Fluids 5 (8), 084607.CrossRefGoogle Scholar
Moarref, R. & Jovanović, M.R. 2012 Model-based design of transverse wall oscillations for turbulent drag reduction. J. Fluid Mech. 707, 205–240.CrossRefGoogle Scholar
Moarref, R., Jovanović, M.R., Tropp, J.A., Sharma, A.S. & McKeon, B.J. 2014 A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization. Phys. Fluids 26 (5), 051701.CrossRefGoogle 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
Morra, P., Semeraro, O., Henningson, D.S. & Cossu, C. 2019 On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows. J. Fluid Mech. 867, 969–984.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
Pickering, E., Rigas, G., Schmidt, O.T., Sipp, D. & Colonius, T. 2021 Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets. J. Fluid Mech. 917, A29.CrossRefGoogle Scholar
Praskovsky, A.A., Gledzer, E.B., Karyakin, M.Y. & Zhou, Y. 1993 The sweeping decorrelation hypothesis and energy-inertial scale interaction in high Reynolds number flows. J. Fluid Mech. 248, 493–511.CrossRefGoogle Scholar
Ran, W., Zare, A. & Jovanović, M.R. 2021 Model-based design of riblets for turbulent drag reduction. J. Fluid Mech. 906, A7.CrossRefGoogle Scholar
Reynolds, W.C. & Hussain, A.K.M.F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.CrossRefGoogle Scholar
Rosenberg, K., Symon, S. & McKeon, B.J. 2019 Role of parasitic modes in nonlinear closure via the resolvent feedback loop. Phys. Rev. Fluids 4 (5), 052601.CrossRefGoogle Scholar
Rubinstein, R. & Zhou, Y. 1999 Effects of helicity on Lagrangian and Eulerian time correlations in turbulence. Phys. Fluids 11 (8), 2288–2290.CrossRefGoogle Scholar
Rubinstein, R. & Zhou, Y. 2000 The frequency spectrum of sound radiated by isotropic turbulence. Phys. Lett. A 267, 379–383.CrossRefGoogle Scholar
Schmidt, O.T., Towne, A., Rigas, G., Colonius, T. & Brès, G.A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982.CrossRefGoogle Scholar
Semeraro, O., Jaunet, V., Jordan, P., Cavalieri, A.V.G. & Lesshafft, L. 2016 Stochastic and harmonic optimal forcing in subsonic jets. In 22nd AIAA/CEAS Aeroacoustics Conference, Lyon, France, p. 2935. American Institute of Aeronautics and Astronautics (AIAA).CrossRefGoogle Scholar
Slama, M., Leblond, C. & Sagaut, P. 2018 A Kriging-based elliptic extended anisotropic model for the turbulent boundary layer wall pressure spectrum. J. Fluid Mech. 840, 25–55.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
Symon, S., Illingworth, S.J. & Marusic, I. 2021 Energy transfer in turbulent channel flows and implications for resolvent modelling. J. Fluid Mech. 911, A3.CrossRefGoogle Scholar
Tennekes, H. 1975 Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561–567.CrossRefGoogle Scholar
Towne, A., Brès, G.A. & Lele, S.K. 2017 A statistical jet-noise model based on the resolvent framework. In 23rd AIAA/CEAS Aeroacoustics Conference, Denver, CO, USA, p. 3706. American Institute of Aeronautics and Astronautics (AIAA).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
Van Atta, C.W. & Wyngaard, J.C. 1975 On higher-order spectra of turbulence. J. Fluid Mech. 72 (4), 673–694.CrossRefGoogle Scholar
Wang, H.P. & Gao, Q. 2021 A study of inner–outer interactions in turbulent channel flows by interactive POD. Theor. Appl. Mech. Lett. 11 (1), 100222.CrossRefGoogle Scholar
Wang, H.P., Wang, S.Z. & He, G.W. 2018 The spanwise spectra in wall-bounded turbulence. Acta Mechanica Sin. 34 (3), 452–461.CrossRefGoogle Scholar
Wilczek, M. & Narita, Y. 2012 Wave-number–frequency spectrum for turbulence from a random sweeping hypothesis with mean flow. Phys. Rev. E 86, 066308.CrossRefGoogle ScholarPubMed
Wilczek, M., Stevens, R.J.A.M. & Meneveau, C. 2015 a Height-dependence of spatio-temporal spectra of wall-bounded turbulence – LES results and model predictions. J. Turbul. 16 (10), 937–949.CrossRefGoogle Scholar
Wilczek, M., Stevens, R.J.A.M. & Meneveau, C. 2015 b Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models. J. Fluid Mech. 769, R1.CrossRefGoogle Scholar
Wu, T., Geng, C.H., Yao, Y.C., Xu, C.X. & He, G.W. 2017 Characteristics of space–time energy spectra in turbulent channel flows. Phys. Rev. Fluids 2 (8), 084609.CrossRefGoogle Scholar
Wu, T. & He, G.W. 2020 Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows. J. Fluid Mech. 886, A11.CrossRefGoogle Scholar
Wu, T. & He, G.W. 2021 a Space–time energy spectra in turbulent shear flows. Phys. Rev. Fluids 6 (10), 100504.CrossRefGoogle Scholar
Wu, T. & He, G.W. 2021 b Stochastic dynamical model for space–time energy spectra in turbulent shear flows. Phys. Rev. Fluids 6, 054602.CrossRefGoogle Scholar
Yang, B.W., Jin, G.D., Wu, T., Yang, Z.X. & He, G.W. 2020 Numerical implementation and evaluation of resolvent-based estimation for space–time energy spectra in turbulent channel flows. Acta Mechanica Sin. 36 (4), 775–788.CrossRefGoogle Scholar
Zare, A., Georgiou, T.T. & Jovanović, M.R. 2020 Stochastic dynamical modeling of turbulent flows. Annu. Rev. Control Robot. Auton. Syst. 3, 195–219.CrossRefGoogle Scholar
Zare, A., Jovanović, M.R. & Georgiou, T.T. 2017 Colour of turbulence. J. Fluid Mech. 812, 636–680.CrossRefGoogle Scholar
Zhao, X. & He, G.W. 2009 Space–time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79, 046316.CrossRefGoogle ScholarPubMed