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A second-order resolvent formulation for the analysis of turbulent flow structures
Quentin Chevalier1  ; Lesshafft Lutz1 ; André V. G. Cavalieri2
1 Laboratoire d’Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
2 Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, Brazil
Comptes Rendus. Mécanique, Volume 351 (2023), pp. 355-371.

An attempt to improve the accuracy of resolvent-based predictions by including velocity correlations in the linear model is developed here. Closure assumptions for unresolved nonlinearities are thus pushed back to a higher order. Turbulent channel flow is considered as a test case: response and forcing modes obtained from singular value decomposition of the new resolvent model are compared to Spectral Proper Orthogonal Decomposition (SPOD) modes extracted from a Direct Numerical Simulation (DNS) database. The performance of the approach is also measured against previous resolvent-based models. The new model does not yield significant global improvement, but does improve predictions in some regions. Further work on the method should target the linear modeling of the velocity-pressure gradient correlation tensor.

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DOI : 10.5802/crmeca.193
Mots clés : Resolvent analysis, Turbulence, Reduced-order modeling, Theoretical fluid mechanics, Linear analysis
Quentin Chevalier 1 ; Lesshafft Lutz 1 ; André V. G. Cavalieri 2

1 Laboratoire d’Hydrodynamique, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
2 Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, Brazil
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A second-order resolvent formulation for the analysis of turbulent flow structures},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {355--371},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {351},
     year = {2023},
     doi = {10.5802/crmeca.193},
     language = {en},
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Quentin Chevalier; Lesshafft Lutz; André V. G. Cavalieri. A second-order resolvent formulation for the analysis of turbulent flow structures. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 355-371. doi : 10.5802/crmeca.193. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.193/

[1] Yongyun Hwang; Carlo Cossu Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow, J. Fluid Mech., Volume 664 (2010), pp. 51-73 | DOI | MR | Zbl

[2] Aaron Towne; Oliver T. Schmidt; Tim Colonius Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis, J. Fluid Mech., Volume 847 (2018), pp. 821-867 | DOI | MR | Zbl

[3] Stephen B. Pope Turbulent Flows, Cambridge University Press, 2000 | DOI | Zbl

[4] R. Moarref; M. R. Jovanović; J. A. Tropp; A. S. Sharma; B. J. McKeon A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization, Phys. Fluids, Volume 26 (2014) no. 5, 051701 | DOI

[5] M. A. Ahmed; H. J. Bae; A. F. Thompson; B. J. McKeon Resolvent analysis of stratification effects on wall-bounded shear flows, Phys. Rev. Fluids, Volume 6 (2021) no. 8, 084804 | DOI

[6] Kevin Rosenberg; Beverley J. McKeon Computing exact coherent states in channels starting from the laminar profile: A resolvent-based approach, Phys. Rev. E, Volume 100 (2019) no. 2, 021101 | DOI | MR

[7] Leandra I. Abreu; André V. G. Cavalieri; Philipp Schlatter; Ricardo Vinuesa; Dan S. Henningson Resolvent modelling of near-wall coherent structures in turbulent channel flow, Int. J. Heat Fluid Flow, Volume 85 (2020), 108662 | DOI

[8] Pierluigi Morra; Onofrio Semeraro; Dan S. Henningson; Carlo Cossu On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows, J. Fluid Mech., Volume 867 (2019), pp. 969-984 | DOI | MR | Zbl

[9] Pierluigi Morra; Petrônio A. S. Nogueira; André V. G. Cavalieri; Dan S. Henningson The colour of forcing statistics in resolvent analyses of turbulent channel flows, J. Fluid Mech., Volume 907 (2021), a24 | DOI | MR | Zbl

[10] Filipe R. Amaral; André V. G. Cavalieri; Eduardo Martini; Peter Jordan; Aaron Towne Resolvent-based estimation of turbulent channel flow using wall measurements, J. Fluid Mech., Volume 927 (2021), a17 | DOI | MR | Zbl

[11] Sean Symon; Simon J. Illingworth; Ivan Marusic Energy transfer in turbulent channel flows and implications for resolvent modelling, J. Fluid Mech., Volume 911 (2021), a3 | DOI | MR | Zbl

[12] Sean Symon; Anagha Madhusudanan; Simon J. Illingworth; Ivan Marusic On the use of eddy viscosity in resolvent analysis of turbulent channel flow (2022) (preprint, arXiv:2205.11216) | DOI

[13] B. F. Farrell; D. F. Gayme; P. J. Ioannou A statistical state dynamics approach to wall turbulence, Philos. Trans. R. Soc. Lond., Ser. A, Volume 375 (2017) no. 2089, 20160081 | DOI

[14] J. B. Marston; G. P. Chini; S. M. Tobias Generalized Quasilinear Approximation: Application to Zonal Jets, Phys. Rev. Lett., Volume 116 (2016) no. 21, 214501 | DOI | MR

[15] Satish C. Reddy; J. André C. Weideman The Accuracy of the Chebyshev Differencing Method for Analytic Functions, SIAM J. Numer. Anal., Volume 42 (2005) no. 5, pp. 2176-2187 | DOI | MR | Zbl

[16] Oliver T. Schmidt; Tim Colonius Guide to Spectral Proper Orthogonal Decomposition, AIAA J., Volume 58 (2020) no. 3, pp. 1023-1033 | DOI

[17] Eduardo Martini; André V. G. Cavalieri; Peter Jordan; Lutz Lesshafft Accurate Frequency Domain Identification of ODEs with Arbitrary Signals (2020) (preprint, arXiv:1907.04787) | DOI

[18] W. C. Reynolds; W. G. Tiederman Stability of turbulent channel flow, with application to Malkus’s theory, J. Fluid Mech., Volume 27 (1967) no. 2, pp. 253-272 | DOI

[19] Aaron Towne; Tim Colonius; Peter Jordan; André V. G. Cavalieri; Guillaume A. Brès Stochastic and nonlinear forcing of wavepackets in a Mach 0.9 jet, 21st AIAA/CEAS Aeroacoustics Conference, American Institute of Aeronautics and Astronautics, Inc. (2015) | DOI

[20] U. Karban; Eduardo Martini; André V. G. Cavalieri; Lutz Lesshafft; P. Jordan Self-similar mechanisms in wall turbulence studied using resolvent analysis, J. Fluid Mech., Volume 939 (2022), A36 | DOI | MR | Zbl

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