Optimal white-noise stochastic forcing for linear models of turbulent channel flow

Holford, Jacob J.; Lee, Myoungkyu; Hwang, Yongyun

doi:10.1017/jfm.2023.234

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

Journal Article · Mon Apr 24 04:00:00 EDT 2023 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2023.234· OSTI ID:2423241

; ;

In the present study an optimisation problem is formulated to determine the forcing of an eddy-viscosity-based linearised Navier–Stokes model in channel flow at$$Re_\tau \approx 5200$$($$Re_\tau$$is the friction Reynolds number), where the forcing is white-in-time and spatially decorrelated. The objective functional is prescribed such that the forcing drives a response to best match a set of velocity spectra from direct numerical simulation (DNS), as well as remaining sufficiently smooth. Strong quantitative agreement is obtained between the velocity spectra from the linear model with optimal forcing and from DNS, but only qualitative agreement between the Reynolds shear stress co-spectra from the model and DNS. The forcing spectra exhibit a level of self-similarity, associated with the primary peak in the velocity spectra, but they also reveal a non-negligible amount of energy spent in phenomenologically mimicking the non-self-similar part of the velocity spectra associated with energy cascade. By exploiting linearity, the effect of the individual forcing components is assessed and the contributions from the Orr mechanism and the lift-up effect are also identified. Finally, the effect of the strength of the eddy viscosity on the optimisation performance is investigated. The inclusion of the eddy viscosity diffusion operator is shown to be essential in modelling of the near-wall features, while still allowing the forcing of the self-similar primary peak. In particular, reducing the strength of the eddy viscosity results in a considerable increase in the near-wall forcing of wall-parallel components.

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility (ALCF)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC02-06CH11357

OSTI ID:: 2423241

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 961; ISSN 0022-1120

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

References (73)

Momentum transfer by linearised eddies in turbulent channel flows Encinar, Miguel P.; Jiménez, Javier Journal of Fluid Mechanics, Vol. 895 https://doi.org/10.1017/jfm.2020.302	journal	May 2020
Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions de Giovanetti, Matteo; Sung, Hyung Jin; Hwang, Yongyun Journal of Fluid Mechanics, Vol. 832 https://doi.org/10.1017/jfm.2017.697	journal	October 2017
Linear-model-based estimation in wall turbulence: improved stochastic forcing and eddy viscosity terms Gupta, Vikrant; Madhusudanan, Anagha; Wan, Minping Journal of Fluid Mechanics, Vol. 925 https://doi.org/10.1017/jfm.2021.671	journal	August 2021
Generalized Stability Theory. Part II: Nonautonomous Operators Farrell, Brian F.; Ioannou, Petros J. Journal of the Atmospheric Sciences, Vol. 53, Issue 14 https://doi.org/10.1175/1520-0469(1996)053<2041:GSTPIN>2.0.CO;2	journal	July 1996
Self-Sustained Process at Large Scales in Turbulent Channel Flow Hwang, Yongyun; Cossu, Carlo Physical Review Letters, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevLett.105.044505	journal	July 2010
Minimal multi-scale dynamics of near-wall turbulence Doohan, Patrick; Willis, Ashley P.; Hwang, Yongyun Journal of Fluid Mechanics, Vol. 913 https://doi.org/10.1017/jfm.2020.1182	journal	February 2021
The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments Reynolds, W. C.; Hussain, A. K. M. F. Journal of Fluid Mechanics, Vol. 54, Issue 2 https://doi.org/10.1017/S0022112072000679	journal	July 1972
Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels Moarref, Rashad; Sharma, Ati S.; Tropp, Joel A. Journal of Fluid Mechanics, Vol. 734 https://doi.org/10.1017/jfm.2013.457	journal	October 2013
Colour of turbulence Zare, Armin; Jovanović, Mihailo R.; Georgiou, Tryphon T. Journal of Fluid Mechanics, Vol. 812 https://doi.org/10.1017/jfm.2016.682	journal	January 2017
Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets Pickering, Ethan; Rigas, Georgios; Schmidt, Oliver T. Journal of Fluid Mechanics, Vol. 917 https://doi.org/10.1017/jfm.2021.232	journal	April 2021
Statistical structure of self-sustaining attached eddies in turbulent channel flow Hwang, Yongyun Journal of Fluid Mechanics, Vol. 767 https://doi.org/10.1017/jfm.2015.24	journal	February 2015
Use of eddy viscosity in resolvent analysis of turbulent channel flow Symon, Sean; Madhusudanan, Anagha; Illingworth, Simon J. Physical Review Fluids, Vol. 8, Issue 6 https://doi.org/10.1103/PhysRevFluids.8.064601	journal	June 2023
The colour of forcing statistics in resolvent analyses of turbulent channel flows Morra, Pierluigi; Nogueira, Petrônio A. S.; Cavalieri, André V. G. Journal of Fluid Mechanics, Vol. 907 https://doi.org/10.1017/jfm.2020.802	journal	November 2020
A note on an algebraic instability of inviscid parallel shear flows Landahl, M. T. Journal of Fluid Mechanics, Vol. 98, Issue 2 https://doi.org/10.1017/S0022112080000122	journal	May 1980
Estimating large-scale structures in wall turbulence using linear models Illingworth, Simon J.; Monty, Jason P.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 842 https://doi.org/10.1017/jfm.2018.129	journal	March 2018
Orr mechanism in transition of parallel shear flow Jiao, Yuxin; Hwang, Yongyun; Chernyshenko, Sergei I. Physical Review Fluids, Vol. 6, Issue 2 https://doi.org/10.1103/PhysRevFluids.6.023902	journal	February 2021
Componentwise energy amplification in channel flows JovanoviĆ, Mihailo R.; Bamieh, Bassam Journal of Fluid Mechanics, Vol. 534 https://doi.org/10.1017/S0022112005004295	journal	June 2005
State estimation in wall-bounded flow systems. Part 2. Turbulent flows Chevalier, Mattias; HŒPffner, JÉRÔMe; Bewley, Thomas R. Journal of Fluid Mechanics, Vol. 552, Issue -1 https://doi.org/10.1017/S0022112005008578	journal	March 2006
Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number Lee, Myoungkyu; Moser, Robert D. Journal of Fluid Mechanics, Vol. 860 https://doi.org/10.1017/jfm.2018.903	journal	December 2018
Coherent structure generation in near-wall turbulence Schoppa, W.; Hussain, F. Journal of Fluid Mechanics, Vol. 453 https://doi.org/10.1017/S002211200100667X	journal	February 2002
Attached Eddy Model of Wall Turbulence Marusic, Ivan; Monty, Jason P. Annual Review of Fluid Mechanics, Vol. 51, Issue 1 https://doi.org/10.1146/annurev-fluid-010518-040427	journal	January 2019
How linear is wall-bounded turbulence? Jiménez, Javier Physics of Fluids, Vol. 25, Issue 11 https://doi.org/10.1063/1.4819081	journal	September 2013
A note on optimal transient growth in turbulent channel flows Pujals, Gregory; García-Villalba, Manuel; Cossu, Carlo Physics of Fluids, Vol. 21, Issue 1 https://doi.org/10.1063/1.3068760	journal	January 2009
Predictive Model for Wall-Bounded Turbulent Flow Marusic, I.; Mathis, R.; Hutchins, N. Science, Vol. 329, Issue 5988 https://doi.org/10.1126/science.1188765	journal	July 2010
The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers Kolmogorov, A. N. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 434, Issue 1890 https://doi.org/10.1098/rspa.1991.0075	journal	July 1991
Mesolayer of attached eddies in turbulent channel flow Hwang, Yongyun Physical Review Fluids, Vol. 1, Issue 6 https://doi.org/10.1103/PhysRevFluids.1.064401	journal	October 2016
Self-sustained processes in the logarithmic layer of turbulent channel flows Hwang, Yongyun; Cossu, Carlo Physics of Fluids, Vol. 23, Issue 6 https://doi.org/10.1063/1.3599157	journal	June 2011
Self-similar mechanisms in wall turbulence studied using resolvent analysis Karban, U.; Martini, E.; Cavalieri, A. V. G. Journal of Fluid Mechanics, Vol. 939 https://doi.org/10.1017/jfm.2022.225	journal	April 2022
Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner-outer interaction model Baars, Woutijn J.; Hutchins, Nicholas; Marusic, Ivan Physical Review Fluids, Vol. 1, Issue 5 https://doi.org/10.1103/PhysRevFluids.1.054406	journal	September 2016
A theoretical and experimental study of wall turbulence Perry, A. E.; Henbest, S.; Chong, M. S. Journal of Fluid Mechanics, Vol. 165, Issue -1 https://doi.org/10.1017/S002211208600304X	journal	April 1986
Resolvent-based estimation of space–time flow statistics Towne, Aaron; Lozano-Durán, Adrián; Yang, Xiang Journal of Fluid Mechanics, Vol. 883 https://doi.org/10.1017/jfm.2019.854	journal	November 2019
A critical-layer framework for turbulent pipe flow McKEON, B. J.; Sharma, A. S. Journal of Fluid Mechanics, Vol. 658 https://doi.org/10.1017/S002211201000176X	journal	July 2010
Active and inactive components of the streamwise velocity in wall-bounded turbulence Deshpande, Rahul; Monty, Jason P.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 914 https://doi.org/10.1017/jfm.2020.884	journal	March 2021
Stability and Transition in Shear Flows Schmid, Peter J.; Henningson, Dan S. Applied Mathematical Sciences https://doi.org/10.1007/978-1-4613-0185-1	book	January 2001
Evidence of very long meandering features in the logarithmic region of turbulent boundary layers Hutchins, N.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 579 https://doi.org/10.1017/S0022112006003946	journal	May 2007
Direct numerical simulation of turbulent channel flow up to Lee, Myoungkyu; Moser, Robert D. Journal of Fluid Mechanics, Vol. 774 https://doi.org/10.1017/jfm.2015.268	journal	June 2015
Linear energy amplification in turbulent channels del ÁLAMO, Juan C.; JimÉNez, Javier Journal of Fluid Mechanics, Vol. 559 https://doi.org/10.1017/S0022112006000607	journal	July 2006
Turbulent Flows Pope, Stephen B. https://doi.org/10.1017/CBO9780511840531	book	July 2012
Scale interactions and spectral energy transfer in turbulent channel flow Cho, Minjeong; Hwang, Yongyun; Choi, Haecheon Journal of Fluid Mechanics, Vol. 854 https://doi.org/10.1017/jfm.2018.643	journal	September 2018
Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow Hwang, Yongyun; Cossu, Carlo Journal of Fluid Mechanics, Vol. 664 https://doi.org/10.1017/S0022112010003629	journal	September 2010
State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows HŒPffner, JÉRÔMe; Chevalier, Mattias; Bewley, Thomas R. Journal of Fluid Mechanics, Vol. 534 https://doi.org/10.1017/S0022112005004210	journal	June 2005
The lift-up effect: The linear mechanism behind transition and turbulence in shear flows Brandt, Luca European Journal of Mechanics - B/Fluids, Vol. 47 https://doi.org/10.1016/j.euromechflu.2014.03.005	journal	September 2014
The structure of turbulent boundary layers Kline, S. J.; Reynolds, W. C.; Schraub, F. A. Journal of Fluid Mechanics, Vol. 30, Issue 4 https://doi.org/10.1017/S0022112067001740	journal	December 1967
The mean logarithm emerges with self-similar energy balance Hwang, Yongyun; Lee, Myoungkyu Journal of Fluid Mechanics, Vol. 903 https://doi.org/10.1017/jfm.2020.730	journal	October 2020
From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint Jovanović, Mihailo R. Annual Review of Fluid Mechanics, Vol. 53, Issue 1 https://doi.org/10.1146/annurev-fluid-010719-060244	journal	January 2021
Streak instability in near-wall turbulence revisited Cassinelli, Andrea; de Giovanetti, Matteo; Hwang, Yongyun Journal of Turbulence, Vol. 18, Issue 5 https://doi.org/10.1080/14685248.2017.1294757	journal	March 2017
Near-wall turbulent fluctuations in the absence of wide outer motions Hwang, Yongyun Journal of Fluid Mechanics, Vol. 723 https://doi.org/10.1017/jfm.2013.133	journal	April 2013
Stochastic Dynamical Modeling of Turbulent Flows Zare, A.; Georgiou, T. T.; Jovanović, M. R. Annual Review of Control, Robotics, and Autonomous Systems, Vol. 3, Issue 1 https://doi.org/10.1146/annurev-control-053018-023843	journal	May 2020
Generalized Stability Theory. Part I: Autonomous Operators Farrell, Brian F.; Ioannou, Petros J. Journal of the Atmospheric Sciences, Vol. 53, Issue 14 https://doi.org/10.1175/1520-0469(1996)053<2025:GSTPIA>2.0.CO;2	journal	July 1996
Coherent large-scale structures from the linearized Navier–Stokes equations Madhusudanan, Anagha; Illingworth, Simon. J.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 873 https://doi.org/10.1017/jfm.2019.391	journal	June 2019
Regeneration mechanisms of near-wall turbulence structures Hamilton, James M.; Kim, John; Waleffe, Fabian Journal of Fluid Mechanics, Vol. 287 https://doi.org/10.1017/S0022112095000978	journal	March 1995
Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow McMullen, Ryan M.; Rosenberg, Kevin; McKeon, Beverley J. Physical Review Fluids, Vol. 5, Issue 8 https://doi.org/10.1103/PhysRevFluids.5.084607	journal	August 2020
Cause-and-effect of linear mechanisms sustaining wall turbulence Lozano-Durán, Adrián; Constantinou, Navid C.; Nikolaidis, Marios-Andreas Journal of Fluid Mechanics, Vol. 914 https://doi.org/10.1017/jfm.2020.902	journal	March 2021
Self-sustaining process of minimal attached eddies in turbulent channel flow Hwang, Yongyun; Bengana, Yacine Journal of Fluid Mechanics, Vol. 795 https://doi.org/10.1017/jfm.2016.226	journal	April 2016
Optimal perturbations and streak spacing in wall-bounded turbulent shear flow Butler, Kathryn M.; Farrell, Brian F. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 3 https://doi.org/10.1063/1.858663	journal	March 1993
A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization Moarref, R.; Jovanović, M. R.; Tropp, J. A. Physics of Fluids, Vol. 26, Issue 5 https://doi.org/10.1063/1.4876195	journal	May 2014
Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow Nogueira, Petrônio A. S.; Morra, Pierluigi; Martini, Eduardo Journal of Fluid Mechanics, Vol. 908 https://doi.org/10.1017/jfm.2020.918	journal	December 2020
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis Towne, Aaron; Schmidt, Oliver T.; Colonius, Tim Journal of Fluid Mechanics, Vol. 847 https://doi.org/10.1017/jfm.2018.283	journal	May 2018
Scaling of turbulence intensities up to Reτ=106 with a resolvent-based quasilinear approximation Skouloudis, Nikolaos; Hwang, Yongyun Physical Review Fluids, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevFluids.6.034602	journal	March 2021
Nonmodal Stability Theory Schmid, Peter J. Annual Review of Fluid Mechanics, Vol. 39, Issue 1 https://doi.org/10.1146/annurev.fluid.38.050304.092139	journal	January 2007
Coherent structures near the wall in a turbulent channel flow Jeong, J.; Hussain, F.; Schoppa, W. Journal of Fluid Mechanics, Vol. 332 https://doi.org/10.1017/S0022112096003965	journal	February 1997
On the mechanism of wall turbulence Perry, A. E.; Chong, M. S. Journal of Fluid Mechanics, Vol. 119 https://doi.org/10.1017/S0022112082001311	journal	June 1982
Linear stability of optimal streaks in the log-layer of turbulent channel flows Alizard, Frédéric Physics of Fluids, Vol. 27, Issue 10 https://doi.org/10.1063/1.4932178	journal	October 2015
Efficient representation of exact coherent states of the Navier–Stokes equations using resolvent analysis Rosenberg, Kevin; McKeon, Beverley J. Fluid Dynamics Research, Vol. 51, Issue 1 https://doi.org/10.1088/1873-7005/aab1ab	journal	January 2019
Optimal excitation of three-dimensional perturbations in viscous constant shear flow Farrell, Brian F.; Ioannou, Petros J. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 6 https://doi.org/10.1063/1.858574	journal	June 1993
On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows Morra, Pierluigi; Semeraro, Onofrio; Henningson, Dan S. Journal of Fluid Mechanics, Vol. 867 https://doi.org/10.1017/jfm.2019.196	journal	April 2019
Similarity and the Turbulent Energy Spectrum Lumley, J. L. Physics of Fluids, Vol. 10, Issue 4 https://doi.org/10.1063/1.1762200	journal	January 1967
On a self-sustaining process in shear flows Waleffe, Fabian Physics of Fluids, Vol. 9, Issue 4 https://doi.org/10.1063/1.869185	journal	April 1997
Model-based spectral coherence analysis Abootorabi, Seyedalireza; Zare, Armin Journal of Fluid Mechanics, Vol. 958 https://doi.org/10.1017/jfm.2023.82	journal	March 2023
Attached eddy model revisited using a minimal quasi-linear approximation Hwang, Yongyun; Eckhardt, Bruno Journal of Fluid Mechanics, Vol. 894 https://doi.org/10.1017/jfm.2020.285	journal	May 2020
Energy transfer in turbulent channel flows and implications for resolvent modelling Symon, Sean; Illingworth, Simon J.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 911 https://doi.org/10.1017/jfm.2020.929	journal	January 2021
Stochastic forcing of the linearized Navier–Stokes equations Farrell, Brian F.; Ioannou, Petros J. Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 11 https://doi.org/10.1063/1.858894	journal	November 1993
Stability of linear flow Ellingsen, T.; Palm, E. Physics of Fluids, Vol. 18, Issue 4 https://doi.org/10.1063/1.861156	journal	January 1975

Similar Records

Prandtl number effects on extreme mixing events in forced stratified turbulence

Journal Article · Mon Mar 11 20:00:00 EDT 2024 · Journal of Fluid Mechanics · OSTI ID:2323351

Flow in additively manufactured super-rough channels

Journal Article · Thu Jul 28 20:00:00 EDT 2022 · Flow · OSTI ID:1878655

Asymptotic coefficients of the attached-eddy model derived from an adiabatic atmosphere

Journal Article · Mon May 12 20:00:00 EDT 2025 · Journal of Fluid Mechanics · OSTI ID:2566008

Related Subjects

Mechanics
Physics

Optimal white-noise stochastic forcing for linear models of turbulent channel flow

Citation Formats

References (73)

Similar Records

Related Subjects