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Characterization of energy transfer and triadic interactions of coherent structures in turbulent wakes

Published online by Cambridge University Press:  12 September 2023

Dinesh Kumar Kinjangi  and
Daniel Foti Open the ORCID record for Daniel Foti [Opens in a new window]
Dinesh Kumar Kinjangi
Affiliation:
Department of Mechanical Engineering, University of Memphis, Memphis, TN 38152, USA
Daniel Foti*
Affiliation:
Department of Mechanical Engineering, University of Memphis, Memphis, TN 38152, USA
*
†Email address for correspondence: dvfoti@memphis.edu
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Abstract

Turbulent wakes are often characterized by dominant coherent structures over disparate scales. Dynamics of their behaviour can be attributed to interscale energy dynamics and triadic interactions. We develop a methodology to quantify the dynamics of kinetic energy of specific scales. Coherent motions are characterized by the triple decomposition and used to define mean, coherent and random velocity. Specific scales of coherent structures are identified through dynamic mode decomposition, whereby the total coherent velocity is separated into a set of velocities classified by frequency. The coherent kinetic energy of a specific scale is defined by a frequency triad of scale-specific velocities. Equations for the balance of scale-specific coherent kinetic energy are derived to interpret interscale dynamics. The methodology is demonstrated on three wake flows: (i) ${Re}=175$ flow over a cylinder; (ii) a direct numerical simulation of ${Re}=3900$ flow over a cylinder; and (iii) a large-eddy simulation of a utility-scale wind turbine. The cylinder wake cases show that energy transfer starts with vortex shedding and redistributes energy through resonance of higher harmonics. The scale-specific coherent kinetic energy balance quantifies the distribution of transport and transfer among coherent, mean and random scales. The coherent kinetic energy in the rotor scales and the hub vortex scale in the wind turbine interact to produce new scales. The analysis reveals that vortices at the blade root interact with the hub vortex formed behind the nacelle, which has implications for the proliferation of scales in the downwind near wake.

JFM classification

Wakes/Jets: Wakes
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 971 , 25 September 2023 , A7
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© The Author(s), 2023. Published by Cambridge University Press

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References

Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767, 1–101.CrossRefGoogle Scholar
Armenio, V. & Piomelli, U. 2000 A Lagrangian mixed subgrid-scale model in generalized coordinates. Flow Turbul. Combust. 65 (1), 51–81.CrossRefGoogle Scholar
Arslan, T., El Khoury, G.K., Pettersen, B. & Andersson, H.I. 2012 Simulations of flow around a three-dimensional square cylinder using LES and DNS. In The Seventh International Colloquium on Bluff Body Aerodynamics and Applications, Shanghai, China, pp. 909–918. International Association for Wind Engineering.Google Scholar
Bai, H. & Alam, M.M. 2018 Dependence of square cylinder wake on Reynolds number. Phys. Fluids 30 (1), 015102.CrossRefGoogle Scholar
Baj, P. & Buxton, O.R.H. 2017 Interscale energy transfer in the merger of wakes of a multiscale array of rectangular cylinders. Phys. Rev. Fluids 2 (11), 114607.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Biswas, N., Cicolin, M.M. & Buxton, O.R.H. 2022 Energy exchanges in the flow past a cylinder with a leeward control rod. J. Fluid Mech. 941, A36.CrossRefGoogle Scholar
Borazjani, I., Ge, L. & Sotiropoulos, F. 2008 Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227 (16), 7587–7620.CrossRefGoogle ScholarPubMed
Brasseur, J.G. & Wei, C.-H. 1994 Interscale dynamics and local isotropy in high Reynolds number turbulence within triadic interactions. Phys. Fluids 6 (2), 842–870.CrossRefGoogle Scholar
Brown, G.L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.CrossRefGoogle Scholar
Cal, R.B., Lebrón, J., Castillo, L., Kang, H.S. & Meneveau, C. 2010 Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer. J. Renew. Sustain. Energy 2 (1), 013106.CrossRefGoogle Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22 (1), 015110.CrossRefGoogle Scholar
Cantwell, B.J. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13 (1), 457–515.CrossRefGoogle Scholar
Carbone, M. & Bragg, A.D. 2020 Is vortex stretching the main cause of the turbulent energy cascade? J. Fluid Mech. 883, R2.CrossRefGoogle Scholar
Cerutti, S. & Meneveau, C. 1998 Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence. Phys. Fluids 10 (4), 928–937.CrossRefGoogle Scholar
Chan, C.I., Schlatter, P. & Chin, R.C. 2021 Interscale transport mechanisms in turbulent boundary layers. J. Fluid Mech. 921, A13.CrossRefGoogle Scholar
Chen, X., Yao, J. & Hussain, F. 2021 Theoretical framework for energy flux analysis of channels under drag control. Phys. Rev. Fluids 6 (1), 013902.CrossRefGoogle Scholar
Chrisohoides, A. & Sotiropoulos, F. 2003 Experimental visualization of Lagrangian coherent structures in aperiodic flows. Phys. Fluids 15 (3), L25–L28.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E., Jimenez, J. & Casciola, C.M. 2016 Cascades and wall-normal fluxes in turbulent channel flows. J. Fluid Mech. 796, 417–436.CrossRefGoogle Scholar
Cohen, L. 1995 Time-Frequency Analysis, vol. 778. Prentice Hall.Google Scholar
Corke, T.C., Shakib, F. & Nagib, H.M. 1991 Mode selection and resonant phase locking in unstable axisymmetric jets. J. Fluid Mech. 223, 253–311.CrossRefGoogle Scholar
Domaradzki, J.A., Liu, W. & Brachet, M.E. 1993 An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5 (7), 1747–1759.CrossRefGoogle Scholar
Domaradzki, J.A., Liu, W., Härtel, C. & Kleiser, L. 1994 Energy transfer in numerically simulated wall-bounded turbulent flows. Phys. Fluids 6 (4), 1583–1599.CrossRefGoogle Scholar
Domaradzki, J.A. & Rogallo, R.S. 1990 Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2 (3), 413–426.CrossRefGoogle Scholar
Dong, S., Huang, Y., Yuan, X. & Lozano-Durán, A. 2020 The coherent structure of the kinetic energy transfer in shear turbulence. J. Fluid Mech. 892, A22.CrossRefGoogle Scholar
Donoho, D.L. 2006 Compressed sensing. IEEE Trans. Inf. Theory 52 (4), 1289–1306.CrossRefGoogle Scholar
Du, Z. & Selig, M. 1998 A 3-D stall-delay model for horizontal axis wind turbine performance prediction. In 1998 ASME Wind Energy Symposium, Reno, NV, USA, p. 21. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Dubief, Y. & Delcayre, F. 2000 On coherent-vortex identification in turbulence. J. Turbul. 1 (1), 011–011.CrossRefGoogle Scholar
Dubrulle, B. 2019 Beyond Kolmogorov cascades. J. Fluid Mech. 867, P1.CrossRefGoogle Scholar
Durao, D.F.G., Heitor, M.V. & Pereira, J.C.F. 1988 Measurements of turbulent and periodic flows around a square cross-section cylinder. Exp. Fluids 6 (5), 298–304.CrossRefGoogle Scholar
Farazmand, M. & Sapsis, T.P. 2017 A variational approach to probing extreme events in turbulent dynamical systems. Sci. Adv. 3 (9), e1701533.CrossRefGoogle ScholarPubMed
Foti, D. 2016 Quantification and reduction of uncertainty of model predictions of wind turbines and plants via high-fidelity simulations. PhD thesis, University of Minnesota, Minneapolis, MN.Google Scholar
Foti, D. 2021 Coherent vorticity dynamics and dissipation in a utility-scale wind turbine wake with uniform inflow. Theor. Appl. Mech. Lett. 11 (5), 100292.CrossRefGoogle Scholar
Foti, D., Giorno, S. & Duraisamy, K. 2020 An adaptive mesh refinement approach based on optimal sparse sensing. Theor. Comput. Fluid Dyn. 34 (4), 457–482.CrossRefGoogle Scholar
Foti, D., Yang, X., Campagnolo, F., Maniaci, D. & Sotiropoulos, F. 2018 a Wake meandering of a model wind turbine operating in two different regimes. Phys. Rev. Fluids 3 (5), 054607.CrossRefGoogle Scholar
Foti, D., Yang, X., Guala, M. & Sotiropoulos, F. 2016 Wake meandering statistics of a model wind turbine: insights gained by large eddy simulations. Phys. Rev. Fluids 1 (4), 044407.CrossRefGoogle Scholar
Foti, D., Yang, X., Shen, L. & Sotiropoulos, F. 2019 Effect of wind turbine nacelle on turbine wake dynamics in large wind farms. J. Fluid Mech. 869, 1–26.CrossRefGoogle Scholar
Foti, D., Yang, X. & Sotiropoulos, F. 2018 b Similarity of wake meandering for different wind turbine designs for different scales. J. Fluid Mech. 842, 5–25.CrossRefGoogle Scholar
Fowler, J.E. 2009 Compressive-projection principal component analysis. IEEE Trans. Image Process. 18 (10), 2230–2242.CrossRefGoogle ScholarPubMed
Gatti, D., Chiarini, A., Cimarelli, A. & Quadrio, M. 2020 Structure function tensor equations in inhomogeneous turbulence. J. Fluid Mech. 898, A5.CrossRefGoogle Scholar
Gatti, D., Cimarelli, A., Hasegawa, Y., Frohnapfel, B. & Quadrio, M. 2018 Global energy fluxes in turbulent channels with flow control. J. Fluid Mech. 857, 345–373.CrossRefGoogle Scholar
Ge, L. & Sotiropoulos, F. 2007 A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225 (2), 1782–1809.CrossRefGoogle ScholarPubMed
Gee, K.L., Atchley, A.A., Falco, L.E., Shepherd, M.R., Ukeiley, L.S., Jansen, B.J. & Seiner, J.M. 2010 Bicoherence analysis of model-scale jet noise. J. Acoust. Soc. Am. 128 (5), EL211–EL216.CrossRefGoogle ScholarPubMed
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J.C. 2015 The energy cascade in near-field non-homogeneous non-isotropic turbulence. J. Fluid Mech. 771, 676–705.CrossRefGoogle Scholar
Goto, S., Saito, Y. & Kawahara, G. 2017 Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers. Phys. Rev. Fluids 2 (6), 064603.CrossRefGoogle Scholar
Guala, M., Hommema, S.E. & Adrian, R.J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162.CrossRefGoogle Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287 (1), 317–348.CrossRefGoogle Scholar
Hill, R.J. 2002 Exact second-order structure-function relationships. J. Fluid Mech. 468, 317–326.CrossRefGoogle Scholar
Holmes, P., Lumley, J.L., Berkooz, G. & Rowley, C.W. 2012 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Hong, J., Katz, J., Meneveau, C. & Schultz, M.P. 2012 Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow. J. Fluid Mech. 712, 92–128.CrossRefGoogle Scholar
Hong, J., Toloui, M., Chamorro, L.P., Guala, M., Howard, K., Riley, S., Tucker, J. & Sotiropoulos, F. 2014 Natural snowfall reveals large-scale flow structures in the wake of a 2.5-MW wind turbine. Nat. Commun. 5, 4216.CrossRefGoogle ScholarPubMed
Hu, J.C., Zhou, Y. & Dalton, C. 2006 Effects of the corner radius on the near wake of a square prism. Exp. Fluids 40, 106–118.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Center for Turbulence Research, Proceedings of the Summer Program 1988, Center for Turbulence Research Report CTR-S88, pp. 193–208. Center for Turbulence Research.Google Scholar
Hussain, A.K.M.F. 1983 Coherent structures—reality and myth. Phys. Fluids 26 (10), 2816–2850.CrossRefGoogle Scholar
Hussain, A.K.M. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.CrossRefGoogle Scholar
Hussain, A.K.M.F. & Reynolds, W.C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41 (2), 241–258.CrossRefGoogle Scholar
Hussain, A.K.M.F. & Zaman, K.B.M.Q. 1985 An experimental study of organized motions in the turbulent plane mixing layer. J. Fluid Mech. 159, 85–104.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
Iungo, G.V., Viola, F., Camarri, S., Porté-Agel, F. & Gallaire, F. 2013 Linear stability analysis of wind turbine wakes performed on wind tunnel measurements. J. Fluid Mech. 737, 499–526.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jin, B., Symon, S. & Illingworth, S.J. 2021 Energy transfer mechanisms and resolvent analysis in the cylinder wake. Phys. Rev. Fluids 6 (2), 024702.CrossRefGoogle Scholar
Joukowski, N.E. 1912 Vortex theory of a rowing screw. Trudy Otdeleniya Fizicheskikh Nauk Obshchestva Lubitelei Estestvoznaniya 16 (1), 1–31.Google Scholar
Jovanović, M.R., Schmid, P.J. & Nichols, J.W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 024103.CrossRefGoogle Scholar
Kang, S., Lightbody, A., Hill, C. & Sotiropoulos, F. 2011 High-resolution numerical simulation of turbulence in natural waterways. Adv. Water Resour. 34 (1), 98–113.CrossRefGoogle Scholar
Kang, S., Yang, X. & Sotiropoulos, F. 2014 On the onset of wake meandering for an axial flow turbine in a turbulent open channel flow. J. Fluid Mech. 744, 376–403.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Cr Acad. Sci. URSS 30, 301–305.Google Scholar
Kraichnan, R.H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (7), 1417–1423.CrossRefGoogle Scholar
Kraichnan, R.H. 1971 Inertial-range transfer in two-and three-dimensional turbulence. J. Fluid Mech. 47 (3), 525–535.CrossRefGoogle Scholar
Kravchenko, A.G., Choi, H. & Moin, P. 1993 On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5 (12), 3307–3309.CrossRefGoogle Scholar
Kutz, J.N. 2013 Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data. Oxford University Press.Google Scholar
Lee, M.-B. & Kim, G.-C. 2001 A study on the near wake of a square cylinder using particle image velocimetry (i)-mean flow field. Trans. Korean Soc. Mech. Engrs B 25 (10), 1408–1416.Google Scholar
Lii, K.S., Rosenblatt, M. & Van Atta, C. 1976 Bispectral measurements in turbulence. J. Fluid Mech. 77 (1), 45–62.CrossRefGoogle Scholar
Lyn, D.A., Einav, S., Rodi, W. & Park, J.-H. 1995 A laser-doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder. J. Fluid Mech. 304, 285–319.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
Mezić, I. 2013 Analysis of fluid flows via spectral properties of the Koopman operator. Annu. Rev. Fluid Mech. 45, 357–378.CrossRefGoogle Scholar
Mininni, P.D., Alexakis, A. & Pouquet, A. 2006 Large-scale flow effects, energy transfer, and self-similarity on turbulence. Phys. Rev. E 74 (1), 016303.CrossRefGoogle ScholarPubMed
Mizota, T. & Okajima, A. 1981 Experimental studies of time mean flows around rectangular prisms. In Proceedings of the Japan Society of Civil Engineers, vol. 1981, pp. 39–47. Japan Society of Civil Engineers.CrossRefGoogle Scholar
Motoori, Y. & Goto, S. 2019 Generation mechanism of a hierarchy of vortices in a turbulent boundary layer. J. Fluid Mech. 865, 1085–1109.CrossRefGoogle Scholar
Norberg, C. 1993 Flow around rectangular cylinders: pressure forces and wake frequencies. J. Wind Engng Ind. Aerodyn. 49 (1–3), 187–196.CrossRefGoogle Scholar
Okulov, V.L., Naumov, I.V., Mikkelsen, R.F. & Sørensen, J.N. 2015 Wake effect on a uniform flow behind wind-turbine model. In Journal of Physics: Conference Series, vol. 625, p. 012011. IOP.CrossRefGoogle Scholar
Pan, S., Arnold-Medabalimi, N. & Duraisamy, K. 2020 Sparsity-promoting algorithms for the discovery of informative koopman invariant subspaces. J. Fluid Mech. 917, A18.Google Scholar
Piomelli, U., Cabot, W.H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3 (7), 1766–1771.CrossRefGoogle Scholar
Piomelli, U., Yu, Y. & Adrian, R.J. 1996 Subgrid-scale energy transfer and near-wall turbulence structure. Phys. Fluids 8 (1), 215–224.CrossRefGoogle Scholar
Portela, F.A., Papadakis, G. & Vassilicos, J.C. 2017 The turbulence cascade in the near wake of a square prism. J. Fluid Mech. 825, 315–352.CrossRefGoogle Scholar
Qatramez, A. & Foti, D. 2021 Reduced-order model predictions of wind turbines via mode decomposition and sparse sampling. In AIAA Scitech 2021 Forum, p. 1602. American Institute of Aeronautics and Astronautics.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
Richardson, L.F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Robinson, S.K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Rowley, C.W., Colonius, T. & Murray, R.M. 2004 Model reduction for compressible flows using POD and Galerkin projection. Physica D 189 (1–2), 115–129.CrossRefGoogle Scholar
Rowley, C.W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641 (1), 115–127.CrossRefGoogle Scholar
Schmid, P.J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Schmidt, O.T. 2020 Bispectral mode decomposition of nonlinear flows. Nonlinear Dyn. 102 (4), 2479–2501.CrossRefGoogle Scholar
Schmidt, O.T., Towne, A., Colonius, T., Cavalieri, A.V.G., Jordan, P. & Brès, G.A. 2017 Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability. J. Fluid Mech. 825, 1153–1181.CrossRefGoogle Scholar
Sharma, A. & Eswaran, V. 2004 Heat and fluid flow across a square cylinder in the two-dimensional laminar flow regime. Numer. Heat Transfer A 45 (3), 247–269.CrossRefGoogle Scholar
Shen, W.Z., Mikkelsen, R., Sørensen, J.N. & Bak, C. 2005 Tip loss corrections for wind turbine computations. Wind Energy 8 (4), 457–475.CrossRefGoogle Scholar
Shen, W.Z., Sørensen, J.N. & Zhang, J. 2007 Actuator surface model for wind turbine flow computations. In Proceedings of European Wind Energy Conference & Exhibition 2007.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561–571.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weath. Rev. 91 (3), 99–164.2.3.CO;2>CrossRefGoogle Scholar
Sohankar, A., Norberg, C. & Davidson, L. 1999 Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Phys. Fluids 11 (2), 288–306.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
Thiesset, F., Danaila, L., A Antonia, R. & Zhou, T. 2011 Scale-by-scale energy budgets which account for the coherent motion. In Journal of Physics: Conference Series, vol. 318, p. 052040. IOP.CrossRefGoogle Scholar
Thiesset, F., Danaila, L. & Antonia, R.A. 2014 Dynamical interactions between the coherent motion and small scales in a cylinder wake. J. Fluid Mech. 749, 201–226.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
Trias, F.X., Gorobets, A. & Oliva, A. 2015 Turbulent flow around a square cylinder at Reynolds number 22,000: a DNS study. Comput. Fluids 123, 87–98.CrossRefGoogle Scholar
Valente, P.C. & Vassilicos, J.C. 2015 The energy cascade in grid-generated non-equilibrium decaying turbulence. Phys. Fluids 27 (4), 045103.CrossRefGoogle Scholar
VerHulst, C. & Meneveau, C. 2015 Altering kinetic energy entrainment in large eddy simulations of large wind farms using unconventional wind turbine actuator forcing. Energies 8 (1), 370–386.CrossRefGoogle Scholar
Viola, F., Iungo, G.V., Camarri, S., Porté-Agel, F. & Gallaire, F. 2014 Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data. J. Fluid Mech. 750, R1.CrossRefGoogle Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4 (2), 350–363.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477–539.CrossRefGoogle Scholar
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J. Fluid Mech. 168, 31–71.CrossRefGoogle Scholar
Yang, X., Hong, J., Barone, M. & Sotiropoulos, F. 2016 Coherent dynamics in the rotor tip shear layer of utility-scale wind turbines. J. Fluid Mech. 804, 90–115.CrossRefGoogle Scholar
Yang, X., Howard, K.B., Guala, M. & Sotiropoulos, F. 2015 Effects of a three-dimensional hill on the wake characteristics of a model wind turbine. Phys. Fluids 27 (2), 025103.CrossRefGoogle Scholar
Yang, X. & Sotiropoulos, F. 2018 A new class of actuator surface models for wind turbines. Wind Energy 21 (5), 285–302.CrossRefGoogle Scholar
Yang, X., Zhang, X., Li, Z. & He, G.-W. 2009 A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 228 (20), 7821–7836.CrossRefGoogle Scholar
Zaman, K.B.M.Q. 1996 Axis switching and spreading of an asymmetric jet: the role of coherent structure dynamics. J. Fluid Mech. 316, 1–27.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y. & Watanabe, T. 2019 Extreme events and non-Kolmogorov $-5/3$ spectra in turbulent flows behind two side-by-side square cylinders. J. Fluid Mech. 874, 677–698.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y., Watanabe, T., Ito, Y. & Hayase, T. 2020 Energy transfer in turbulent flows behind two side-by-side square cylinders. J. Fluid Mech. 903, A4.CrossRefGoogle Scholar