1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 53, 2021
  5. Article

Annual Review of Fluid Mechanics

Volume 53, 2021

From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint

Abstract

Transient growth and resolvent analyses are routinely used to assess nonasymptotic properties of fluid flows. In particular, resolvent analysis can be interpreted as a special case of viewing flow dynamics as an open system in which free-stream turbulence, surface roughness, and other irregularities provide sources of input forcing. We offer a comprehensive summary of the tools that can be employed to probe the dynamics of fluctuations around a laminar or turbulent base flow in the presence of such stochastic or deterministic input forcing and describe how input–output techniques enhance resolvent analysis. Specifically, physical insights that may remain hidden in the resolvent analysis are gained by detailed examination of input–output responses between spatially localized body forces and selected linear combinations of state variables. This differentiating feature plays a key role in quantifying the importance of different mechanisms for bypass transition in wall-bounded shear flows and in explaining how turbulent jets generate noise. We highlight the utility of a stochastic framework, with white or colored inputs, in addressing a variety of open challenges including transition in complex fluids, flow control, and physics-aware data-driven turbulence modeling. Applications with temporally or spatially periodic base flows are discussed and future research directions are outlined.

Keyword(s): convex optimization, flow modeling and control, frequency responses, input–output analysis, physics-aware data-driven modeling, stochastic dynamics, transition to turbulence, turbulent flows
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010719-060244
2021-01-05
2024-04-20
Loading full text...

Full text loading...

/deliver/fulltext/fluid/53/1/annurev-fluid-010719-060244.html?itemId=/content/journals/10.1146/annurev-fluid-010719-060244&mimeType=html&fmt=ahah

Literature Cited

  1. Agarwal A, Brandt L, Zaki TA 2014. Linear and nonlinear evolution of a localized disturbance in polymeric channel flow. J. Fluid Mech. 760:278–303
     [Google Scholar]
  2. Ahmadi M, Valmorbida G, Gayme D, Papachristodoulou A 2019. A framework for input–output analysis of wall-bounded shear flows. J. Fluid Mech. 873:742–85
     [Google Scholar]
  3. Bamieh B, Dahleh M. 2001. Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13:3258–69Provides a Reynolds number scaling of energy amplification.
     [Google Scholar]
  4. Bandyopadhyay PR. 2006. Stokes mechanism of drag reduction. J. Appl. Mech. 73:483–89
     [Google Scholar]
  5. 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
     [Google Scholar]
  6. Beneddine S, Yegavian R, Sipp D, Leclaire B 2017. Unsteady flow dynamics reconstruction from mean flow and point sensors: an experimental study. J. Fluid Mech. 824:174–201
     [Google Scholar]
  7. Benner P, Li JR, Penzl T 2008. Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. Numer. Linear Algebra Appl. 15:755–77
     [Google Scholar]
  8. Bertolotti FP, Herbert T. 1991. Analysis of the linear stability of compressible boundary layers using the PSE. Theor. Comput. Fluid Dyn. 3:117–24
     [Google Scholar]
  9. Bewley TR. 2009. A fundamental limit on the balance of power in a transpiration-controlled channel flow. J. Fluid Mech. 632:443–46
     [Google Scholar]
  10. Bewley TR, Liu S. 1998. Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365:305–49
     [Google Scholar]
  11. Bewley TR, Luchini P, Pralits J 2016. Methods for solution of large optimal control problems that bypass open-loop model reduction. Meccanica 51:2997–3014
     [Google Scholar]
  12. Bird RB, Curtiss CF, Armstrong RC, Hassager O 1987. Dynamics of Polymeric Liquids 2 New York: Wiley. , 2nd. ed.
  13. Boyd JP. 2001. Chebyshev and Fourier Spectral Methods New York: Dover:. , 2nd. ed.
  14. Boyd S, Vandenberghe L. 2004. Convex Optimization Cambridge, UK: Cambridge Univ. Press
  15. Brandt L, Sipp D, Pralits JO, Marquet O 2011. Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer. J. Fluid Mech. 687:503–28
     [Google Scholar]
  16. Brunton SL, Noack BR, Koumoutsakos P 2020. Machine learning for fluid mechanics. Annu. Rev. Fluid Mech. 52:477–508
     [Google Scholar]
  17. Butler KM, Farrell BF. 1992. Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4:1637Provides a transient growth analysis of transition.
     [Google Scholar]
  18. Butler KM, Farrell BF. 1993. Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids A 5:774–77
     [Google Scholar]
  19. Candler GV. 2019. Rate effects in hypersonic flows. Annu. Rev. Fluid Mech. 51:379–402
     [Google Scholar]
  20. Chavarin A, Luhar M. 2020. Resolvent analysis for turbulent channel flow with riblets. AIAA J 58:589–99
     [Google Scholar]
  21. Chen KK, Rowley CW. 2011. H2 optimal actuator and sensor placement in the linearised complex Ginzburg–Landau system. J. Fluid Mech. 681:241–60
     [Google Scholar]
  22. Chevalier M, Hœpffner J, Bewley TR, Henningson DS 2006. State estimation in wall-bounded flow systems. Part 2. Turbulent flows. J. Fluid Mech. 552:167–87
     [Google Scholar]
  23. Choi KS. 2002. Near-wall structure of turbulent boundary layer with spanwise-wall oscillation. Phys. Fluids 14:2530–42
     [Google Scholar]
  24. Choi KS, DeBisschop JR, Clayton BR 1998. Turbulent boundary-layer control by means of spanwise-wall oscillation. AIAA J 36:1157–63
     [Google Scholar]
  25. Cossu C, Pujals G, Depardon S 2009. Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619:79–94
     [Google Scholar]
  26. del Álamo JC, Jiménez J 2003. Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15:41–44
     [Google Scholar]
  27. del Álamo JC, Jiménez J 2006. Linear energy amplification in turbulent channels. J. Fluid Mech. 559:205–13Provides a transient growth analysis of eddy viscosity–enhanced linearized NS equations.
     [Google Scholar]
  28. del Álamo JC, Jiménez J, Zandonade P, Moser RD 2004. Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500:135–44
     [Google Scholar]
  29. Dhanak M, Si C. 1999. On reduction of turbulent wall friction through spanwise wall oscillations. J. Fluid Mech. 383:175–95
     [Google Scholar]
  30. Dhingra NK, Jovanović MR, Luo ZQ 2014. An ADMM algorithm for optimal sensor and actuator selection. Proceedings of the 53rd IEEE Conference on Decision and Control4039–44 New York: IEEE
     [Google Scholar]
  31. Duraisamy K, Iaccarino G, Xiao H 2019. Turbulence modeling in the age of data. Annu. Rev. Fluid Mech. 51:357–77
     [Google Scholar]
  32. Dwivedi A, Hildebrand N, Nichols JV, Candler GV, Jovanović MR 2020. Transient growth analysis of oblique shock waveboundary-layer interactions at Mach 5.92. Phys. Rev. Fluids 5:063904
     [Google Scholar]
  33. Dwivedi A, Sidharth GS, Nichols JW, Candler GV, Jovanović MR 2019. Reattachment vortices in hypersonic compression ramp flow: an input–output analysis. J. Fluid Mech. 880:113–35Provides an input–output analysis of hypersonic flow.
     [Google Scholar]
  34. Farrell BF, Ioannou PJ. 1993. Stochastic forcing of the linearized Navier–Stokes equations. Phys. Fluids A 5:2600–9Provides a first use of the linearized NS equations with stochastic forcing to study transition.
     [Google Scholar]
  35. Farrell BF, Ioannou PJ. 2012. Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech. 708:149–96
     [Google Scholar]
  36. Fazel M. 2002. Matrix rank minimization with applications PhD Thesis, Stanford Univ Stanford, CA:
  37. Fedorov A. 2011. Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43:79–95
     [Google Scholar]
  38. Fransson JHM, Talamelli A, Brandt L, Cossu C 2006. Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96:064501
     [Google Scholar]
  39. Fukagata K, Sugiyama K, Kasagi N 2009. On the lower bound of net driving power in controlled duct flows. Physica D 238:1082–86
     [Google Scholar]
  40. Gardner W. 1990. Introduction to Random Processes: With Applications to Signals and Systems New York: McGraw-Hill
  41. Garnaud X, Sandberg RD, Lesshafft L 2013. Global response to forcing in a subsonic jet: instability wavepackets and acoustic radiation Paper presented at AIAACEAS Aeroacoustics Conference 19th Berlin, AIAA: Pap. 2013-2232
  42. Georgiou TT. 2002a. Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parametrization. IEEE Trans. Autom. Control 47:1811–23
     [Google Scholar]
  43. Georgiou TT. 2002b. The structure of state covariances and its relation to the power spectrum of the input. IEEE Trans. Autom. Control 47:1056–66
     [Google Scholar]
  44. Groisman A, Steinberg V. 2000. Elastic turbulence in a polymer solution flow. Nature 405:53–55
     [Google Scholar]
  45. Gustavsson LH. 1991. Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224:241–60
     [Google Scholar]
  46. Halko N, Martinsson PG, Tropp JA 2011. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev 53:217–88
     [Google Scholar]
  47. Hariharan G, Jovanović MR, Kumar S 2018. Amplification of localized body forces in channel flows of viscoelastic fluids. J. Non-Newton. Fluid Mech. 260:40–53
     [Google Scholar]
  48. Hildebrand N, Dwivedi A, Nichols JW, Jovanović MR, Candler GV 2018. Simulation and stability analysis of oblique shock waveboundary layer interactions at Mach 5.92. Phys. Rev. Fluids 3:013906
     [Google Scholar]
  49. Hoda N, Jovanović MR, Kumar S 2008. Energy amplification in channel flows of viscoelastic fluids. J. Fluid Mech. 601:407–24Provides, along with Hoda et al. (2009), an input–output analysis of viscoelastic fluids.
     [Google Scholar]
  50. Hoda N, Jovanović MR, Kumar S 2009. Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids. J. Fluid Mech. 625:411–34
     [Google Scholar]
  51. Hœpffner J. 2005. Modeling flow statistics using convex optimization. Proceedings of the 2005 European Control Conference and the 44th IEEE Conference on Decision and Control4287–92 New York: IEEE
     [Google Scholar]
  52. Hœpffner J, Chevalier M, Bewley TR, Henningson DS 2005. State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows. J. Fluid Mech. 534:263–94
     [Google Scholar]
  53. Hœpffner J, Fukagata K. 2009. Pumping or drag reduction. ? J. Fluid Mech. 635:171–87
     [Google Scholar]
  54. Högberg M, Bewley TR, Henningson DS 2003a. Linear feedback control and estimation of transition in plane channel flow. J. Fluid Mech. 481:149–75
     [Google Scholar]
  55. Högberg M, Bewley TR, Henningson DS 2003b. Relaminarization of Reτ = 100 turbulence using linear state-feedback control. Phys. Fluids 15:3572–75
     [Google Scholar]
  56. Hwang Y, Cossu C. 2010a. Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number. J. Fluid Mech. 643:333–48Provides, along with Hwang & Cossu (2010b), an input–output analysis of eddy–viscosity enhanced linearized NS equations.
     [Google Scholar]
  57. Hwang Y, Cossu C. 2010b. Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664:51–73
     [Google Scholar]
  58. Hwang Y, Eckhardt B. 2020. Attached eddy model revisited using a minimal quasi-linear approximation. J. Fluid Mech. 894:A23
     [Google Scholar]
  59. Jeun J, Nichols JW, Jovanović MR 2016. Input-output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28:047101Provides an input–output analysis of jet noise.
     [Google Scholar]
  60. Jordan P, Colonius T. 2013. Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45:173–95
     [Google Scholar]
  61. Joshi SS, Speyer JL, Kim J 1997. A systems theory approach to the feedback stabilization of infinitesimal and finite-amplitude disturbances in plane Poiseuille flow. J. Fluid Mech. 332:157–84
     [Google Scholar]
  62. Jovanović MR. 2004. Modeling, analysis, and control of spatially distributed systems PhD Thesis, Univ. California Santa Barbara:
  63. Jovanović MR. 2008. Turbulence suppression in channel flows by small amplitude transverse wall oscillations. Phys. Fluids 20:014101
     [Google Scholar]
  64. Jovanović MR, Bamieh B. 2001. Modelling flow statistics using the linearized Navier-Stokes equations. Proceedings of the 40th IEEE Conference on Decision and Control4944–49 New York: IEEE
     [Google Scholar]
  65. Jovanović MR, Bamieh B. 2005. Componentwise energy amplification in channel flows. J. Fluid Mech. 534:145–83Provides a componentwise input–output analysis of transition: a more informative tool than resolvent analysis.
     [Google Scholar]
  66. Jovanović MR, Fardad M. 2008. H2 norm of linear time-periodic systems: a perturbation analysis. Automatica 44:2090–98
     [Google Scholar]
  67. Jovanović MR, Georgiou TT. 2010. Reproducing second order statistics of turbulent flows using linearized Navier-Stokes equations with forcing Paper presented at 63rd Annual Meeting of the APS Division of Fluid Dynamics Long Beach, CA: Nov. 21
  68. Jovanović MR, Kumar S. 2010. Transient growth without inertia. Phys. Fluids 22:023101Discovers, along with Jovanović & Kumar (2011), a viscoelastic lift-up mechanism.
     [Google Scholar]
  69. Jovanović MR, Kumar S. 2011. Nonmodal amplification of stochastic disturbances in strongly elastic channel flows. J. Non-Newton. Fluid Mech. 166:755–78
     [Google Scholar]
  70. Jovanović MR, Schmid PJ, Nichols JW 2014. Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26:024103
     [Google Scholar]
  71. Jung W, Mangiavacchi N, Akhavan R 1992. Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4:1605–7
     [Google Scholar]
  72. Kalur A, Seiler PJ, Hemati M 2020. Stability and performance analysis of nonlinear and non-normal systems using quadratic constraints Paper presented at the 2020 AIAA SciTech Forum and Exposition Orlando, FL: AIAA Pap. 2020-0833
  73. Kerswell RR. 2018. Nonlinear nonmodal stability theory. Annu. Rev. Fluid Mech. 50:319–45
     [Google Scholar]
  74. Kim J, Bewley TR. 2007. A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39:383–417
     [Google Scholar]
  75. Kim J, Lim J. 2000. A linear process in wall-bounded turbulent shear flows. Phys. Fluids 12:1885–88
     [Google Scholar]
  76. Kim J, Moin P, Moser R 1987. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177:133–66
     [Google Scholar]
  77. Kwakernaak H, Sivan R. 1972. Linear Optimal Control Systems New York: Wiley
  78. Laadhari F, Skandaji L, Morel R 1994. Turbulence reduction in a boundary layer by a local spanwise oscillating surface. Phys. Fluids 6:3218–20
     [Google Scholar]
  79. Landahl MT. 1975. Wave breakdown and turbulence. SIAM J. Appl. Math. 28:735–56Discovers a lift-up mechanism.
     [Google Scholar]
  80. Larson RG, Shaqfeh ESG, Muller SJ 1990. A purely elastic instability in Taylor–Couette flow. J. Fluid Mech. 218:573–600
     [Google Scholar]
  81. Lee C, Min T, Kim J 2008. Stability of a channel flow subject to wall blowing and suction in the form of a traveling wave. Phys. Fluids 20:101513
     [Google Scholar]
  82. Lee MJ, Kim J, Moin P 1990. Structure of turbulence at high shear rate. J. Fluid Mech. 216:561–83
     [Google Scholar]
  83. Lieu BK, Jovanović MR, Kumar S 2013. Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids. J. Fluid Mech. 723:232–63
     [Google Scholar]
  84. Lieu BK, Moarref R, Jovanović MR 2010. Controlling the onset of turbulence by streamwise traveling waves. Part 2: direct numerical simulations. J. Fluid Mech. 663:100–19
     [Google Scholar]
  85. Lin F, Fardad M, Jovanović MR 2013. Design of optimal sparse feedback gains via the alternating direction method of multipliers. IEEE Trans. Autom. Control 58:2426–31
     [Google Scholar]
  86. Lin F, Jovanović MR. 2009. Least-squares approximation of structured covariances. IEEE Trans. Autom. Control 54:1643–48
     [Google Scholar]
  87. Luhar M, Sharma AS, McKeon BJ 2014. Opposition control within the resolvent analysis framework. J. Fluid Mech. 749:597–626
     [Google Scholar]
  88. Lumley JL. 2007. Stochastic Tools in Turbulence Mineola, NY: Dover
  89. Malik MR. 1989. Prediction and control of transition in supersonic and hypersonic boundary layers. AIAA J 27:1487–93
     [Google Scholar]
  90. Malkus WVR. 1956. Outline of a theory of turbulent shear flow. J. Fluid Mech. 1:521–39
     [Google Scholar]
  91. Marusic I, Joseph DD, Mahesh K 2007. Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570:467–77
     [Google Scholar]
  92. McKeon BJ, Sharma AS. 2010. A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658:336–82Provides a resolvent analysis of turbulent flow.
     [Google Scholar]
  93. McMullen RM, Rosenberg K, McKeon BJ 2020. Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow. arXiv:2001.02785 [physics.flu-dyn]
  94. Megretski A, Rantzer A. 1997. System analysis via integral quadratic constraints. IEEE Trans. Autom. Control 42:819–30
     [Google Scholar]
  95. Min T, Kang SM, Speyer JL, Kim J 2006. Sustained sub-laminar drag in a fully developed channel flow. J. Fluid Mech. 558:309–18Demonstrates a sublaminar drag via traveling waves.
     [Google Scholar]
  96. Moarref R, Jovanović MR. 2010. Controlling the onset of turbulence by streamwise traveling waves. Part 1: receptivity analysis. J. Fluid Mech. 663:70–99Provides a model-based design of traveling waves.
     [Google Scholar]
  97. Moarref R, Jovanović MR. 2012. Model-based design of transverse wall oscillations for turbulent drag reduction. J. Fluid Mech. 707:205–40Provides a model-based design of wall oscillations.
     [Google Scholar]
  98. Moarref R, Jovanović MR, Tropp JA, Sharma AS, McKeon BJ 2014. A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization. Phys. Fluids 26:051701
     [Google Scholar]
  99. Moarref R, Sharma AS, Tropp JA, McKeon BJ 2013. Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels. J. Fluid Mech. 734:275–316
     [Google Scholar]
  100. Mohammadi H, Zare A, Soltanolkotabi M, Jovanović MR 2019. Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem. arXiv:1912.11899 [math.OC]
  101. Moin P, Moser RD. 1989. Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200:471–509
     [Google Scholar]
  102. Morra P, Semeraro O, Henningson DS, Cossu C 2019. On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows. J. Fluid Mech. 867:969–84
     [Google Scholar]
  103. Noack BR, Morzyński M, Tadmor G 2011. Reduced-Order Modelling for Flow Control Vienna: Springer-Verlag
  104. Odeh F, Keller JB. 1964. Partial differential equations with periodic coefficients and Bloch waves in crystals. J. Math. Phys. 5:1499–504
     [Google Scholar]
  105. Page J, Zaki TA. 2014. Streak evolution in viscoelastic Couette flow. J. Fluid Mech. 742:520–51
     [Google Scholar]
  106. Pope SB. 2000. Turbulent Flows Cambridge, UK: Cambridge Univ. Press
  107. Pujals G, García-Villalba M, Cossu C, Depardon S 2009. A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21:015109
     [Google Scholar]
  108. Qin B, Salipante PF, Hudson SD, Arratia PE 2019a. Flow resistance and structures in viscoelastic channel flows at low Re. Phys. Rev. Lett. 123:194501
     [Google Scholar]
  109. Qin B, Salipante PF, Hudson SD, Arratia PE 2019b. Upstream vortex and elastic wave in the viscoelastic flow around a confined cylinder. J. Fluid Mech. 864:R2
     [Google Scholar]
  110. Quadrio M, Ricco P. 2004. Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521:251–71
     [Google Scholar]
  111. Ran W, Zare A, Hack MJP, Jovanović MR 2019a. Modeling mode interactions in boundary layer flows via parabolized Floquet equations. Phys. Rev. Fluids 4:023901
     [Google Scholar]
  112. Ran W, Zare A, Hack MJP, Jovanović MR 2019b. Stochastic receptivity analysis of boundary layer flow. Phys. Rev. Fluids 4:093901Provides an input–output analysis of boundary layer with stochastic forcing.
     [Google Scholar]
  113. Ran W, Zare A, Jovanović MR 2020. Model-based design of riblets for turbulent drag reduction. J. Fluid Mech. In press Provides, along with Chavarin & Luhar (2020), an input–output analysis of turbulent channel flow with riblets.
     [Google Scholar]
  114. Recht B, Fazel M, Parrilo PA 2010. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev 52:471–501
     [Google Scholar]
  115. Reynolds WC, Hussain AKMF. 1972. The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54:263–88
     [Google Scholar]
  116. Reynolds WC, Tiederman WG. 1967. Stability of turbulent channel flow with application to Malkus's theory. J. Fluid Mech. 27:253–72
     [Google Scholar]
  117. Ricco P. 2004. Modification of near-wall turbulence due to spanwise wall oscillations. J. Turbul. 5:N24
     [Google Scholar]
  118. Ricco P. 2011. Laminar streaks with spanwise wall forcing. Phys. Fluids 23:064103
     [Google Scholar]
  119. Ricco P, Quadrio M. 2008. Wall-oscillation conditions for drag reduction in turbulent channel flow. Int. J. Heat Fluid Flow 29:891–902
     [Google Scholar]
  120. Rigas G, Sipp D, Colonius T 2020. Non-linear input/output analysis: application to boundary layer transition. arXiv:2001.09440 [physics.flu-dyn]
  121. Rosenberg K, McKeon BJ. 2019. Efficient representation of exact coherent states of the Navier–Stokes equations using resolvent analysis. Fluid Dyn. Res. 51:011401
     [Google Scholar]
  122. Rowley CW. 2005. Model reduction for fluids using balanced proper orthogonal decomposition. Int. J. Bifurc. Chaos 15:997–1013
     [Google Scholar]
  123. Rowley CW, Dawson ST. 2017. Model reduction for flow analysis and control. Annu. Rev. Fluid Mech. 49:387–417
     [Google Scholar]
  124. Schmid PJ. 2007. Nonmodal stability theory. Annu. Rev. Fluid Mech. 39:129–62Provides an outstanding review of nonmodal stability theory.
     [Google Scholar]
  125. Schmid PJ. 2010. Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656:5–28
     [Google Scholar]
  126. Schmid PJ, Henningson DS. 2001. Stability and Transition in Shear Flows New York: Springer
  127. Sidharth G, Dwivedi A, Candler GV, Nichols JW 2018. Onset of three-dimensionality in supersonic flow over a slender double wedge. Phys. Rev. Fluids 3:093901
     [Google Scholar]
  128. Sipp D, Marquet O. 2013. Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer. Theor. Comput. Fluid Dyn. 27:617–35Provides an input–output analysis of boundary layer.
     [Google Scholar]
  129. Tadmor G, Noack BR. 2011. Bernoulli, Bode, and budgie. IEEE Control Syst. Mag 31:218–23
     [Google Scholar]
  130. Thomas VL, Lieu BK, Jovanović MR, Farrell BF, Ioannou PJ, Gayme DF 2014. Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow. Phys. Fluids 26:105112
     [Google Scholar]
  131. Toedtli SS, Luhar M, McKeon BJ 2019. Predicting the response of turbulent channel flow to varying-phase opposition control: resolvent analysis as a tool for flow control design. Phys. Rev. Fluids 4:073905
     [Google Scholar]
  132. Towne A, Lozano-Durán A, Yang X 2020. Resolvent-based estimation of space-time flow statistics. J. Fluid Mech. 883:A17
     [Google Scholar]
  133. Towne A, Schmidt OT, Colonius T 2018. Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847:821–67
     [Google Scholar]
  134. Trefethen LN, Embree M. 2005. Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators Princeton, NJ: Princeton Univ. Press
  135. Trefethen LN, Trefethen AE, Reddy SC, Driscoll TA 1993. Hydrodynamic stability without eigenvalues. Science 261:578–84Must-read; provides the first use of resolvent analysis and pseudo-spectra in fluid mechanics.
     [Google Scholar]
  136. Waleffe F. 1997. On a self-sustaining process in shear flows. Phys. Fluids 9:883–900Discovers a self-sustaining mechanism.
     [Google Scholar]
  137. Weideman JAC, Reddy SC. 2000. A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 26:465–519
     [Google Scholar]
  138. Zare A, Chen Y, Jovanović MR, Georgiou TT 2017a. Low-complexity modeling of partially available second-order statistics: theory and an efficient matrix completion algorithm. IEEE Trans. Autom. Control 62:1368–83
     [Google Scholar]
  139. Zare A, Georgiou TT, Jovanović MR 2020a. Stochastic dynamical modeling of turbulent flows. Annu. Rev. Control Robot. Auton. Syst. 3:195–219
     [Google Scholar]
  140. Zare A, Jovanović MR, Georgiou TT 2017b. Colour of turbulence. J. Fluid Mech. 812:636–80Provides turbulence modeling using the linearized NS equations with stochastic forcing.
     [Google Scholar]
  141. Zare A, Mohammadi H, Dhingra NK, Georgiou TT, Jovanović MR 2020b. Proximal algorithms for large-scale statistical modeling and sensor/actuator selection. IEEE Trans. Autom. Control 65:3441–56Develops, along with Dhingra et al. (2014), algorithms for optimal sensor and actuator placement.
     [Google Scholar]
  142. Zhou K, Doyle JC, Glover K 1996. Robust and Optimal Control Upper Saddle River, NJ: Prentice-Hall
/content/journals/10.1146/annurev-fluid-010719-060244
Loading
From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint
Annual Review of Fluid Mechanics 53, 311 (2021); https://doi.org/10.1146/annurev-fluid-010719-060244
/content/journals/10.1146/annurev-fluid-010719-060244
/content/journals/10.1146/annurev-fluid-010719-060244
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error