1932

Abstract

Since its birth in the 1920s, quantum mechanics has motivated and advanced the analysis of linear operators. In this effort, it significantly contributed to the development of sophisticated mathematical tools in spectral theory. Many of these tools have also found their way into classical fluid mechanics and enabled elegant and effective solution strategies as well as physical insights into complex fluid behaviors. This review provides supportive evidence for synergistically adopting mathematical techniques beyond the classical repertoire, both for fluid research and for the training of future fluid dynamicists. Deeper understanding, compelling solution methods, and alternative interpretations of practical problems can be gained by an awareness of mathematical techniques and approaches from quantum mechanics. Techniques such as spectral analysis, series expansions, considerations on symmetries, and integral transforms are discussed, and applications from acoustics and incompressible flows are presented with a quantum mechanical perspective.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-031022-044209
2023-01-19
2024-03-28
Loading full text...

Full text loading...

/deliver/fulltext/fluid/55/1/annurev-fluid-031022-044209.html?itemId=/content/journals/10.1146/annurev-fluid-031022-044209&mimeType=html&fmt=ahah

Literature Cited

  1. Ahn B, Indlekofer T, Dawson J, Worth N 2021. Transient thermo-acoustic responses of methane/hydrogen flames in a pressurized annular combustor. J. Eng. Gas Turbines Power 144:011018
    [Google Scholar]
  2. Arecchi FT, Courtens E, Gilmore R, Thomas H. 1972. Atomic coherent states in quantum optics. Phys. Rev. A 6:62211–37
    [Google Scholar]
  3. Aurégan Y, Pagneux V. 2017. PT-symmetric scattering in flow duct acoustics. Phys. Rev. Lett. 118:17174301
    [Google Scholar]
  4. Bakas NA, Farrell BF. 2010. The role of nonnormality in overreflection theory. J. Atmos. Sci. 67:2547–58
    [Google Scholar]
  5. Barenblatt GI. 1996. Scaling, Self-Similarity, and Intermediate Asymptotics Cambridge, UK: Cambridge Univ. Press
  6. Bauerheim M, Cazalens M, Poinsot T. 2015. A theoretical study of mean azimuthal flow and asymmetry effects on thermo-acoustic modes in annular combustors. Proc. Combust. Inst. 35:3219–27
    [Google Scholar]
  7. Bauerheim M, Nicoud F, Poinsot T. 2016. Progress in analytical methods to predict and control azimuthal combustion instability modes in annular chambers. Phys. Fluids 28:2021303
    [Google Scholar]
  8. Bender CM. 2019. PT Symmetry: In Quantum and Classical Physics London: World Sci.
  9. Bender CM, Boettcher S. 1998. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80:245243–46
    [Google Scholar]
  10. Bender CM, Orszag SA. 1999. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory New York: Springer
  11. Berry MV, Wilkinson M. 1984. Diabolical points in the spectra of triangles. Proc. R. Soc. A 392:180215–43
    [Google Scholar]
  12. Birkhoff G, Von Neumann J 1936. The logic of quantum mechanics. Ann. Math. 37:4823–43
    [Google Scholar]
  13. Bloch F. 1929. Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52:7–8555–600
    [Google Scholar]
  14. Bloch F. 1946. Nuclear induction. Phys. Rev. 70:7–8460
    [Google Scholar]
  15. Bluman G, Kumei S. 1996. Symmetries and Differential Equations New York: Springer
  16. Bothien M, Noiray N, Schuermans B. 2015. Analysis of azimuthal thermo-acoustic modes in annular gas turbine combustion chambers. J. Eng. Gas Turbines Power 137:061505
    [Google Scholar]
  17. Bourgouin JF, Durox D, Moeck JP, Schuller T, Candel S. 2013. Self-sustained instabilities in an annular combustor coupled by azimuthal and longitudinal acoustic modes. Proceedings of the ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, Vol. 1B: Combustion, Fuels and Emissions Pap. V01BT04A007 New York: ASME
    [Google Scholar]
  18. Bourgouin JF, Durox D, Moeck JP, Schuller T, Candel S. 2015. A new pattern of instability observed in an annular combustor: the slanted mode. Proc. Combust. Inst. 35:33237–44
    [Google Scholar]
  19. Bourquard C, Noiray N. 2019. Stabilization of acoustic modes using Helmholtz and Quarter-Wave resonators tuned at exceptional points. J. Sound Vib. 445:288–307
    [Google Scholar]
  20. Bridges J, Wernet M. 2002. Turbulence measurements of separate flow nozzles with mixing enhancement features Paper presented at 8th AIAA/CEAS Aeroacoustics Conference & Exhibit, Breckenridge, CO, AIAA Pap. 2002-2484
  21. Bush JW. 2015. Pilot-wave hydrodynamics. Annu. Rev. Fluid Mech. 47:269–92
    [Google Scholar]
  22. Candel S. 2002. Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29:1–28
    [Google Scholar]
  23. Cantwell BJ. 2002. Introduction to Symmetry Analysis Cambridge, UK: Cambridge Univ. Press
  24. Charru F. 2011. Hydrodynamic Instabilities Cambridge, UK: Cambridge Univ. Press
  25. Chomaz JM. 2005. Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37:357–92
    [Google Scholar]
  26. Chomaz JM, Huerre P, Redekopp L. 1991. A frequency selection criterion in spatially developing flows. Stud. Appl. Math. 84:119–44
    [Google Scholar]
  27. Couder Y, Fort E, Gautier CH, Boudaoud A. 2005. From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94:17177801
    [Google Scholar]
  28. Crawford JD, Knobloch E. 1991. Symmetry and symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid Mech. 23:341–87
    [Google Scholar]
  29. Culick FEC. 2006. Unsteady motions in combustion chambers for propulsion systems Tech. Rep. AG-AVT-039, RTO (Res. Technol. Organ.) NATO (N. Atl. Treaty Organ.), Neuilly-sur-Seine France:
  30. Davey A. 1978. On the stability of flow in an elliptic pipe which is nearly circular. J. Fluid Mech. 87:2233–41
    [Google Scholar]
  31. Davey A, Salwen H. 1994. On the stability of flow in an elliptic pipe which is nearly circular. J. Fluid Mech. 281:357–69
    [Google Scholar]
  32. Davies E. 1999. Semi-classical states for non-self-adjoint Schrödinger operators. Commun. Math. Phys. 200:35–41
    [Google Scholar]
  33. Dawson S, McKeon BJ. 2019. On the shape of resolvent modes in wall-bounded turbulence. J. Fluid Mech. 877:682–716
    [Google Scholar]
  34. Dencker N, Sjöstrand J, Zworski M. 2004. Pseudo-spectra of semi-classical (pseudo) differential operators. Commun. Pure Appl. Math. 57:384–415
    [Google Scholar]
  35. Dirac PAM. 1930. The Principles of Quantum Mechanics Oxford: Oxford Univ. Press
  36. Doppler J, Mailybaev AA, Böhm J, Kuhl U, Girschik A et al. 2016. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537:761876–79
    [Google Scholar]
  37. Dowling AP, Mahmoudi Y. 2015. Combustion noise. Proc. Combust. Inst. 35:65–100
    [Google Scholar]
  38. Durán I, Moreau S, Poinsot T. 2013. Analytical and numerical study of combustion noise through a subsonic nozzle. AIAA J. 51:42–52
    [Google Scholar]
  39. Duran I, Morgans AS. 2015. On the reflection and transmission of circumferential waves through nozzles. J. Fluid Mech. 773:137–53
    [Google Scholar]
  40. Fabre D, Longobardi R, Citro V, Luchini P. 2020. Acoustic impedance and hydrodynamic instability of the flow through a circular aperture in a thick plate. J. Fluid Mech. 885:A11
    [Google Scholar]
  41. Faure-Beaulieu A, Indlekofer T, Dawson JR, Noiray N. 2021. Imperfect symmetry of real annular combustors: beating thermoacoustic modes and heteroclinic orbits. J. Fluid Mech. 925:R1
    [Google Scholar]
  42. Fedorov A. 2011. Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43:79–95
    [Google Scholar]
  43. Floquet G. 1883. Sur les équations différentielles linéaires à coefficients périodiques. Ann. Sci. l'Éc. Norm. Supér. Sér. 2 12:47–88
    [Google Scholar]
  44. Ghani A, Polifke W. 2021. An exceptional point switches stability of a thermoacoustic experiment. J. Fluid Mech. 920:R3
    [Google Scholar]
  45. Ghirardo G, Bothien MR. 2018. Quaternion structure of azimuthal instabilities. Phys. Rev. Fluids 3:11113202
    [Google Scholar]
  46. Ghirardo G, Boudy F, Bothien MR. 2018. Amplitude statistics prediction in thermoacoustics. J. Fluid Mech. 844:216–46
    [Google Scholar]
  47. Ghirardo G, Di Giovine C, Moeck JP, Bothien MR. 2019. Thermoacoustics of can-annular combustors. J. Eng. Gas Turbines Power 141:011007
    [Google Scholar]
  48. Ghirardo G, Gant F. 2019. Background noise pushes azimuthal instabilities away from spinning states. arXiv:1904.00213 [physics.flu-dyn]. https://doi.org/10.48550/arXiv.1904.00213
    [Crossref]
  49. Ghirardo G, Gant F. 2021. Averaging of thermoacoustic azimuthal instabilities. J. Sound Vib. 490:115732
    [Google Scholar]
  50. Ghirardo G, Juniper MP. 2013. Azimuthal instabilities in annular combustors: standing and spinning modes. Proc. R. Soc. A 469:20130232
    [Google Scholar]
  51. Ghirardo G, Juniper MP, Moeck JP. 2016. Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors. J. Fluid Mech. 805:52–87
    [Google Scholar]
  52. Giusti A, Worth NA, Mastorakos E, Dowling AP. 2017. Experimental and numerical investigation into the propagation of entropy waves. AIAA J. 55:2446–58
    [Google Scholar]
  53. Golubitsky M, Stewart I. 1985. Hopf bifurcation in the presence of symmetry. Arch. Ratio. Mech. Anal. 87:107–65
    [Google Scholar]
  54. Griffiths DJ. 1995. Introduction to Quantum Mechanics Upper Saddle River, NJ: Prentice-Hall
  55. Güttel S, Tisseur F. 2017. The nonlinear eigenvalue problem. Acta Numer. 26:1–94
    [Google Scholar]
  56. Hamermesh M. 1989. Group Theory and Its Application to Physical Problems New York: Dover
  57. Heiss WD. 2004. Exceptional points of non-Hermitian operators. J. Phys. A 37:62455–64
    [Google Scholar]
  58. Heiss WD. 2012. The physics of exceptional points. J. Phys. A 45:444016
    [Google Scholar]
  59. Helffer B 2008. Four lectures in semiclassical analysis for non-self-adjoint problems with applications to hydrodynamic instability. Pseudo-Differential Operators Quantization and Signals HG Feichtinger, B Helffer, MP Lamoureux, N Lerner, J Toft 35–77 Berlin: Springer-Verlag
    [Google Scholar]
  60. Helffer B, Lafitte O. 2003. Asymptotic growth rate for the linearized Rayleigh equation for the Rayleigh–Taylor instability. Asymptot. Anal. 33:189–235
    [Google Scholar]
  61. Herbert T. 1988. Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20:487–526
    [Google Scholar]
  62. Hörmander L. 1960. Differential equations without solutions. Math. Ann. 140:169–73
    [Google Scholar]
  63. Howe MS, Liu JTC. 1977. The generation of sound by vorticity waves in swirling duct flows. J. Fluid Mech. 81:369–83
    [Google Scholar]
  64. Huerre P, Monkewitz PA. 1990. Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22:473–537
    [Google Scholar]
  65. Ihme M. 2017. Combustion and engine-core noise. Annu. Rev. Fluid Mech. 49:277–310
    [Google Scholar]
  66. Inui T, Tanabe Y, Onodera Y. 1990. Group Theory and Its Applications in Physics Berlin: Springer-Verlag
  67. Jain A, Magri L. 2022. A physical model for indirect noise in non-isentropic nozzles: transfer functions and stability. J. Fluid Mech. 935:A33
    [Google Scholar]
  68. Joannopoulos JD, Johnson SG, Winn JN, Meade RD. 2008. Photonic Crystals Princeton, NJ: Princeton Univ. Press. , 2nd ed..
  69. Jones CA. 1988. Multiple eigenvalues and mode classification in plane Poiseuille flow. Q. J. Mech. Appl. Math. 41:3363–82
    [Google Scholar]
  70. Jovanović MR. 2021. From bypass transition to flow control and data-driven turbulence modeling: an input–output viewpoint. Annu. Rev. Fluid Mech. 53:311–45
    [Google Scholar]
  71. Juniper MP, Sujith RI. 2018. Sensitivity and nonlinearity of thermocoustic oscillations. Annu. Rev. Fluid Mech. 50:661–89
    [Google Scholar]
  72. Kato T. 1980. Perturbation Theory for Linear Operators New York: Springer. , 2nd ed..
  73. Kern JS, Hanifi A, Henningson DS. 2022. Subharmonic eigenvalue orbits in the spectrum of pulsating Poiseuille flow. J. Fluid Mech. 945:A11
    [Google Scholar]
  74. Kerswell RR. 2018. Nonlinear nonmodal stability theory. Annu. Rev. Fluid Mech. 50:319–45
    [Google Scholar]
  75. Kirillov ON. 2017. Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics. Proc. R. Soc. A 473:220520170344
    [Google Scholar]
  76. Kirillov ON. 2021. Nonconservative Stability Problems of Modern Physics Berlin: De Gruyter. , 2nd ed..
  77. Kopiev VF, Ostrikov NN, Chernyshev SA, Elliott JW. 2004. Aeroacoustics of supersonic jet issued from corrugated nozzle: new approach and prospects. Int. J. Aeroacoust. 3:3199–228
    [Google Scholar]
  78. Kristiansen UR, Wiik GA. 2007. Experiments on sound generation in corrugated pipes with flow. J. Acoust. Soc. Am. 121:31337–44
    [Google Scholar]
  79. Kronig RD, Penney WG. 1931. Quantum mechanics of electrons in crystal lattices. Proc. R. Soc. A 130:499–513
    [Google Scholar]
  80. Laera D, Schuller T, Prieur K, Durox D, Camporeale SM, Candel S. 2017. Flame describing function analysis of spinning and standing modes in an annular combustor and comparison with experiments. Combust. Flame 184:136–52
    [Google Scholar]
  81. Lajús FC, Sinha A, Cavalieri AVG, Deschamps CJ, Colonius T. 2019. Spatial stability analysis of subsonic corrugated jets. J. Fluid Mech. 876:766–91
    [Google Scholar]
  82. Lieuwen TC, Yang V 2005. Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling Reston, VA: AIAA
  83. Lifschitz A, Hameiri E. 1991. Local stability conditions in fluid dynamics. Phys. Fluids 3:2644
    [Google Scholar]
  84. Lindzen RS. 1988. Instability of plane parallel shear flow (toward a mechanistic picture of how it works). Pure Appl. Geophys. 126:103–21
    [Google Scholar]
  85. Lindzen RS, Barker JW. 1985. Instability and wave over-reflection in stably stratified shear flow. J. Fluid Mech. 151:189–217
    [Google Scholar]
  86. Lindzen RS, Farrell BF, Tung KK. 1980. The concept of wave overreflection and its application to baroclinic instability. J. Atmos. Sci. 37:44–63
    [Google Scholar]
  87. Loewe B, Souslov A, Goldbart PM. 2018. Flocking from a quantum analogy: spin-orbit coupling in an active fluid. New J. Phys. 20:013020
    [Google Scholar]
  88. Luchini P, Bottaro A. 2014. Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46:493–517
    [Google Scholar]
  89. Lyu B, Dowling AP. 2019. Temporal stability analysis of jets of lobed geometry. J. Fluid Mech. 860:5–39
    [Google Scholar]
  90. Magri L. 2017. On indirect noise in multi-component nozzle flows. J. Fluid Mech. 828:R2
    [Google Scholar]
  91. Magri L. 2019. Adjoint methods as design tools in thermoacoustics. Appl. Mech. Rev. 71:2020801
    [Google Scholar]
  92. Magri L, Bauerheim M, Nicoud F, Juniper MP. 2016. Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity. J. Comput. Phys. 325:411–21
    [Google Scholar]
  93. Marble FE, Candel SM. 1977. Acoustic disturbance from gas non-uniformities convected through a nozzle. J. Sound Vibr. 55:2225–43
    [Google Scholar]
  94. Mazur M, Kwah YH, Indlekofer T, Dawson JR, Worth NA. 2021. Self-excited longitudinal and azimuthal modes in a pressurised annular combustor. Proc. Combust. Inst. 38:45997–6004
    [Google Scholar]
  95. Mensah GA, Campa G, Moeck JP. 2016. Efficient computation of thermoacoustic modes in industrial annular combustion chambers based on Bloch-wave theory. J. Eng. Gas Turbines Power 138:8081502
    [Google Scholar]
  96. Mensah GA, Magri L, Orchini A, Moeck JP. 2019. Effects of asymmetry on thermoacoustic modes in annular combustors: a higher-order perturbation study. J. Eng. Gas Turbines Power 141:4041030
    [Google Scholar]
  97. Mensah GA, Magri L, Silva C, Buschmann P, Moeck J. 2018. Exceptional points in the thermoacoustic spectrum. J. Sound Vibr. 433:124–28
    [Google Scholar]
  98. Miri MA, Alú A. 2019. Exceptional points in optics and photonics. Science 363:6422eaar7709
    [Google Scholar]
  99. Moarref R, Jovanović MR. 2010. Controlling the onset of turbulence by streamwise travelling waves. Part 1. Receptivity analysis. J. Fluid Mech. 663:70–99
    [Google Scholar]
  100. Moeck JP, Paul M, Paschereit CO. 2010. Thermoacoustic instabilities in an annular Rijke tube. ASME Turbo Expo 2010: Power for Land, Sea, and Air, Vol. 2: Combustion, Fuels and Emissions1219–32 New York: ASME
    [Google Scholar]
  101. Moiseyev N. 2011. Non-Hermitian Quantum Mechanics Cambridge, UK: Cambridge Univ. Press
  102. Morgans AS, Duran I. 2016. Entropy noise: a review of theory, progress and challenges. Int. J. Spray Combust. Dyn. 8:4285–98
    [Google Scholar]
  103. Murthy SR, Sayadi T, LeChenadec V, Schmid PJ, Bodony D. 2019. Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors. J. Fluid Mech. 881:384–419
    [Google Scholar]
  104. Nicoud F, Benoit L, Sensiau C, Poinsot T. 2007. Acoustic modes in combustors with complex impedances and multidimensional active flames. AIAA J. 45:2426–41
    [Google Scholar]
  105. Noether E. 1918. Invariante Variationsprobleme. Nachr. Ges. Wiss. Gött. Math.-Phys. Klasse 1918:235–57
    [Google Scholar]
  106. Noiray N, Bothien M, Schuermans B. 2011. Investigation of azimuthal staging concepts in annular gas turbines. Combust. Theory Model. 15:5585–606
    [Google Scholar]
  107. Noiray N, Schuermans B. 2013. On the dynamic nature of azimuthal thermoacoustic modes in annular gas turbine combustion chambers. Proc. R. Soc. A 469:215120120535
    [Google Scholar]
  108. Obrist D. 2009. Directivity of acoustic emissions from wave packets to the far field. J. Fluid Mech. 640:165–86
    [Google Scholar]
  109. Obrist D, Schmid PJ. 2010. Algebraically decaying modes and wavepacket pseudomodes in swept Hiemenz flow. J. Fluid Mech. 643:309–32
    [Google Scholar]
  110. Orchini A, Magri L, Silva CF, Mensah GA, Moeck JP. 2020a. Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points. J. Fluid Mech. 903:A37
    [Google Scholar]
  111. Orchini A, Mensah GA, Moeck JP. 2021. Perturbation theory of nonlinear, non-self-adjoint eigenvalue problems: semisimple eigenvalues. J. Sound Vibr. 507:116150
    [Google Scholar]
  112. Orchini A, Silva CF, Mensah GA, Moeck JP. 2020b. Thermoacoustic modes of intrinsic and acoustic origin and their interplay with exceptional points. Combust. Flame 214:251–62
    [Google Scholar]
  113. Pier B, Huerre P. 2001. Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435:145–74
    [Google Scholar]
  114. Poignand G, Olivier C, Penelet G. 2021. Parity-time symmetric system based on the thermoacoustic effect. J. Acoust. Soc. Am. 149:31913–22
    [Google Scholar]
  115. Ran W, Zare A, Jovanović MR. 2021. Model-based design of riblets for turbulent drag reduction. J. Fluid Mech. 906:A7
    [Google Scholar]
  116. Rayleigh L. 1878. The explanation of certain acoustical phenomena. Nature 18:319–21
    [Google Scholar]
  117. Rayleigh L. 1896. The Theory of Sound, Vol. 2 London: Macmillan. , 2nd ed..
  118. Redparth P. 2001. Spectral properties of non-self-adjoint operators in the semi-classical regime. J. Differ. Equ. 177:307–30
    [Google Scholar]
  119. Rigas G, Esclapez L, Magri L. 2017. Symmetry breaking in a 3D bluff-body wake. arXiv:1703.07405 [physics.flu-dyn] https://doi.org/10.48550/arXiv.1703.07405
    [Crossref]
  120. Rigas G, Morgans AS, Brackston RD, Morrison JF. 2015. Diffusive dynamics and stochastic models of turbulent axisymmetric wakes. J. Fluid Mech. 778:R2
    [Google Scholar]
  121. Rigas G, Pickering EM, Schmidt OT, Nogueira PA, Cavalieri AV et al. 2019. Streaks and coherent structures in jets from round and serrated nozzles Paper presented at 25th AIAA/CEAS Aeroacoustics Conference, Delft, The Netherlands, AIAA Pap 2019–2597
  122. Russo S, Fabre D, Giannetti F, Luchini P. 2016. The speed of sound in periodic ducts. J. Sound Vib. 361:243–50
    [Google Scholar]
  123. Saintillan D. 2018. Rheology of active fluids. Annu. Rev. Fluid Mech. 50:563–92
    [Google Scholar]
  124. Sakurai JJ, Napolitano J. 2011. Modern Quantum Mechanics Boston: Addison-Wesley. , 2nd ed..
  125. Schmid PJ. 2007. Nonmodal stability theory. Ann. Rev. Fluid Mech. 39:129–62
    [Google Scholar]
  126. Schmid PJ, Fosas de Pando M, Peake N 2017. Stability analysis for n-periodic arrays of fluid systems. Phys. Rev. Fluids 2:11113902
    [Google Scholar]
  127. Schmid PJ, Henningson DS. 2001. Stability and Transition of Shear Flows New York: Springer
  128. Schrödinger E. 1928. Collected Papers on Wave Mechanics London: Blackie & Son
  129. Schuermans B, Paschereit C, Monkewitz P. 2006. Non-linear combustion instabilities in annular gas-turbine combustors Paper presented at 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Pap 2006–549
  130. Seyranian AP, Kirillov ON, Mailybaev AA. 2005. Coupling of eigenvalues of complex matrices at diabolic and exceptional points. J. Phys. A 38:81723
    [Google Scholar]
  131. Seyranian AP, Mailybaev AA. 2003. Multiparameter Stability Theory with Mechanical Applications London: World Sci.
  132. Sinha A, Gudmundsson K, Xia H, Colonius T. 2016. Parabolized stability analysis of jets from serrated nozzles. J. Fluid Mech. 789:36–63
    [Google Scholar]
  133. Sogaro FS, Schmid PJ, Morgans AS. 2019. Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities. J. Fluid Mech. 878:190–220
    [Google Scholar]
  134. Steen LA. 1973. Highlights in the history of spectral theory. Am. Math. Mon. 80:4359–81
    [Google Scholar]
  135. Stewartson K. 1974. Multistructured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14:145–239
    [Google Scholar]
  136. Stuart JT. 1971. Nonlinear stability theory. Annu. Rev. Fluid Mech. 3:347–70
    [Google Scholar]
  137. Theofilis V. 2011. Global linear instability. Annu. Rev. Fluid Mech. 43:319–52
    [Google Scholar]
  138. Towne A, Cavalieri AVG, Jordan P, Colonius T, Schmidt O et al. 2017. Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825:1113–52
    [Google Scholar]
  139. Trefethen LN. 2005. Wave packet pseudomodes of variable coefficient differential operators. Proc. R. Soc. A 461:3099–122
    [Google Scholar]
  140. Trefethen LN, Embree M. 2005. Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators Princeton, NJ: Princeton University Press
  141. Trefethen LN, Trefethen AE, Reddy SC, Driscoll TA. 1993. Hydrodynamic stability without eigenvalues. Science 261:578–84
    [Google Scholar]
  142. van Gils SA, Mallet-Paret J. 1986. Hopf bifurcation and symmetry: travelling and standing waves on the circle. Proc. R. Soc. Edinburgh. A 104:3–4279–307
    [Google Scholar]
  143. von Neumann J, Wigner EP. 1929. Über das Verhalten von Eigenwerten bei adiabatischen Prozessen. Phys. Z. 30:467–70
    [Google Scholar]
  144. von Saldern JGR, Moeck JP, Orchini A. 2021. Nonlinear interaction between clustered unstable thermoacoustic modes in can-annular combustors. Proc. Combust. Inst. 38:46145–53
    [Google Scholar]
  145. Wolf P, Staffelbach G, Gicquel LY, Müller JD, Poinsot T. 2012. Acoustic and large eddy simulation studies of azimuthal modes in annular combustion chambers. Combust. Flame 159:113398–413
    [Google Scholar]
  146. Worth NA, Dawson JR. 2013. Modal dynamics of self-excited azimuthal instabilities in an annular combustion chamber. Combust. Flame 160:112476–89
    [Google Scholar]
  147. Wu Y, Yang M, Sheng P. 2018. Perspective: Acoustic metamaterials in transition. J. Appl. Phys. 123:9090901
    [Google Scholar]
/content/journals/10.1146/annurev-fluid-031022-044209
Loading
/content/journals/10.1146/annurev-fluid-031022-044209
Loading

Data & Media loading...

  • Article Type: Review Article
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