Schmid, P. J., and Brandt, L., 2013, “Analysis of Fluid Systems: Stability, Receptivity, Sensitivity,” ASME Appl. Mech. Rev., 66(2), p. 024804.

[CrossRef]Barkley, D., 2006, “Linear Analysis of the Cylinder Wake Mean Flow,” Europhys. Lett., 75, pp. 750–756.

[CrossRef]Sipp, D., and Lebedev, A., 2007, “Global Stability of Base and Mean Flows: A General Approach and Its Applications to Cylinder and Open Cavity Flows,” J. Fluid Mech., 593, pp. 333–358.

[CrossRef]Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O., and Schlatter, P., 2006, “Steady Solutions of the Navier–Stokes Equations by Selective Frequency Damping,” Phys. Fluids, 18, p. 068102.

[CrossRef]Kleiser, L., and Zang, T. A., 1991, “Numerical Simulation of Transition in Wall-Bounded Shear Flows,” Annu. Rev. Fluid Mech., 23, pp. 495–537.

[CrossRef]Fasel, H., Rist, U., and Konzelmann, U., 1990, “Numerical Investigation of the Three–Dimensional Development in Boundary Layer Transition,” AIAA J., 28(1), pp. 29–37.

[CrossRef]Lundbladh, A., Henningson, D. S., and Johansson, A. V., 1992, “An Efficient Spectral Integration Method for the Solution of the Navier–Stokes Equations,” FFA-TN 1992-28, Aeronautical Research Institute of Sweden, Bromma.

Lin, C. C., 1955, *Theory of Hydrodynamic Stability*, Cambridge University, Cambridge, UK.

Drazin, P. G., and Reid, W. H., 1981, *Hydrodynamic Stability*, Cambridge University, Cambridge, UK.

Mack, L. M., 1984, “Boundary Layer Stability Theory: Special Course on Stability and Transition of Laminar Flow,” AGARD Report 709.

Herbert, Th., 1997, “Parabolized Stability Equations,” Annu. Rev. Fluid Mech., 29, pp. 245–283.

[CrossRef]Theofilis, V., 2011, “Global Linear Instability,” Annu. Rev. Fluid Mech., 43, pp. 319–352.

[CrossRef]Rayleigh, J. W., 1898, *The Theory of Sound*, Vols. 1 and 2, Dover, New York.

Smith, A. M. O., and Gamberoni, N., 1956, “Transition, Pressure Gradient, and Stability Theory,” Douglas Aircraft Co, Technical Report ES 26388.

van Ingen, J. L., 1956, “A Suggested Semi-Empirical Method for the Calculation of the Boundary Layer Transition Region,” University of Technology, Department of Aerospace Engineering, Delft, Report VTH-74.

Arnal, D., 1993, “Boundary Layer Transition: Predictions Based on Linear Theory. Special Course on “Progress in Transition Modeling,” Mar.—Apr. 1993, AGARD-R-793, 2-1–2-63.

Morkovin, M. V., 1969, “The Many Faces of Transition,” *Viscous Drag Reduction*, C. S.Wells, ed., Plenum Press, New York.

Reshotko, E., 1976, “Boundary-Layer Stability and Transition,” Annu. Rev., 8, pp. 311–350.

Crouch, J. D., 1992, “Non-Localized Receptivity of Boundary Layers,” J. Fluid Mech., 244, pp. 567–581.

[CrossRef]Saric, W., Reed, H., and Kerschen, E., 2000, “Boundary-Layer Receptivity to Freestream Disturbances,” Annu. Rev. Fluid Mech., 34, pp. 291–319.

[CrossRef]Pralits, J. O., Airiau, C., Hanifi, A., and Henningson, D. S., 2000, “Sensitivity Analysis Using Adjoint Parabolized Stability Equations for Compressible Flows,” Flow, Turbul. Combust., 65(3), pp. 321–346.

[CrossRef]Tempelmann, D., Schrader, L.-U., Hanifi, A., Brandt, L., and Henningson, D. S., 2012, “Swept Wing Boundary-Layer Receptivity to Localized Surface Roughness,” J. Fluid Mech., 711, pp. 516–544.

[CrossRef]Zuccher, S., and Luchini, P., 2014, “Boundary-Layer Receptivity to External Disturbances Using Multiple Scales,” Meccanica, 49(2), pp. 441–467.

[CrossRef]Huerre, P., and Monkewitz, P. A., 1990, “Local and Global Instabilities in Spatially Developing Flows,” Annu. Rev. Fluid Mech., 22, pp. 473–537.

[CrossRef]Huerre, P., and Rossi, M., 1998, “Hydrodynamic Instabilities in Open Flows,” *Hydrodynamics and Nonlinear Instabilities*, C.Godreche and P.Manneville, eds. Cambridge University, Cambridge, UK.

Huerre, P., 2000, “Open Shear Flow Instabilities,” G. K.Batchelor, H. K.Moffat, and M. G. W., C.U.P. eds., *Perspectives in Fluid Dynamics: A Collective Introduction to Current Research*, Cambridge University, Cambridge, UK.

Theofilis, V., 2003, “Advances in Global Linear Instability Analysis of Nonparallel and Three-Dimensional Flows,” Prog. Aeronaut. Sci., 39, pp. 249–315.

[CrossRef]Mack, L. M., 1984, “Boundary-Layer Stability Theory,” AGARD Report No. 709.

Schmid, P., and Henningson, D. S., 2001, *Stability and Transition in Shear Flows*. Springer, New York.

Fedorov, A., 2011, “Transition and Stability of High-Speed Boundary Layers,” Annu. Rev. Fluid Mech., 43, pp. 79–95.

[CrossRef]Zhong, X., and Wang, X., 2012, “Direct Numerical Simulation on the Receptivity, Instability, and Transition of Hypersonic Boundary Layers,” Annu. Rev. Fluid Mech., 44, pp. 527–561.

[CrossRef]Yu, M.-H., and Monkewitz, P. A., 1990, “The Effect of Nonuniform Density on the Absolute Instability of Two-Dimensional Inertial Jets and Wakes,” Phys. Fluids A, 2(7), pp. 1175–1181.

[CrossRef]Juniper, M. P., 2007, “The Full Impulse Response of Two-Dimensional Shear Flows and Implications for Confinement,” J. Fluid Mech., 590, pp. 163–185.

[CrossRef]Rees, S. J., and Juniper, M. P., 2009, “The Effect of Surface Tension on the Stability of Unconfined and Confined Planar Jets and Wakes,” J. Fluid Mech., 633, pp. 71–97.

[CrossRef]Healey, J. J., 2006, “A New Convective Instability of the Rotating-Disk Boundary Layer With Growth Normal to the Plate,” J. Fluid Mech., 560, pp. 279–310.

[CrossRef]Gaster, M., 1962, “A Note on the Relation Between Temporally-Increasing and Spatially-Increasing Disturbances in Hydrodynamic Stability,” J. Fluid Mech., 14, pp. 222–224.

[CrossRef]Huerre, P., and Monkewitz, P. A., 1990, “Local and Global Instabilities in Spatially Developing Flows,” Annu. Rev. Fluid Mech., 22, pp. 473–537.

[CrossRef]Orszag, S. A., 1969, “Numerical Methods for the Simulations of Turbulence,” Phys. Fluids, Suppl., Vol. II, pp. 250–257.

Kirchner, N., 2000, “Computational Aspects of the Spectral Galerkin FEM for the Orr–Sommerfeld Equation,” Int. J. Numer. Methods Fluids, 32, pp. 119–137.

[CrossRef]Michalke, A., 1964, “On the Inviscid Instability of the Hyperbolic-Tangent Velocity Profile,” J. Fluid Mech., 19, pp. 543–556.

[CrossRef]Herbert, T., 1984, “Secondary Instability of Shear Flows,” AGARD–R–709 Special Course on Stability and Transition of Laminar Flow, pp. 7.1–7.13.

Herbert, T., 1984, “Analysis of the Subharmonic Route to Transition in Boundary Layers,” AIAA Paper No. 84-0009.

[CrossRef]Herbert, T., 1988, “Secondary Instability of Boundary Layers,” Annu. Rev. Fluid Mech., 20, pp. 487–526.

[CrossRef]Kachanov, Y. S., and Levchenko, V. Y., 1984, “The Resonant Interaction of Disturbances at Laminar-Turbulent Transition in a Boundary Layer,” J. Fluid Mech., 138, pp. 209–247.

[CrossRef]Kachanov, Y. S., 1994, “Physical Mechanisms of Laminar-Boundary-Layer Transition,” Annu. Rev. Fluid Mech., 26, pp. 411–482.

[CrossRef]Orszag, S. A., and Patera, A. T., 1983, “Secondary Instability of Wall-Bounded Shear Flows,” J. Fluid Mech., 128, pp. 347–385.

[CrossRef]Herbert, T., 1991, “Boundary-Layer Transition—Analysis and Prediction Revisited,” AIAA Paper No. 91-0737.

Saric, W. S., and Thomas, A. S. W., 1984, “Experiments on the Subharmonic Route to Turbulence in Boundary Layers,” *Turbulence and Chaotic Phenomena in Fluids*, T.Tatsumi, ed., Amsterdam, North-Holland, pp. 117–122.

Herbert, T., 1983, “Secondary Instability of Plane Channel Flow to Subharmonic Three-Dimensional Disturbances,” Phys. Fluids, 26, pp. 871–874.

[CrossRef]Bouthier, M., 1972, “Stabilité linéaire des écoulements presque parallélles,” J. de Mec., 11, pp. 599–621.

Gaster, M., 1975, “A Theoretical Model for the Development of a Wave Packet in a Laminar Boundary Layer,” Proc. R. Soc. London, Ser. A, 347, pp. 271–289.

[CrossRef]Saric, W. S., and Nayfeh, A. H., 1975, “Non-Parallel Stability of Boundary Layer Flows,” Phys. Fluids, 18, pp. 945–950.

[CrossRef]Gaponov, S. A., 1981, “The Influence of Flow Non-Parallelism on Disturbance Development in the Supersonic Boundary Layers,” Proceedings of the 8th Canadian Congress of Applied Mechanics, pp. 673–674.

El-Hady, N., 1991, “Nonparallel Instability of Supersonic and Hypersonic Boundary Layers,” Phys. Fluids A, 3, pp. 2164–2178.

[CrossRef]Hall, P., 1983, “The Linear Development of Görtler Vortices in Growing Boundary Layers,” J. Fluid Mech., 130, pp. 41–58.

[CrossRef]Itoh, N., 1981, “Secondary Instability of Laminar Flows,” Proc. R. Soc. London, Ser. A, 375, pp. 565–578.

[CrossRef]Herbert, T., and Bertolotti, F. P., 1987, “Stability Analysis of Nonparallel Boundary Layers,” Bull. Am. Phys. Soc., 32, p. 2079.

Bertolotti, F. P., Herbert, T., and Spalart, S., 1992, “Linear and Nonlinear Stability of the Blasius Boundary Layer,” J. Fluid Mech., 242, pp. 441–474.

[CrossRef]Simen, M., 1992, “Local and Non-Local Stability Theory of Spatially Varying Flows,” M.Hussaini, A.Kumar, and C.Streett, eds., *Instability, Transition, and Turbulence*, Springer, New York, pp. 181–201.

Andersson, P., Berggren, M., and Henningson, D., 1999, “Optimal Disturbances and Bypass Transition in Boundary Layers,” Phys. Fluids, 11, pp. 134–150.

[CrossRef]Luchini, P., 1996, “Reynolds Number Independent Instability of the Blasius Boundary Layer Over a Flat Surface,” J. Fluid Mech., 327, pp. 101–115.

[CrossRef]Tempelmann, D., Hanifi, A., and Henningson, D., 2010, “Spatial Optimal Growth in Three-Dimensional Boundary Layers,” J. Fluid Mech., 646, pp. 5–37.

[CrossRef]Tempelmann, D., Hanifi, A., and Henningson, D. S., 2012, “Spatial Optimal Growth in Three-Dimensional Compressible Boundary Layers,” J. Fluid Mech., 704, pp. 251–279.

[CrossRef]Bertolotti, F. P., 1991, “Linear and Nonlinear Stability of Boundary Layers With Streamwise Varying Properties,” Ph.D. thesis, The Ohio State University, Department of Mechanical Engineering, Columbus, OH.

Herbert, T., 1994, “Parabolized Stability Equations,” Tech. Rep. AGARD 793.

Hanifi, A., Henningson, D., Hein, S., Bertolotti, F. P., and Simen, M., 1994, “Linear Nonlocal Instability Analysis—The Linear NOLOT Code,” FFA Tech. Rep. FFA TN 1994-54. See also Hein et al. [67].

Hein, S., Bertolotti, F. P., Simen, M., Hanifi, A., and Henningson, D. S., 1994, “Linear Non-Local Instability Analysis—The Linear NOLOT Code,” Deutsche Forschunganstalt für Luft- und Raumfahrt, Tech. Rep. DLR-IB 223-94 A 43.

Bertolotti, F. P., Herbert, T., and Spalart, S. P., 1992, “Linear and Nonlinear Stability of the Blasius Boundary Layer,” J. Fluid Mech., 242, pp. 441–474.

[CrossRef]Berlin, S., Hanifi, A., and Henningson, D. S., 1998, “The Neutral Stability Curve for Non-Parallel Boundary Layer Flow in Oblique Waves in Boundary Layer Transition,” Ph.D. thesis, Royal Institute of Technology, Stockholm.

Klingmann, B. G. B., Boiko, A. V., Westin, K. J. A., Kozlov, V. V., and Alfredsson, P. H., 1993, “Experiments on the Stability of Tollmien–Schlichting Waves,” Eur. J. Mech., B/Fluids, 12, pp. 493–514.

Haj-Hariri, H., 1994, “Characteristics Analysis of the Parabolized Stability Equations,” Stud. Appl. Math., 92, pp. 41–53.

Li, F., and Malik, M. R., 1995, “Mathematical Nature of Parabolized Stability Equations,” *Laminar-Turbulent Transition*, R.Kobayashi, ed., Springer-Verlag, Berlin, pp. 205–212.

Airiau, C., 1994, “Linear and Weakly Nonlinear Stability of an Incompressible Laminar Boundary Layer by the Parabolized Stability Equations (PSE),” Ph.D. thesis, L’École Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France.

Andersson, P., Henningson, D. S., and Hanifi, A., 1998, “On a Stabilization Procedure for the Parabolic Stability Equations,” J. Eng. Math., 33, pp. 311–332.

[CrossRef]Tatsumi, T., and Yoshimura, T., 1990, “Stability of the Laminar Flow in a Rectangular Duct,” J. Fluid Mech., 212, pp. 437–449.

[CrossRef]Henningson, D. S., 1987, “Stability of Parallel Inviscid Shear Flow With Mean Spanwise Variation,” FFA Tech. Rep. TN 1987-57.

Theofilis, V., Hein, S., and Dallmann, U., 2000, “On the Origins of Unsteadiness and Three-Dimensionality in a Laminar Separation Bubble,” Philos. Trans. R. Soc., A, 358, pp. 3229–324.

[CrossRef]Åkervik, E., Ehrensteinb, U., Gallaire, F., and Henningson, D. S., 2008, “Global Two-Dimensional Stability Measures of the Flat Plate Boundary-Layer Flow,” Eur. J. Mech. B/ Fluids, 27(5), pp. 501–513.

[CrossRef]Rodríguez, D., and Theofilis, V., 2008, “On Instability and Structural Sensitivity of Incompressible Laminar Separation Bubbles in a Flat-Plate Boundary Layer,” AIAA Paper No. 2008-4148.

Paredes, P., Theofilis, V., Rodríguez, D., and Tendero, J. A., 2011, “The PSE-3D Instability Analysis Methodology for Flows Depending Strongly on Two and Weakly on the Third Spatial Dimension,” “6th AIAA Theoretical Fluid Mechanics Conference,” Honolulu, HI, June 27–30, AIAA Paper No. 2011-3752.

Bridges, T., and Morris, P., 1984, “Differential Eigenvalue Problems in Which the Parameter Appears Nonlinearly,” J. Comput. Phys., 55, pp. 437–460.

[CrossRef]Theofilis, V., 1995, “Spatial Stability of Incompressible Attachment Line Flow,” Theory Comput. Fluid Dyn., 7, pp. 159–171.

[CrossRef]de Tullio, N., Paredes, P., Sandham, N. D., and Theofilis, V., 2013, “Roughness-Induced Instability and Breakdown to Turbulence in a Supersonic Boundary-Layer,” J. Fluid Mech., 735, pp. 613–646.

[CrossRef]Paredes, P., Hermanns, M., Clainche, S. L., and Theofilis, V., 2013, “O(10

^{4}) Speedup in Global Linear Instability Analysis Using Matrix Formation,” Comput. Methods Appl. Mech. Eng., 253, pp. 287–304.

[CrossRef]Morse, P. M., and Feshbach, H., 1953, *Methods of Theoretical Physics, Parts I, II*. McGraw-Hill, New York.

Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., 1987, *Spectral Methods in Fluid Dynamics*, Springer, New York.

Mack, L. M., 1976, “A Numerical Study of the Temporal Eigenvalue Spectrum of the Blasius Boundary Layer,” J. Fluid Mech., 73, pp. 497–520.

[CrossRef]Theofilis, V., 1994, “The Discrete Temporal Eigenvalue Spectrum of the Generalised Hiemenz Flow as Solution of the Orr–Sommerfeld Equation,” J. Eng. Math., 28, pp. 241–259.

[CrossRef]Akervik, E., Ehrenstein, U., Gallaire, F., and Henningson, D. S., 2008, “Global Two-Dimensional Stability Measures of the Flat Plate Boundary-Layer Flow,” Eur. J. Mech. B/Fluids, 27(5), pp. 501–513.

[CrossRef]Theofilis, V., Duck, P. W., and Owen, J., 2004, “Viscous Linear Stability Analysis of Rectangular Duct and Cavity Flows,” J. Fluid. Mech., 505, pp. 249–286.

[CrossRef]Lele, S., 1992, “Compact Finite Difference Schemes With Spectral-Like Resolution,” J. Comput. Phys., 103, pp. 16–42.

[CrossRef]Tam, C., and Webb, J., 1993, “Dispersion-Relation-Preserving Finite-Difference Schemes for Computational Acoustics,” J. Comp. Phys., 107(2), pp. 262–281.

[CrossRef]Hermanns, M., and Hernández, J. A., 2008, “Stable High-Order Finite-Difference Methods Based on Non-Uniform Grid Point Distributions,” Int. J. Numer. Methods Fluids, 56, pp. 233–255.

[CrossRef]Karniadakis, G. E., and Sherwin, S. J., 2005, *Spectral/Hp Element Methods for Computational Fluid Dynamics*, 2nd ed., Oxford University, New York.

Golub, G. H., and van Loan, C. F., 1996, *Matrix Computations*, 3rd ed., The Johns Hopkins University, Johns Hopkins University Press, Baltimore, MD.

Theofilis, V., 2000, “Globally Unstable Basic Flows in Open Cavities,” 6th AIAA Aeroacoustics Conference and Exhibit, AIAA-2000-1965.

Theofilis, V., Fedorov, A., and Collis, S. S., 2006, “Leading-Edge Boundary Layer Flow: Prandtl's Vision, Current Developments, and Future Perspectives,” *One Hundred Years Boundary Layer Research*, G. E. A.Meier and K.Sreenivasan, eds., DLR, Springer, The Netherlands, pp. 73–82.

Arnoldi, W. E., 1951, “The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem,” Q. Appl. Math., 9, pp. 17–29.

Saad, Y., 1980, “Variations of Arnoldi's Method for Computing Eigen Elements of Large Unsymmetric Matrices,” Linear Algebra Appl., 34, pp. 269–295.

[CrossRef]Gómez, F., Gómez, R., and Theofilis, V., 2014, “On Three-Dimensional Global Linear Instability Analysis of Flows With Standard Aerodynamics Codes,” Aerosp. Sci. Tech., 32 pp. 223–234.

[CrossRef]