Mechanisms underlying transient growth of planar perturbations in unbounded compressible shear flow, Journal of Fluid Mechanics, vol.27, pp.479-507 ,
DOI : 10.1063/1.858153
THE EFFECT OF RAPID DISTORTION OF A FLUID IN TURBULENT MOTION, The Quarterly Journal of Mechanics and Applied Mathematics, vol.7, issue.1, pp.83-103, 1954. ,
DOI : 10.1093/qjmam/7.1.83
Histories of Adiabatic Quantum Transitions, Proc. R. Soc. Lond. A 429, pp.61-72, 1990. ,
DOI : 10.1098/rspa.1990.0051
Time-harmonic acoustic propagation in the presence of a shear flow, Journal of Computational and Applied Mathematics, vol.204, issue.2, pp.428-439, 2007. ,
DOI : 10.1016/j.cam.2006.02.048
Wavetrains in Inhomogeneous Moving Media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.302, issue.1471, pp.529-554, 1968. ,
DOI : 10.1098/rspa.1968.0034
Waves and mean flows, 2009. ,
DOI : 10.1017/cbo9780511605499
Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A : Fluid Dyn, pp.1637-1650, 1992. ,
Stability analysis and large-eddy simulation of rotating turbulence with organized eddies, Journal of Fluid Mechanics, vol.93, issue.-1, pp.175-200, 1994. ,
DOI : 10.1063/1.1694822
LINEAR AND NONLINEAR MODELS OF ANISOTROPIC TURBULENCE, Annual Review of Fluid Mechanics, vol.31, issue.1, pp.1-53, 1999. ,
DOI : 10.1146/annurev.fluid.31.1.1
New linear mechanisms of acoustic wave generation in smooth shear flows -(Nonmodal study) In Sound-flow interactions, pp.210-237, 2002. ,
Mechanism of energy transformations in shear magnetohydrodynamic flows, Physical Review E, vol.47, issue.1, pp.366-374, 1993. ,
DOI : 10.1103/PhysRevE.47.366
Acoustic waves in unbounded shear flows, Physics of Fluids, vol.9, issue.7, pp.1955-1962, 1997. ,
DOI : 10.1063/1.869314
Hydrodynamic stability of compressible plane Couette flow, Physical Review E, vol.50, issue.6, pp.4283-4285, 1994. ,
DOI : 10.1103/PhysRevE.50.R4283
Linear Mechanism of Wave Emergence from Vortices in Smooth Shear Flows, Physical Review Letters, vol.79, issue.17, pp.3178-3181, 1997. ,
DOI : 10.1103/PhysRevLett.79.3178
Evolution of wavelike disturbances in shear flows : A class of exact solutions of the navier-stokes equations, Proc. R. Soc. Lond. A 406, pp.13-26, 1986. ,
The Evolution of Linearized Perturbations of Parallel Flows, Studies in Applied Mathematics, vol.128, issue.2, pp.123-157, 1990. ,
DOI : 10.1002/sapm1990832123
Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case, The Journal of Chemical Physics, vol.64, issue.8, pp.3129-3137, 1976. ,
DOI : 10.1063/1.432648
Coupled rayleigh surface waves in a slowly varying elastic waveguide, Proc. R. Soc. Lond. A 455, pp.917-931, 1999. ,
Localized Instabilities in Fluids, Handbook of mathematical fluid dynamics, pp.289-353, 2003. ,
DOI : 10.1016/S1874-5792(03)80010-1
Emergence of acoustic waves from vorticity fluctuations: Impact of non-normality, Physical Review E, vol.80, issue.4, p.321, 2009. ,
DOI : 10.1103/PhysRevE.80.046321
Linear coupling and overreflection phenomena of magnetohydrodynamic waves in smooth shear flows, Physics of Plasmas, vol.11, issue.10, pp.4672-4685, 2004. ,
DOI : 10.1063/1.1789998
Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles, Journal of Fluid Mechanics, vol.49, issue.03, pp.433-468, 1978. ,
DOI : 10.1017/S0022112078002682
Quasi-modes of a weakly curved waveguide, Proc. R. Soc. Lond. A 459, 2003. ,
DOI : 10.1098/rspa.2003.1141
Time Development of Exponentially Small Non-Adiabatic Transitions, Communications in Mathematical Physics, vol.137, issue.2, pp.393-413, 2004. ,
DOI : 10.1007/s00220-004-1124-5
URL : https://hal.archives-ouvertes.fr/hal-00348757
Perturbation methods. Cambridge texts in applied mathematics, 1991. ,
Introduction to perturbation methods. Texts in applied mathematics, 1995. ,
Local and Global Instabilities in Spatially Developing Flows, Annual Review of Fluid Mechanics, vol.22, issue.1, pp.473-537 ,
DOI : 10.1146/annurev.fl.22.010190.002353
Hydrodynamic instabilities in open flows, Hydrodynamics and nonlinear instabilities, pp.81-294, 1998. ,
DOI : 10.1017/CBO9780511524608.004
On the implementation of the method of magnus series for linear differential equations, Bit Numerical Mathematics, vol.39, issue.2, pp.281-304, 1999. ,
DOI : 10.1023/A:1022393913721
Superadiabatic tracking of quantum evolution, Journal of Physics A: Mathematical and General, vol.24, issue.14, pp.3255-3264, 1991. ,
DOI : 10.1088/0305-4470/24/14/014
What Can the Kinematic Complexity of Astrophysical Shear Flows Lead To?, The Astrophysical Journal, vol.518, issue.2, pp.814-820, 1999. ,
DOI : 10.1086/307319
Problems in flow acoustics, Reviews of Modern Physics, vol.55, issue.3, pp.707-724, 1983. ,
DOI : 10.1103/RevModPhys.55.707
Multimodal admittance method in waveguides and singularity behavior at high frequencies, Journal of Computational and Applied Mathematics, vol.234, issue.6, pp.1834-1841, 2010. ,
DOI : 10.1016/j.cam.2009.08.034
Lamb wave propagation in elastic waveguides with variable thickness, Proc. R. Soc. A 462, pp.1315-1339, 2006. ,
DOI : 10.1098/rspa.2005.1612
Pseudospectra of the Orr???Sommerfeld Operator, SIAM Journal on Applied Mathematics, vol.53, issue.1, pp.15-47, 1993. ,
DOI : 10.1137/0153002
ACOUSTICS OF KINEMATICALLY COMPLEX SHEAR FLOWS, Journal of Computational Acoustics, vol.09, issue.03, pp.869-888, 2001. ,
DOI : 10.1142/S0218396X01001078
Coupling of sound and internal waves in shear flows, Physical Review E, vol.55, issue.1, 1997. ,
DOI : 10.1103/PhysRevE.55.1185
Nonmodal Stability Theory, Nonmodal stability theory, pp.129-162, 2007. ,
DOI : 10.1146/annurev.fluid.38.050304.092139
URL : https://hal.archives-ouvertes.fr/hal-01023333
Propagation in Slowly-Varying Wave-Guides, SIAM Journal on Applied Mathematics, vol.33, issue.1, pp.39-50, 1977. ,
DOI : 10.1137/0133004
Non-Adiabatic Crossing of Energy Levels, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.137, issue.833, pp.696-702, 1932. ,
DOI : 10.1098/rspa.1932.0165
Histories of Adiabatic Quantum Transitions, Proc. R. Soc. Lond. A 429, pp.61-72, 1990. ,
DOI : 10.1098/rspa.1990.0051
Superadiabatic transitions in quantum molecular dynamics, Proc. R. Soc. A 465, 2009. ,
DOI : 10.1098/rspa.2009.0337
The devil's invention : Asymptotic, superasymptotic and hyperasymptotic series, Acta Applicandae Mathematicae, vol.56, issue.1, pp.1-98, 1999. ,
DOI : 10.1023/A:1006145903624
New linear mechanisms of acoustic wave generation in smooth shear flows -(Nonmodal study) In Sound-flow interactions, pp.210-237, 2002. ,
Mechanism of energy transformations in shear magnetohydrodynamic flows, Physical Review E, vol.47, issue.1, pp.366-374, 1993. ,
DOI : 10.1103/PhysRevE.47.366
Acoustic waves in unbounded shear flows, Physics of Fluids, vol.9, issue.7, pp.1955-1962, 1997. ,
DOI : 10.1063/1.869314
Hydrodynamic stability of compressible plane Couette flow, Physical Review E, vol.50, issue.6, pp.4283-4285, 1994. ,
DOI : 10.1103/PhysRevE.50.R4283
Effect of coupling and linear transformation of waves in shear flows, Physical Review E, vol.53, issue.6, pp.6028-6031, 1996. ,
DOI : 10.1103/PhysRevE.53.6028
Linear Mechanism of Wave Emergence from Vortices in Smooth Shear Flows, Physical Review Letters, vol.79, issue.17, pp.3178-3181, 1997. ,
DOI : 10.1103/PhysRevLett.79.3178
Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case, The Journal of Chemical Physics, vol.64, issue.8, pp.3129-3137, 1976. ,
DOI : 10.1063/1.432648
Adiabatic perturbation of discrete spectrum states. Sov. Phys, pp.941-943, 1962. ,
Adiabatic transition histories of population transfer in the ?? system, Physical Review A, vol.52, issue.5, pp.4017-4022, 1995. ,
DOI : 10.1103/PhysRevA.52.4017
Acoustic-vorticity coupling in linearly varying shear flows using the WKB method (Revised manuscript submitted for publication to, Proc. R. Soc. A, Chapter, 2012. ,
Emergence of acoustic waves from vorticity fluctuations: Impact of non-normality, Physical Review E, vol.80, issue.4, p.321, 2009. ,
DOI : 10.1103/PhysRevE.80.046321
Linear coupling and overreflection phenomena of magnetohydrodynamic waves in smooth shear flows, Physics of Plasmas, vol.11, issue.10, pp.4672-4685, 2004. ,
DOI : 10.1063/1.1789998
Time Development of Exponentially Small Non-Adiabatic Transitions, Communications in Mathematical Physics, vol.137, issue.2, pp.393-413, 2004. ,
DOI : 10.1007/s00220-004-1124-5
URL : https://hal.archives-ouvertes.fr/hal-00348757
Overlapping Stokes smoothings in adiabatic quantum transitions, Journal of Physics A: Mathematical and General, vol.26, issue.24, p.7615, 1993. ,
DOI : 10.1088/0305-4470/26/24/031
Superadiabatic tracking of quantum evolution, Journal of Physics A: Mathematical and General, vol.24, issue.14, pp.3255-3264, 1991. ,
DOI : 10.1088/0305-4470/24/14/014
What Can the Kinematic Complexity of Astrophysical Shear Flows Lead To?, The Astrophysical Journal, vol.518, issue.2, pp.814-820, 1999. ,
DOI : 10.1086/307319
ACOUSTICS OF KINEMATICALLY COMPLEX SHEAR FLOWS, Journal of Computational Acoustics, vol.09, issue.03, pp.869-888, 2001. ,
DOI : 10.1142/S0218396X01001078
Coupling of sound and internal waves in shear flows, Physical Review E, vol.55, issue.1, 1997. ,
DOI : 10.1103/PhysRevE.55.1185
Non-Adiabatic Crossing of Energy Levels, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.137, issue.833, pp.696-702, 1932. ,
DOI : 10.1098/rspa.1932.0165
Modelling of sound propagation in a non-uniform lined duct using a Multi-Modal Propagation Method, Journal of Sound and Vibration, vol.289, issue.4-5, 2006. ,
DOI : 10.1016/j.jsv.2005.03.021
An improved multimodal method for sound propagation in nonuniform lined ducts, The Journal of the Acoustical Society of America, vol.122, issue.1, pp.280-290, 2007. ,
DOI : 10.1121/1.2736785
Diffraction Grating EfficienciesConformal Mapping Method for a Good Real Conductor, Optica Acta: International Journal of Optics, vol.22, issue.11, pp.1459-1473, 1982. ,
DOI : 10.1080/713820790
Surface Impedance Boundary Condition for Metallic Diffraction Gratings in the Optical and Infrared Range, Optica Acta: International Journal of Optics, vol.268, issue.3, pp.313-322, 1983. ,
DOI : 10.1080/713821187
Sound propagation in rigid bends: A multimodal approach, The Journal of the Acoustical Society of America, vol.110, issue.3, pp.1329-1337, 2001. ,
DOI : 10.1121/1.1391249
Multimodal analysis of acoustic propagation in three-dimensional bends, Wave Motion, vol.36, issue.2, pp.157-168, 2002. ,
DOI : 10.1016/S0165-2125(02)00009-4
Conformal-mapping- based coordinate generation method for flows in periodic configurations, Journal of Computational Physics, vol.62, issue.1, pp.221-247, 1986. ,
DOI : 10.1016/0021-9991(86)90108-7
On the implementation of the method of magnus series for linear differential equations, Bit Numerical Mathematics, vol.39, issue.2, pp.281-304, 1999. ,
DOI : 10.1023/A:1022393913721
On the solution of linear differential equations in lie group, Phil. Trans. R. Soc. A, vol.357, pp.983-1019, 1999. ,
Multimodal admittance method in waveguides and singularity behavior at high frequencies, Journal of Computational and Applied Mathematics, vol.234, issue.6, 2010. ,
DOI : 10.1016/j.cam.2009.08.034
A study of wave propagation in varying cross???section waveguides by modal decomposition. Part I. Theory and validation, The Journal of the Acoustical Society of America, vol.100, issue.4, pp.2034-2048 ,
DOI : 10.1121/1.417913
Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane, The Journal of the Acoustical Society of America, vol.109, issue.3, pp.878-885, 2001. ,
DOI : 10.1121/1.1348297
A Natural Approach to the Numerical Integration of Riccati Differential Equations, SIAM Journal on Numerical Analysis, vol.36, issue.5, pp.1392-1413, 1999. ,
DOI : 10.1137/S0036142996307946
Rigorous integral approach to the problem of scattering from a modulated periodic medium obtained through conformal mapping, Journal of the Optical Society of America A, vol.12, issue.6, 1995. ,
DOI : 10.1364/JOSAA.12.001283
The Chebfun Development Team, Chebfun Version, vol.4, issue.2, 2011. ,
Conformal mapping on rough boundaries.mI. Applications to harmonic problems, Physical Review E, vol.55, issue.5, pp.6171-6185, 1997. ,
DOI : 10.1103/PhysRevE.55.6171
URL : https://hal.archives-ouvertes.fr/hal-00002508
Conformal mapping on rough boundaries. II. Applications to biharmonic problems, Physical Review E, vol.55, issue.5, pp.6186-6196, 1997. ,
DOI : 10.1103/PhysRevE.55.6186
URL : https://hal.archives-ouvertes.fr/hal-00002508
Wave scattering from rough surfaces Springer series on wave phenomena References Iserles On the implementation of the method of magnus series for linear differential equations, BIT, vol.39, pp.281-304, 1999. ,
Double structures of steady streaming in the oscillatory viscous flow over a wavy wall, Journal of Fluid Mechanics, vol.17, issue.04, 1979. ,
DOI : 10.1017/S0022112079001993
Unsteady viscous flow over a wavy wall, Journal of Fluid Mechanics, vol.175, issue.01, pp.33-43, 1971. ,
DOI : 10.1017/S0022112071002441
Viscous and resistive eddies near a sharp corner, Journal of Fluid Mechanics, vol.6, issue.01, pp.1-18, 1964. ,
DOI : 10.1017/S0022112064000015
Multimodal admittance method in waveguides and singularity behavior at high frequencies, Journal of Computational and Applied Mathematics, vol.234, issue.6, pp.1834-1841, 2010. ,
DOI : 10.1016/j.cam.2009.08.034
A study of wave propagation in varying cross???section waveguides by modal decomposition. Part I. Theory and validation, The Journal of the Acoustical Society of America, vol.100, issue.4, pp.2034-2048 ,
DOI : 10.1121/1.417913
Unsteady viscous flow over irregular boundaries, Journal of Fluid Mechanics, vol.50, issue.-1, pp.11-34, 1993. ,
DOI : 10.1103/PhysRevLett.61.1595
A Natural Approach to the Numerical Integration of Riccati Differential Equations, SIAM Journal on Numerical Analysis, vol.36, issue.5, pp.1392-1413, 1999. ,
DOI : 10.1137/S0036142996307946
Conformal mapping on rough boundaries.mI. Applications to harmonic problems, Physical Review E, vol.55, issue.5, pp.6171-6185, 1997. ,
DOI : 10.1103/PhysRevE.55.6171
URL : https://hal.archives-ouvertes.fr/hal-00002508
Conformal mapping on rough boundaries. ii. applications to biharmonic problems. Phys. Rev, ) References References Berry, M. V. 1990 Histories of adiabatic quantum transitions. Proc. R. Soc. Lond. A 429, pp.6186-6196, 1997. ,
URL : https://hal.archives-ouvertes.fr/hal-00002508
Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case, The Journal of Chemical Physics, vol.64, issue.8, pp.3129-3137, 1976. ,
DOI : 10.1063/1.432648
A study of wave propagation in varying cross???section waveguides by modal decomposition. Part I. Theory and validation, The Journal of the Acoustical Society of America, vol.100, issue.4, pp.2034-2048 ,
DOI : 10.1121/1.417913