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Volumn 337, Issue 2, 2008, Pages 1425-1441

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

Author keywords

Burgers' equation; Fr chet differentiability; Navier Stokes equations; Nonnormality; Sensitivity analysis; Sensitivity equations; Small disturbances; Transition to turbulence

Indexed keywords


EID: 34548636057     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.07.031     Document Type: Article
Times cited : (5)

References (51)
  • 3
    • 77950880721 scopus 로고
    • Onset of turbulence in a pipe
    • Boberg L., and Brosa U. Onset of turbulence in a pipe. Z. Naturforsch. A 43 8-9 (1988) 697-726
    • (1988) Z. Naturforsch. A , vol.43 , Issue.8-9 , pp. 697-726
    • Boberg, L.1    Brosa, U.2
  • 4
    • 0026805338 scopus 로고
    • Three-dimensional optimal perturbations in viscous shear flow
    • Butler K.M., and Farrell B.F. Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 8 (1992) 1637-1650
    • (1992) Phys. Fluids A , vol.4 , Issue.8 , pp. 1637-1650
    • Butler, K.M.1    Farrell, B.F.2
  • 5
    • 0026119897 scopus 로고
    • Energy growth of three-dimensional disturbances in plane Poiseuille flow
    • Gustavsson L.H. Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224 (1991) 241-260
    • (1991) J. Fluid Mech. , vol.224 , pp. 241-260
    • Gustavsson, L.H.1
  • 6
    • 0027392527 scopus 로고
    • Energy growth in viscous channel flows
    • Reddy S.C., and Henningson D.S. Energy growth in viscous channel flows. J. Fluid Mech. 252 (1993) 209-238
    • (1993) J. Fluid Mech. , vol.252 , pp. 209-238
    • Reddy, S.C.1    Henningson, D.S.2
  • 9
    • 0029107478 scopus 로고
    • A mostly linear model of transition to turbulence
    • Baggett J.S., Driscoll T.A., and Trefethen L.N. A mostly linear model of transition to turbulence. Phys. Fluids 7 4 (1995) 833-838
    • (1995) Phys. Fluids , vol.7 , Issue.4 , pp. 833-838
    • Baggett, J.S.1    Driscoll, T.A.2    Trefethen, L.N.3
  • 10
    • 0001164514 scopus 로고
    • Chaos transition despite linear stability
    • Gebhardt T., and Grossmann S. Chaos transition despite linear stability. Phys. Rev. E (3) 50 5 (1994) 3705-3711
    • (1994) Phys. Rev. E (3) , vol.50 , Issue.5 , pp. 3705-3711
    • Gebhardt, T.1    Grossmann, S.2
  • 11
    • 0014761243 scopus 로고
    • The mathematical problem of hydrodynamic stability
    • Sattinger D.H. The mathematical problem of hydrodynamic stability. J. Math. Mech. 19 9 (1970) 797-817
    • (1970) J. Math. Mech. , vol.19 , Issue.9 , pp. 797-817
    • Sattinger, D.H.1
  • 12
    • 0027535614 scopus 로고
    • Stochastic forcing of the linearized Navier-Stokes equations
    • Farrell B.F., and Ioannou P.J. Stochastic forcing of the linearized Navier-Stokes equations. Phys. Fluids A 5 11 (1993) 2600-2609
    • (1993) Phys. Fluids A , vol.5 , Issue.11 , pp. 2600-2609
    • Farrell, B.F.1    Ioannou, P.J.2
  • 13
    • 0035504272 scopus 로고    scopus 로고
    • Energy amplification in channel flows with stochastic excitation
    • Bamieh B., and Dahleh M. Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13 11 (2001) 3258-3269
    • (2001) Phys. Fluids , vol.13 , Issue.11 , pp. 3258-3269
    • Bamieh, B.1    Dahleh, M.2
  • 14
    • 33847224888 scopus 로고    scopus 로고
    • J.A. Burns, J.R. Singler, Feedback control of low dimensional models of transition to turbulence, in: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, 2005, pp. 3140-3145
  • 15
    • 85133047283 scopus 로고    scopus 로고
    • Modeling transition: New scenarios, system sensitivity and feedback control
    • World Scientific
    • Burns J.A., and Singler J.R. Modeling transition: New scenarios, system sensitivity and feedback control. Transition and Turbulence Control (2006), World Scientific 1-37
    • (2006) Transition and Turbulence Control , pp. 1-37
    • Burns, J.A.1    Singler, J.R.2
  • 16
    • 34548646516 scopus 로고    scopus 로고
    • J.R. Singler, Sensitivity analysis of partial differential equations with applications to fluid flow, PhD thesis, Department of Mathematics, Virginia Polytechnic Institute and State University, 2005
  • 17
    • 34548614731 scopus 로고    scopus 로고
    • Transition to turbulence, small disturbances, and sensitivity analysis II: The Navier-Stokes equations
    • (this issue)
    • Singler J.R. Transition to turbulence, small disturbances, and sensitivity analysis II: The Navier-Stokes equations. J. Math. Anal. Appl. 337 2 (2008) 1442-1456 (this issue)
    • (2008) J. Math. Anal. Appl. , vol.337 , Issue.2 , pp. 1442-1456
    • Singler, J.R.1
  • 18
    • 0022793654 scopus 로고
    • Convergence to steady state of solutions of Burgers' equation
    • Kreiss G., and Kreiss H.-O. Convergence to steady state of solutions of Burgers' equation. Appl. Numer. Math. 2 (1986) 161-179
    • (1986) Appl. Numer. Math. , vol.2 , pp. 161-179
    • Kreiss, G.1    Kreiss, H.-O.2
  • 22
    • 0030622784 scopus 로고    scopus 로고
    • Distributed and boundary control of the viscous Burgers' equation
    • Ly H.V., Mease K.D., and Titi E.S. Distributed and boundary control of the viscous Burgers' equation. Numer. Funct. Anal. Optim. 18 1-2 (1997) 143-188
    • (1997) Numer. Funct. Anal. Optim. , vol.18 , Issue.1-2 , pp. 143-188
    • Ly, H.V.1    Mease, K.D.2    Titi, E.S.3
  • 24
    • 3342959977 scopus 로고    scopus 로고
    • Exponentially slow traveling waves on a finite interval for Burgers' type equation
    • de Groen P.P.N., and Karadzhov G.E. Exponentially slow traveling waves on a finite interval for Burgers' type equation. Electron. J. Differential Equations 1998 30 (1998) 1-38
    • (1998) Electron. J. Differential Equations , vol.1998 , Issue.30 , pp. 1-38
    • de Groen, P.P.N.1    Karadzhov, G.E.2
  • 25
    • 0000765330 scopus 로고
    • Stability of plane-parallel Couette flow
    • Romanov V.A. Stability of plane-parallel Couette flow. Funct. Anal. Appl. 2 (1973) 137-146
    • (1973) Funct. Anal. Appl. , vol.2 , pp. 137-146
    • Romanov, V.A.1
  • 26
    • 0040068167 scopus 로고
    • Observations on the role of vorticity in the stability theory of wall bounded flows
    • Herron I. Observations on the role of vorticity in the stability theory of wall bounded flows. Stud. Appl. Math. 85 3 (1991) 269-286
    • (1991) Stud. Appl. Math. , vol.85 , Issue.3 , pp. 269-286
    • Herron, I.1
  • 27
    • 0019018916 scopus 로고
    • Linear-stability of Poiseuille flow in a circular pipe
    • Salwen H., Cotton F.W., and Grosch C.E. Linear-stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98 (1980) 273-284
    • (1980) J. Fluid Mech. , vol.98 , pp. 273-284
    • Salwen, H.1    Cotton, F.W.2    Grosch, C.E.3
  • 28
    • 0011676835 scopus 로고
    • The linear stability of circular pipe flow to axisymmetric disturbances
    • Herron I. The linear stability of circular pipe flow to axisymmetric disturbances. Stability Appl. Anal. Contin. Media 2 3 (1992) 293-303
    • (1992) Stability Appl. Anal. Contin. Media , vol.2 , Issue.3 , pp. 293-303
    • Herron, I.1
  • 29
    • 0034455616 scopus 로고    scopus 로고
    • Asymptotic-numerical study of supersensitivity for generalized Burgers' equations
    • Garbey M., and Kaper H.G. Asymptotic-numerical study of supersensitivity for generalized Burgers' equations. SIAM J. Sci. Comput. 22 1 (2000) 368-385
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.1 , pp. 368-385
    • Garbey, M.1    Kaper, H.G.2
  • 31
    • 0005441873 scopus 로고
    • On the motion of viscous shocks and the supersensitivity of their steady-state limits
    • Laforgue J.G., and O'Malley R.E. On the motion of viscous shocks and the supersensitivity of their steady-state limits. Methods Appl. Anal. 1 4 (1994) 465-487
    • (1994) Methods Appl. Anal. , vol.1 , Issue.4 , pp. 465-487
    • Laforgue, J.G.1    O'Malley, R.E.2
  • 32
    • 0029287705 scopus 로고
    • Shock layer movement for Burgers' equation
    • Laforgue J.G., and O'Malley R.E. Shock layer movement for Burgers' equation. SIAM J. Appl. Math. 55 2 (1995) 332-347
    • (1995) SIAM J. Appl. Math. , vol.55 , Issue.2 , pp. 332-347
    • Laforgue, J.G.1    O'Malley, R.E.2
  • 33
    • 0002494522 scopus 로고
    • On the exponentially slow motion of a viscous shock
    • Reyna L.G., and Ward M.J. On the exponentially slow motion of a viscous shock. Comm. Pure Appl. Math. 48 (1995) 79-120
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 79-120
    • Reyna, L.G.1    Ward, M.J.2
  • 34
  • 38
    • 0031571990 scopus 로고    scopus 로고
    • A PDE sensitivity equation method for optimal aerodynamic design
    • Borggaard J., and Burns J. A PDE sensitivity equation method for optimal aerodynamic design. J. Comput. Phys. 136 (1997) 366-384
    • (1997) J. Comput. Phys. , vol.136 , pp. 366-384
    • Borggaard, J.1    Burns, J.2
  • 40
    • 32944467268 scopus 로고    scopus 로고
    • A continuous sensitivity equation method for time-dependent incompressible laminar flows
    • Hristova H., Étienne S., Pelletier D., and Borggaard J. A continuous sensitivity equation method for time-dependent incompressible laminar flows. Internat. J. Numer. Methods Fluids 50 7 (2006) 817-844
    • (2006) Internat. J. Numer. Methods Fluids , vol.50 , Issue.7 , pp. 817-844
    • Hristova, H.1    Étienne, S.2    Pelletier, D.3    Borggaard, J.4
  • 42
    • 0003098484 scopus 로고
    • The differentiability with respect to a parameter of the solution of a linear abstract Cauchy problem
    • Brewer D.W. The differentiability with respect to a parameter of the solution of a linear abstract Cauchy problem. SIAM J. Math. Anal. 13 4 (1982) 607-620
    • (1982) SIAM J. Math. Anal. , vol.13 , Issue.4 , pp. 607-620
    • Brewer, D.W.1
  • 43
    • 0002497408 scopus 로고
    • Sensitivity analysis for a class of evolution equations
    • Gibson J.S., and Clark L.G. Sensitivity analysis for a class of evolution equations. J. Math. Anal. Appl. 58 1 (1977) 22-31
    • (1977) J. Math. Anal. Appl. , vol.58 , Issue.1 , pp. 22-31
    • Gibson, J.S.1    Clark, L.G.2
  • 44
    • 0041633610 scopus 로고    scopus 로고
    • Differentiability with respect to parameters of semigroups
    • Grimmer R., and He M. Differentiability with respect to parameters of semigroups. Semigroup Forum 59 3 (1999) 317-333
    • (1999) Semigroup Forum , vol.59 , Issue.3 , pp. 317-333
    • Grimmer, R.1    He, M.2
  • 45
    • 4644325691 scopus 로고    scopus 로고
    • Differentiability with respect to parameters of integrated semigroups
    • Kluwer Academic Publishers, Dordrecht
    • He M. Differentiability with respect to parameters of integrated semigroups. Direct and Inverse Problems of Mathematical Physics (2000), Kluwer Academic Publishers, Dordrecht 125-135
    • (2000) Direct and Inverse Problems of Mathematical Physics , pp. 125-135
    • He, M.1
  • 47
    • 18944369553 scopus 로고    scopus 로고
    • Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem
    • Herdman T., and Spies R. Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem. J. Math. Anal. Appl. 307 2 (2005) 656-676
    • (2005) J. Math. Anal. Appl. , vol.307 , Issue.2 , pp. 656-676
    • Herdman, T.1    Spies, R.2
  • 48
    • 0042496130 scopus 로고    scopus 로고
    • Fréchet differentiability of parameter-dependent analytic semigroups
    • Seubert S., and Wade J.G. Fréchet differentiability of parameter-dependent analytic semigroups. J. Math. Anal. Appl. 232 1 (1999) 119-137
    • (1999) J. Math. Anal. Appl. , vol.232 , Issue.1 , pp. 119-137
    • Seubert, S.1    Wade, J.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.