Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-15T02:13:25.981Z Has data issue: false hasContentIssue false

CHAPTER 6 - Flow Stability and Transition

Published online by Cambridge University Press:  05 June 2012

Andras Z. Szeri
Affiliation:
University of Delaware
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing rotationally symmetric flowQ. J. Mech. Appl. Maths 4 29CrossRefGoogle Scholar
Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous liquidProc. Roy. Soc. London 359 1CrossRefGoogle Scholar
Benjamin, T. B.Mullin, T. 1981 Anomalous modes in the Taylor experimentProc. Roy. Soc. London 377 221CrossRefGoogle Scholar
Benjamin, T. B.Mullin, T. 1982 Notes on the multiplicity of flows in the Taylor experimentJ. Fluid Mech 121 219CrossRefGoogle Scholar
Bilgen, E.Boulos, R. 1973 Functional dependence of torque coefficient of coaxial cylinders on gap width and Reynolds numbersASME Trans., Ser. G 95 122Google Scholar
Brady, J. F.Durlofsky, L. 1987 On rotating disk flowJ. Fluid Mech 175 363CrossRefGoogle Scholar
Brown, W. B. 1961 A stability criterion for three-dimensional boundary layersBoundary Layer and Flow ControlLachman, G. V.913Pergamon PressCrossRefGoogle Scholar
Burkhalter, J. E.Koschmieder, E. L. 1974 Steady supercritical Taylor vortices after sudden startsPhys. Fluids 17 1929CrossRefGoogle Scholar
Caldwell, D. R.Van Atta, C. W. 1970 Characteristics of Ekman boundary layer instabilitiesJ. Fluid Mech 44 79CrossRefGoogle Scholar
Castle, P.Mobbs, F. S. 1968 Hydrodynamic stability of flow between eccentric rotating cylinders: visual observations and torque measurementsProc. Inst. Mech. Eng 182 41Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic StabilityOxford University PressOxfordGoogle Scholar
Cliff, K. A.Mullin, T. 1985 A numerical and experimental study of anomalous modes in the Taylor experimentJ. Fluid Mech 153 243CrossRefGoogle Scholar
Cliff, K. A.Spence, A. 1986 Numerical calculations of bifurcations in the finite Taylor problemNumerical Methods for Fluid DynamicsMorton, K. W.Baines, M. J.155Clarendon PressOxfordGoogle Scholar
Cole, J. A. 1976 Taylor-vortex instability and annulus length effectsJ. Fluid Mech 75 1CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flowJ. Fluid Mech 21 385CrossRefGoogle Scholar
Dai, R. X.Szeri, A. Z. 1990 A numerical study of finite Taylor flowsInternat. J. Nonlinear Mech 25 45CrossRefGoogle Scholar
Dai, R. X.Dong, Q. M.Szeri, A. Z. 1992 Flow between eccentric rotating cylinders: bifurcation and stabilityInternat. J. Engrg. Sci 30 1323Google Scholar
Deng, D. 2007 A numerical and experimental investigation of Taylor flow instabilities in narrow gaps and their relationship to turbulent flow in bearingsPh.D. Dissertation, University of AkronGoogle Scholar
Deng, D.Barun, M. J. 2007 Taylor vortices induced instability (transition flow) versus `turbulence' in concentric cylinders separated by microscale clearancesTribology International 50 573Google Scholar
Dijkstra, D.van Heijst, G. J. F. 1983 The flow between two finite rotating disks enclosed by a cylinderJ. Fluid Mech 128 123CrossRefGoogle Scholar
DiPrima, R. C. 1960 The stability of a viscous fluid between rotating cylinders with axial flowJ. Fluid Mech 9 621CrossRefGoogle Scholar
DiPrima, R. C. 1963 A note on the stability of flow in loaded journal bearingsASLE Trans 6 249CrossRefGoogle Scholar
DiPrima, R. C.Stuart, J. T. 1972 Non-local effects in the stability of flow between eccentric rotating cylindersJ. Fluid Mech 54 393CrossRefGoogle Scholar
DiPrima, R. C.Stuart, J. T. 1975 The nonlinear calculation of Taylor vortex flow between eccentric rotating cylindersJ. Fluid Mech 67 85CrossRefGoogle Scholar
Donelly, R. J. 1958 Experiments on the stability of viscous flow between rotating cylindersProc. Roy. Soc. London 266 312CrossRefGoogle Scholar
Drazin, P. G.Reid, W. H. 1984 Hydrodynamic StabilityCambridge University PressCambridgeGoogle Scholar
Faller, A. J. 1963 An experimental study of the instability of the laminar Ekman boundary layerJ. Fluid Mech 15 560CrossRefGoogle Scholar
Faller, A. J.Kaylor, R. E. 1966 Investigations of stability and transition in rotating boundary layersDynamics of Fluids and PlasmasPai, S. I.239AcademicGoogle Scholar
Frank, G.Meyer-Spasche, R. 1981 Computation of transitions in Taylor vortex flowZ. Agnew. Math. Phys 32 710CrossRefGoogle Scholar
Frêne, J.Godet, M. 1974 Flow transition criteria in a journal bearingASME Journal of Lubrication Technology 96 135CrossRefGoogle Scholar
Gardner, W. W.Ulschmid, J. G. 1974 Turbulence effects in two journal bearing applicationsASME Trans., Ser. F 96 15Google Scholar
Giron, A. 1982 Stability of Rotating Disk FlowsUniversity of PittsburghGoogle Scholar
Gollub, J. P.Benson, S. V. 1980 Many roads to turbulent convectionJ. Fluid Mech 100 449CrossRefGoogle Scholar
Gollub, J. P.Swinney, H. L. 1975 Onset of turbulence in rotating fluidsPhys. Rev. Let 35 927CrossRefGoogle Scholar
Gottlieb, D.Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and ApplicationsSIAM, PhiladelphiaCrossRefGoogle Scholar
Greenspan, H. P. 1968 The Theory of Rotating FluidsCambridge University PressGoogle Scholar
Gregory, N.Stewart, J. T.Walker, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating diskPhilos. Trans. Roy. Soc. London, Ser. A 248 155CrossRefGoogle Scholar
Hinze, J. O. 1974 TurbulenceMcGraw-HillNew YorkGoogle Scholar
Humphrey, J. A. C.Schuler, C. A.Iglesias, I. 1992 Analysis of viscous dissipation in disk storage systems and similar flow configurationsPhys. Fluids A 4 7 1415CrossRefGoogle Scholar
Iooss, G.Joseph, D. D. 1980 Elementary Stability and Bifurcation TheorySpringer-VerlagNew YorkCrossRefGoogle Scholar
Joseph, D. D. 1976 Stability of Fluid MotionsSpringer-VerlagNew YorkGoogle Scholar
Kamal, M. M. 1966 Separation in the flow between eccentric rotating cylindersASME J. Basic Engineering 88 717CrossRefGoogle Scholar
Karman, T. von. 1921 Über laminare und turbulente ReibungZ. Angew. Math. Mech 1 233CrossRefGoogle Scholar
Keller, H. B. 1977 Numerical solutions of bifurcation and nonlinear eigenvalue problemsApplications of Bifurcation TheoryRabinowitz, P.Academic PressNew YorkGoogle Scholar
Kelvin, Lord. 1871 Hydrokinetic solutions and observationsPhil. Mag 42 362Google Scholar
Kobayashi, R.Kohama, Y.Takamadate, C. 1980 Spiral vortices in boundary layer transition regime on a rotating diskActa. Mech 35 71CrossRefGoogle Scholar
Kogelman, S.DiPrima, R. C. 1970 Stability of spatially periodic supercritical flows in hydrodynamicsPhys. Fluids 13 1CrossRefGoogle Scholar
Koschmieder, E. L. 1976 Taylor vortices between eccentric cylindersPhys. Fluids 19 1CrossRefGoogle Scholar
Koschmieder, E. L. 1993 Bénard cells and Taylor VorticesCambridge University PressCambridgeGoogle Scholar
Landau, L. D.Lifshitz, E. M. 1959 Fluid MechanicsPergamon PressOxfordGoogle Scholar
Li, C. H. 1977 The effect of thermal diffusion on flow stability between two rotating cylindersASME Trans., Ser. F 99 318Google Scholar
Lin, C. C. 1967 The Theory of Hydrodynamic StabilityCambridge University PressCambridgeGoogle Scholar
Marcus, P. S. 1984 Simulation of Taylor-Couette flow, I – numerical methods and comparison with experimentJ. Fluid Mech 146 45CrossRefGoogle Scholar
Marcus, P. S. 1984 Simulation of Taylor-Couette flow, II – numerical results for wavy vortex flow with one traveling waveJ. Fluid Mech 146 65CrossRefGoogle Scholar
Meyer-Spasche, R.Keller, H. B. 1978 Numerical study of Taylor-vortex flows between rotating cylindersCaliforniaInstitute of TechnologyGoogle Scholar
Meyer-Spasche, R.Keller, H. B. 1980 Computations of the axisymmetric flow between rotating cylindersJ. Comput. Phys 35 100CrossRefGoogle Scholar
Milne-Thomson, L. M. 1968 Theoretical HydrodynamicsMacmillanNew YorkCrossRefGoogle Scholar
Mobbs, F. R.Younes, M. A. 1974 The Taylor vortex regime in the flow between eccentric rotating cylindersASME Trans., Ser. F 96 127Google Scholar
Nakaya, C. 1974 Domain of stable periodic vortex flows in a viscous fluid between concentric circular cylindersJ. Phys. Soc. Japan 26 1146Google Scholar
Newhouse, S.Ruelle, D.Takens, F. 1978 Occurrence of strange attractors near quasiperiodic flows on , ≥ 3Common. Math. Phys 64 35CrossRefGoogle Scholar
Oikawa, M.Karasndani, T.Funakoshni, M. 1989 Stability of flow between eccentric rotating cylindersJ. Phys. Soc. Japan 58 2355CrossRefGoogle Scholar
Oikawa, M.Karasndani, T.Funakoshni, M. 1989 Stability of flow between eccentric rotating cylinders with wide gapJ. Phys. Soc. Japan 58 2209CrossRefGoogle Scholar
Orr, W. M. F. 1907 The stability or instability of the steady motions of a perfect liquid and of a viscous liquidProc. Roy. Irish Acad 27A 9Google Scholar
Ortega, J. M.Rheinboldt, W. C. 1970 Iterative Solution of Nonlinear Equations in Several VariablesAcademic PressNew YorkGoogle Scholar
Radel, V.Szeri, A. Z. 1997 Symmetry braking bifurcation in finite disk flowPhys. Fluids 9 1CrossRefGoogle Scholar
Ritchie, G. S. 1968 On the stability of viscous flow between eccentric rotating cylindersJ. Fluid Mech 32 131CrossRefGoogle Scholar
Rosenhead, L. 1963 Laminar Boundary LayersOxford University PressGoogle Scholar
Ruelle, D.Takens, F. 1971 On the nature of turbulenceCommun. Math. Phys 20 167CrossRefGoogle Scholar
San Andres, A.Szeri, A. Z. 1984 Flow between eccentric rotating cylindersASME J. Appl. Mech 51 869CrossRefGoogle Scholar
Schlichting, H. 1968 Boundary Layer TheoryPergamonLondonGoogle Scholar
Schwartz, K. W.Springer, B. E.Donelly, R. J. 1964 Modes of instability in spiral flow between rotating cylindersJ. Fluid Mech 20 281CrossRefGoogle Scholar
Serrin, J. 1959 Mathematical Principles of Classical Fluid MechanicsHandbuch der Physik, VIII/IFlügge, S.Truesdell, C.Springer VerlagHeidelbergGoogle Scholar
Serrin, J. 1959 On the stability of viscous motionArch. Rational Mech. Anal 3 1CrossRefGoogle Scholar
Seydel, R. 1988 From Equilibrium to ChaosElsevierNew YorkGoogle Scholar
Smith, M. I.Fuller, D. D. 1956 Journal bearing operations at superlaminar speedsASME Trans., Ser. F 78 469Google Scholar
Stewartson, K. 1953 On the flow between rotating co-axial disksProc. Camb. Phil. Soc 3 333CrossRefGoogle Scholar
Szeri, A. Z.Adams, M. L. 1978 Laminar throughflow between closely spaced rotating disksJ. Fluid Mech 86 1CrossRefGoogle Scholar
Szeri, A. Z.Al-Sharif, A. 1995 Flow between finite, steadily rotating eccentric cylindersTheoret. Comput. Fluid Dyn 7 1CrossRefGoogle Scholar
Szeri, A. Z.Giron, A. 1984 Stability of flow above a rotating diskInt. J. Num. Methods 4 989CrossRefGoogle Scholar
Szeri, A. Z.Schneider, S. J.Labbe, F.Kaufman, H. N. 1983 Flow between rotating disks. Part 1. Basic flowJ. Fluid Mech 134 103CrossRefGoogle Scholar
Szeri, A. Z.Giron, A.Schneider, S. J.Kaufman, H. N. 1983 Flow between rotating disksJ. Fluid Mech 134 133CrossRefGoogle Scholar
Tatro, P. R.Mollo-Christensen, E. L. 1967 Experiments on Ekman layer stabilityJ. Fluid Mech 77 531CrossRefGoogle Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylindersPhilos. Trans. Roy., Soc 223 289CrossRefGoogle Scholar
Tzeng, H. M.Fromm, J. E. 1990 Air flow study in a cylindrical enclosure containing multiple co-rotating disksISROMAC-3HawaiiGoogle Scholar
Tzeng, H.-M.Humphrey, J. A. C. 1991 Co-rotating disk flow in an axisymmetric enclosure with and without a bluff bodyInt. J. Heat and Fluid Flow 12 194CrossRefGoogle Scholar
Versteegen, P. L.Jankowski, D. F. 1969 Experiments in the stability of viscous flow between eccentric rotating cylindersPhys. Fluids 12 1138CrossRefGoogle Scholar
Vohr, J. H. 1968 An experimental study of Taylor vortices and turbulence in flow between eccentric, rotating cylindersASME Trans 90 285Google Scholar
Weidman, P. D.Redekopp, L. G. 1975 On the motion of a rotating fluid in the presence of an infinite rotating diskProc. 12th Biennal Fluid Dyn. SympBialowiczaPolandGoogle Scholar
Weinstein, M. 1977 Wavy vortices in the flow between long eccentric cylinders, I – linear theoryProc. Roy. Soc. London 354 441CrossRefGoogle Scholar
Weinstein, M. 1977 Wavy vortices in the flow between long eccentric cylinders, II – nonlinear theoryProc. Roy. Soc. London 354 459CrossRefGoogle Scholar
Wendt, F. 1933 Turbulente strömungen zwischen zwei rotierenden konaxialen ZylindernIng. Arch 4 577CrossRefGoogle Scholar
White, F. M. 1991 Fluid MechanicsMcGraw-HillNew YorkGoogle Scholar
Wilcox, D. E. 1950 Turbulence in high speed journal bearingsASME Trans., Ser. F 72 825Google Scholar
Zandbergen, P. J.Dijkstra, D. 1987 Von Karman swirling flowsAnnual Rev. Fluid Mech 19 465CrossRefGoogle Scholar
Zienkiewicz, O. C.Woo, J. 1991 Incompressibility without tears: how to avoid restrictions of mixed formulationInternal. J. Numer. Methods Eng 32 1189CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×