Dynamics and symmetry. Predictions for modulated waves in rotating fluids

  • David Rand


Neural Network Complex System Nonlinear Dynamics Electromagnetism 
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  1. T. B. Benjamin (1978), Bifurcation phenomena in steady flows of a viscous fluid. Proc. Roy. Soc. LondonA 239, 1–26; 27–43.ADSCrossRefMATHMathSciNetGoogle Scholar
  2. D. Coles (1965), Transition in circular Couette flow. J. Fluid Mech.21, 385–425.ADSCrossRefMATHGoogle Scholar
  3. P. R. Fenstermacher, H. L. Swinney &J. P. Gollub (1979), Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech.94, 103–128.ADSCrossRefGoogle Scholar
  4. C. Foias &R. Téman (1979), Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J. Math. Pures et Appl.,58, 339–368.MATHMathSciNetGoogle Scholar
  5. J. P. Gollub &S. V. Benson (1980), Many routes to turbulent convection. J. Fluid Mech.100, 449–470.ADSCrossRefGoogle Scholar
  6. M. Gorman &H. L. Swinney (1980), Visual observation of the second characteristic mode in a quasiperiodic flow. Phys. Rev. Lett.43, 1871–1875.ADSCrossRefGoogle Scholar
  7. M. Gorman & H. L. Swinney (1981), Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. (to appear).Google Scholar
  8. M. Gorman, H. L. Swinney &D. A. Rand (1981), Doubly-periodic circular Couette flow: experiments compared with predictions from dynamics and symmetry. Phys. Rev. Lett.46, 15, 992–995.ADSCrossRefMathSciNetGoogle Scholar
  9. R. Hide (1958), An experimental study of thermal convection in a rotating liquid. Phil. Trans. Roy. Soc. LondonA 250, 442–478.ADSGoogle Scholar
  10. R. Hide (1969), Some laboratory experiments on free thermal convection in a rotating fluid subject to a horizontal temperature gradient and their relation to the theory of the global atmospheric circulation. InThe Global Circulation of the Atmosphere, ed. byG. A. Corby, R. Meteor. Soc., London.Google Scholar
  11. R. Hide &P. J. Mason (1975), Sloping convection in a rotating fluid. Adv. in Physics24, 47–100.ADSCrossRefGoogle Scholar
  12. M. W. Hirsch, C. Pugh &M. Shub (1977),Invariant Manifolds, Lec. Notes Math. vol. 583 Springer, New York.MATHGoogle Scholar
  13. E. Hopf (1948), A mathematical model displaying features of turbulence. Comm. Pure and Appl. Math.1, 303–322.CrossRefMATHGoogle Scholar
  14. G. Iooss (1979),Bifurcation of Maps and Applications. North Holland, Amsterdam.MATHGoogle Scholar
  15. G. Iooss &D. D. Joseph (1981)Elementary Stability and Bifurcation Theory. Springer Undergraduate Texts in Mathematics, New York and Berlin.MATHGoogle Scholar
  16. O. A. Ladyzhenskaya (1969),The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York. (Trans. from the Russian byR. A. Silverman & J. Chu.)MATHGoogle Scholar
  17. L. D. Landau &E. M. Lifshitz (1959),Fluid Mechanics. Pergamon, London. (Trans. from the Russian byJ. B. Sykes & W. H. Reid.)MATHGoogle Scholar
  18. J. E. Marsden &M. McCracken (1976),The Hopf Bifurcation and Its Applications. Springer, New York and Berlin.CrossRefMATHGoogle Scholar
  19. R. Pfeffer, G. Buzyna &W. W. Fowlis (1974), Synoptic features and energetics of wave amplitude vacillation in a rotating, differentially heated fluid. J. Atmos. Sci.31, 622–645.ADSCrossRefGoogle Scholar
  20. R. L. Pfeffer, G. Buzyna & R. Kung (1981), Some selected notes and data on wave dispersion in a rotating differentially heated annulus of fluid. Unpublished notes, Geophys. Fluid Dynamics Institute, Florida State University.Google Scholar
  21. R. L. Pfeffer &Y. Chiang (1967), Two kinds of vacillation in rotating laboratory experimets. Mon. Wea. Rev.95, 75–82.ADSCrossRefGoogle Scholar
  22. R. L. Pfeffer &W. W. Fowlis (1968), Wave dispersion in a rotating differentially heated cylindrical annulus of fluid. J. Atmos. Sci.25, 361–371.ADSCrossRefGoogle Scholar
  23. M. Renardy (1981), Bifurcations from rotating waves. Arch. Rational Mech. An. (to appear).Google Scholar
  24. D. Ruelle (1973), Bifurcations in the presence of a symmetry group. Arch. Rational Mech. An.51, 136–152.MATHMathSciNetGoogle Scholar
  25. J. Serrin (1959), On the stability of viscous fluid motions. Arch. Rational Mech. An.3, 1–13.MATHMathSciNetGoogle Scholar
  26. D. E. Shaeffer (1980), Qualitative analysis of a model for boundary effects in the Taylor problem. Math. Proc. Camb. Phil. Soc.87, 307–337.CrossRefMathSciNetGoogle Scholar
  27. G. I. Taylor (1923), Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Royal Soc.A 223, 289–343.ADSCrossRefMATHGoogle Scholar
  28. R. Téman (1979),Navier-Stokes Equations: Theory and Numerical Analysis. North-Holland, New York.MATHGoogle Scholar
  29. H. D. White & E. L. Koshneider (1981), Convection in a rotating, laterally heated annulus. Pattern velocities and amplitude oscillations. Preprint.Google Scholar

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© Springer-Verlag GmbH & Co. KG Berlin Heidelberg 1982

Authors and Affiliations

  • David Rand
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventry CV4 7ALUK

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