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Dynamics and symmetry. Predictions for modulated waves in rotating fluids. (English) Zbl 0495.76031

76B47 Vortex flows for incompressible inviscid fluids
76F99 Turbulence
76E99 Hydrodynamic stability
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems
Full Text: DOI
[1] Benjamin, T. B., Bifurcation phenomena in steady flows of a viscous fluid, Proc. Roy. Soc. London, 239, 27-43, (1978) · Zbl 0366.76034
[2] Coles, D., Transition in circular Couette flow, J. Fluid Mech., 21, 385-425, (1965) · Zbl 0134.21705
[3] Fenstermacher, P. R.; Swinney, H. L.; Gollub, J. P., Dynamical instabilities and the transition to chaotic Taylor vortex flow, J. Fluid Mech., 94, 103-128, (1979)
[4] Foias, C.; Téman, R., Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures et Appl., 58, 339-368, (1979) · Zbl 0406.35053
[5] Gollub, J. P.; Benson, S. V., Many routes to turbulent convection, J. Fluid Mech., 100, 449-470, (1980)
[6] Gorman, M.; Swinney, H. L., Visual observation of the second characteristic mode in a quasiperiodic flow, Phys. Rev. Lett., 43, 1871-1875, (1980)
[7] M. Gorman & H. L. Swinney (1981), Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. (to appear).
[8] Gorman, M.; Swinney, H. L.; Rand, D. A., Doubly-periodic circular Couette flow: experiments compared with predictions from dynamics and symmetry, Phys. Rev. Lett., 46, 992-995, (1981)
[9] Hide, R., An experimental study of thermal convection in a rotating liquid, Phil. Trans. Roy. Soc. London, 250, 442-478, (1958)
[10] Hide, R.; Corby, G. A. (ed.), 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, (1969), London
[11] Hide, R.; Mason, P. J., Sloping convection in a rotating fluid, Adv. in Physics, 24, 47-100, (1975)
[12] M. W. Hirsch, C. Pugh &M. Shub (1977),Invariant Manifolds, Lec. Notes Math. vol. 583 Springer, New York. · Zbl 0355.58009
[13] Hopf, E., A mathematical model displaying features of turbulence, Comm. Pure and Appl. Math., 1, 303-322, (1948) · Zbl 0031.32901
[14] G. Iooss (1979),Bifurcation of Maps and Applications. North Holland, Amsterdam. · Zbl 0408.58019
[15] G. Iooss &D. D. Joseph (1981)Elementary Stability and Bifurcation Theory. Springer Undergraduate Texts in Mathematics, New York and Berlin. · Zbl 0443.34001
[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.) · Zbl 0184.52603
[17] L. D. Landau &E. M. Lifshitz (1959),Fluid Mechanics. Pergamon, London. (Trans. from the Russian byJ. B. Sykes & W. H. Reid.) · Zbl 0146.22405
[18] J. E. Marsden &M. McCracken (1976),The Hopf Bifurcation and Its Applications. Springer, New York and Berlin. · Zbl 0346.58007
[19] Pfeffer, R.; Buzyna, G.; Fowlis, W. W., Synoptic features and energetics of wave amplitude vacillation in a rotating, differentially heated fluid, J. Atmos. Sci., 31, 622-645, (1974)
[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.
[21] Pfeffer, R. L.; Chiang, Y., Two kinds of vacillation in rotating laboratory experimets, Mon. Wea. Rev., 95, 75-82, (1967)
[22] Pfeffer, R. L.; Fowlis, W. W., Wave dispersion in a rotating differentially heated cylindrical annulus of fluid, J. Atmos. Sci., 25, 361-371, (1968)
[23] M. Renardy (1981), Bifurcations from rotating waves. Arch. Rational Mech. An. (to appear).
[24] Ruelle, D., Bifurcations in the presence of a symmetry group, Arch. Rational Mech. An., 51, 136-152, (1973) · Zbl 0259.58009
[25] Serrin, J., On the stability of viscous fluid motions, Arch. Rational Mech. An., 3, 1-13, (1959) · Zbl 0086.20001
[26] Shaeffer, D. E., Qualitative analysis of a model for boundary effects in the Taylor problem, Math. Proc. Camb. Phil. Soc., 87, 307-337, (1980) · Zbl 0461.76016
[27] Taylor, G. I., Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Royal Soc. A, 223, 289-343, (1923) · JFM 49.0607.01
[28] R. Téman (1979),Navier-Stokes Equations: Theory and Numerical Analysis. North-Holland, New York. · Zbl 0406.35053
[29] H. D. White & E. L. Koshneider (1981), Convection in a rotating, laterally heated annulus. Pattern velocities and amplitude oscillations. Preprint.
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