Bifurcations and instabilities in rotating two-layer fluids: I. f-plane

Nonlinear Processes in Geophysics

Volumn 8, Issue 1-2, 2001, Pages 21-36

  Lovegrove, A F ^a,b   Moroz, I M ^a   Read, P L ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b Smith System Engineering Ltd   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

HYDRODYNAMICS; ROTATION; TWO-PHASE FLOW;

ATMOSPHERIC DYNAMICS; BIFURCATION; HYDRODYNAMICS; INSTABILITY; ROTATING FLUID;

EID: 0035089471     PISSN: 10235809     EISSN: None     Source Type: Journal    
DOI: 10.5194/npg-8-21-2001     Document Type: Article

References (34)

1. Appleby, J. C., Comparative theoretical and experimental studies of baroclinic waves in a two-layer system, Ph.D. thesis, University of Leeds, 1982.
2. Booty, M., Gibbon, J. D., and Fowler, A. C., A study of the effect of mode truncation on an exact periodic solution of an infinite set of Lorenz equations, Phys. Lett, 87A, 261-266, 1982.
3. Curry, J. H., A generalised Lorenz system, Commun. math. Phys., 60, 193-204, 1978.
4. Doedel, E., Auto: a program for the automatic bifurcation analysis of autonomous systems, Cong. Numer., 30, 265-284, 1981.
5. Doedel, E. J. and Kernevez, J. P., Auto: software for continuation and bifurcation problems in ordinary differential equations, Tech. rep., Applied Mathematics Report, California Institute of Technology, 1986.
6. Früh, W.-G. and Read, P. L., Wave interactions and the transition to chaos of baroclinic waves in a thermally driven rotating annulus, Phil. Trans. Roy. Soc. Lond, 355, 101-153, 1997.
7. Gibbon, J. D. and McGuinness, M. J., The real and complex Lorenz equations in rotating fluids and lasers, Physica D, 5, 108-122, 1982.
8. Guckenheimer, J. and Holmes, P. J., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
9. Hart, J. E., Finite amplitude baroclinic instability, Ann. Rev. Fluid Mech., 11, 147-172, 1979.
10. Hart, J. E., A model for the transitions to baroclinic chaos, Physica D, 20, 350-362, 1986.
11. Hide, R. and Mason, P. J., Sloping convection in a rotating fluid, Advances in Physics, 24, 47-99, 1975.
12. James, I. N., Stability of a slowly rotating two-layer system. Occasional Note Met. 0.21/77/2, UK Met. Office, 1977.
13. King, J. C., An experimental study of baroclinic wave interactions in a two-layer system, Geophys. Astrophys. Fluid Dyn., 13, 153-167, 1979.
14. Klein, P., Transitions to chaos in unstable baroclinic systems: a review. Fluid Dyn. Res., 5, 235-254, 1990.
15. Klein, P. and Pedlosky, J., A numerical study of baroclinic instability at large supercriticality, J. Atmos. Sci., 43, 1243-1262, 1986.
16. Klein, P. and Pedlosky, J., The role of dissipation mechanisms in the nonlinear dynamics of unstable baroclinic waves, J. Atmos. Sci., 49, 29-48, 1992.
17. Knobloch, E., Symmetry and instability in rotating hydrodynamic and magnetohydrodynamic flows, Phys. Fluids, 8, 1446-1454, 1996.
18. Lewis, S. R., A quasi-geostrophic numerical model of a rotating internally heated fluid, Geophys. Astrophys. Fluid Dyn., 65, 31-55, 1992.
19. Lorenz, E. N., Simplified dynamic equations applied to the rotating basin experiment, J. Atmos. Sci., 19, 39-51, 1962.
20. Lorenz, E. N., Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141, 1963.
21. Lovegrove, A. F. L., Bifurcations and instabilities in rotating two-layer fluids, Ph.D. thesis, University of Oxford, 1998.
22. Moroz, I. M., Slowly varying baroclinic waves in dispersive and dissipative systems, Ph.D. thesis, Leeds, 1981.
23. Mundt, M. D., Hart, J., E., and Ohlsen, D., R., Symmetry, sidewalls, and the transition to chaos in baroclinic systems, J. Fluid Mech., 300, 311-338, 1995.
24. Pedlosky, J., Finite-amplitude baroclinic waves, J. Atmos. Sci., 27, 15-30, 1970.
25. Pedlosky, J., Finite-amplitude baroclinic waves with small dissipation, J. Atmos. Sci., 28, 587-597, 1971.
26. Pedlosky, J., Geophysical Fluid Dynamics, Springer-Verlag, Berlin, 1987.
27. Pedlosky, J. and Frenzen, C., Chaotic and periodic behaviour of finite-amplitude baroclinic waves, J. Atmos. Sci., 37, 1177-1196, 1980.
28. Phillips, N. A., Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level quasi-geostrophic model, Tellus, 6, 273-286, 1954.
29. Polvani, L. M. and Pedlosky, J., The effect of dissipation on spatially growing nonlinear baroclinic waves, J. Atmos. Sci., 45, 1977-1989, 1988.
30. Read, P. L., Bell, M. J., Johnson, D. W., and Small, R. M., Quasiperiodic and chaotic flow regimes in a thermally-driven, rotating fluid annulus, J. Fluid Mech., 238, 599-632, 1992.
31. Robinson, C., Homoclinic bifurcation to a transitive attractor of Lorenz type, Nonlinearity, 2, 495-518, 1989.
32. Rychlik, M. R., Lorenz attractors through Silnikov-type bifurcation, part I, Ergodic Theor. Dyn. Syst., 10, 793-821, 1990.
33. Sparrow, C., The Lorenz Equations, Springer-Verlag, New York, 1982.
34. Wiggins, S., Introduction to applied nonlinear dynamical systems and chaos, Springer-Verlag, New York, 1990.