Barotropic, wind-driven circulation in a small basin

Journal of Marine Research

Volumn 55, Issue 3, 1997, Pages 523-563

  Meacham, S P ^a   Berloff, P S ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAROTROPIC MOTION; CIRCULATION MODELLING; SMALL BASIN; WIND-DRIVEN CIRCULATION;

EID: 0030695160     PISSN: 00222402     EISSN: None     Source Type: Journal    
DOI: 10.1357/0022240973224364     Document Type: Article

References (56)

1. Arnold, V. I. 1965. Small denominators, I: Mappings of the circumference onto itself. AMS Transl. Ser. 2, 46, 213-284.
2. Badii, R. and A. Politi. 1985. Statistical description of chaotic attractors: the dimension function. J. Stat. Phys., 40, 725-750.
3. Berloff, P. S. and S. P. Meacham. 1997a. The dynamics of an equivalent-barotropic model of the wind-driven circulation. J. Mar. Res., 55, 407-451.
4. _ 1997b. The dynamics of a simple baroclinic model of the wind-driven circulation. J. Phys. Oceanogr., (submitted).
5. Brandstater, A., J. Swift, H. L. Swinney, A. Wolf, J. D. Farmer, E. Jen and P. J. Crutchfield. 1983. Low dimensional chaos in a hydrodynamical system. Phys. Rev. Lett., 51, 1442-1445.
6. Brandstater, A. and H. L. Swinney. 1987. Strange attractors in weakly turbulent Couette-Taylor flow. Phys. Rev. A, 35, 2207-2220.
7. Bryan, K. 1963. A numerical investigation of a nonlinear model of a wind-driven ocean. J. Atmos. Sci., 20, 594-606.
8. Cessi, P., R. V. Condie and W. R. Young. 1990. Dissipative dynamics of a western boundary current. J. Mar. Res., 48, 677-700.
9. Cessi, P. and G. R. Ierley. 1995. Symmetry-breaking multiple equilibria in quasi-geostrophic wind-driven flows. J. Phys. Oceanogr., 25, 1196-1205.
10. Charney, J. G. 1955. The Gulf Stream as an inertial boundary layer. Proc. Nat. Acad. Sci., 41, 731-740.
11. Doering, C. R. and J. D. Gibbon. 1995. Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, Cambridge, 223 pp.
12. Farmer, J. D., E. Ott and J. A. Yorke. 1983. The dimension of chaotic attractors. Physica, 7D, 153-180.
13. Fofonoff, N. P. 1954. Steady flow in a frictionless homogeneous ocean. J. Mar. Res., 13, 254-262.
14. Fraser, A. M. and H. L. Swinney. 1986. Independent coordinates for strange attractors from mutual information. Phys. Rev. A, 33, 1134-1140.
15. Gollub, J. P. and H. L. Swinney. 1975. Onset of turbulence in a rotating fluid. Phys. Rev. Lett., 35, 927-930.
16. Hockney, R. 1970. The potential calculation and some applications. Methods in Comput. Phys., 9, 136-211.
17. Holland, W. R. 1978. The role of mesoscale eddies in the general circulation of the ocean: - Numerical experiments using a wind-driven quasi-geostrophic model. J. Phys. Oceanogr., 8, 363-392.
18. Hudson, J. L. and J. C. Mankin. 1981. Chaos in the Belousov-Zhabotinskii reaction. J. Chem. Phys., 74, 6171-6177.
19. Ierley, G. R. 1987. On the onset of inertial recirculation in barotropic general circulation models. J. Phys. Oceanogr., 17, 2366-2374.
20. Ierley, G. R. and V. A. Sheremet. 1995. Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: Slip. J. Mar. Res., 53, 703-737.
21. Ierley, G. and W. Young. 1991. Viscous instabilities in the western boundary layer. J. Phys. Oceanogr., 21, 1323-1332.
22. Il'in, A. M. and V. M. Kamenkovich. 1964. The structure of the boundary layer in the two-dimensional theory of oceanic current. Oceanology, 4, 756-769.
23. Jiang, S., F.-F. Jin and M. Ghil. 1995. Multiple equilibria, periodic and aperiodic solutions in a wind-driven, double-gyre, shallow-water model. J. Phys. Oceanogr., 25, 764-786.
24. Kamenkovich, V. M., V. A. Sheremet, A. R. Pastushkov and S. O. Belotserkovsky. 1995. Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part I. J. Mar. Res., 53, 959-994.
25. Kostelich, E. J. and H. L. Swinney. 1986. Practical considerations in estimating dimension from time series data, in Chaos and Related Nonlinear Phenomena, I. Procaccia and M. Shapiro, eds., Plenum, New York,
26. Ledwell, J. R., A. J. Watson and C. S. Law. 1993. Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature, 364, 701-703.
27. Libchaber, A., C. Laroche and S. Fauve. 1982. Period doubling cascade in mercury, a quantitative measurement. J. de Physique Lett., 43, 211-216.
28. Libchaber, A. and J. Maurer. 1982. A Rayleigh-Benard experiment: helium in a small box, in Nonlinear Phenomena at Phase Transitions and Instabilities, T. Riste, ed., 259-286.
29. Lions, J.-L., R. Temam and S. Wang. 1992. On the equations of the large scale ocean. Nonlinearity, 5, 1007-1053.
30. Lorenz, E. N. 1963. Deterministic non-periodic flow. J. Atmos. Sci., 20, 130-141.
31. Meacham, S. P. 1997. The response of a small basin circulation to variations in forcing. J. Phys. Oceanogr., (submitted).
32. Meacham, S. P. and P. S. Berloff. 1997. Instabilities of a steady, barotropic, wind-driven-circulation. J. Mar. Res., (submitted).
33. Moore, D. W. 1963. Rossby waves in ocean circulation. Deep-Sea Res., 10, 735-747.
34. Morgan, G. W. 1956. On the wind-driven ocean circulation. Tellus, 8, 301-320.
35. Munk, W. H. 1950. On the wind-driven ocean circulation. J. Meteor., 7, 79-93.
36. Munk, W. H., G. Groves and G. F. Carrier. 1950. Note on the dynamics of the Gulf Stream. J. Mar. Res., 9, 218-238.
37. Oguz, T., D. G. Aubrey, V. S. Latun, E. Demirov, L. Koveshnikov, V. Diacanu, H. I. Sur, S. Besiktepe, M. Duman, R. Limeburner and V. Eremeev. 1994. Mesoscale circulation and thermohaline structure of the Black Sea observed during HydroBlack'91. Deep-Sea Res., 41, 603-628.
38. Oguz, T., V. S. Latun, M. A. Latif, V. V. Vladimirov, H. I. Sur, A. A. Markov, E. Ozsoy, B. B. Kotovshchikov, V. V. Eremeev and U. Unluata. 1993. Circulation in the surface and intermediate layers of the Black Sea. Deep-Sea Res., 40, 1597-1612.
39. Oguz, T., P. E. La Violette and U. Unluata. 1992. The upper layer circulation of the Black Sea: Its variability as inferred from hydrographic and satellite observations. J. Geophys. Res., 97, 12569-12584.
40. Packard, N. H., J. P. Crutchfield, J. D. Farmer and R. S. Shaw. 1980. Geometry from a time series. Phys. Rev. Lett., 45, 712-716.
41. Pedlosky, J. 1987. Geophysical Fluid Dynamics, 2nd ed, Springer-Verlag, New York.
42. Rhines, P. B. 1975. Waves and turbulence on a beta-plane. J. Fluid Mech., 69, 417-443.
43. _ 1979. Geostrophic turbulence. Ann. Rev. Fluid Mech., 11, 401-441.
44. Roache, P. J. 1982. Computational Fluid Dynamics, Hermosa, Albuquerque.
45. Robinson, J. C. 1995. Finite-dimensional behavior in dissipative partial differential equations. Chaos, 5, 330-345.
46. Roux, J.-C., R. H. Simoyi and H. L. Swinney. 1983. Observation of a strange attractor. Physica, 8D, 257-266.
47. Ruelle, D. and F. Takens. 1971a. On the nature of turbulence. Comm. Math. Phys., 20, 167-192.
48. _ 1971b. On the nature of turbulence. Comm. Math. Phys., 23, 343-344.
49. _ 1976. A two-dimensional mapping with a strange attractor. Comm. Math. Phys., 50, 69-77.
50. Sheremet, V. A., V. M. Kamenkovich and A. R. Pastushkov. 1995. Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part II. J. Mar. Res., 53, 995-1024.
51. Simoyi, R. H., A. Wolf and H. L. Swinney. 1982. One-dimensional dynamics in a multicomponent chemical reaction. Phys. Rev. Lett., 49, 245-248.
52. Speich, S., H. Dijkstra and M. Ghil. 1995. Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation. Nonlinear Proc. Geophys., 2, 241-268.
53. Stommel, H. 1948. The westward intensification of wind-driven ocean currents. Trans. Am. Geophys. Union, 29, 202-206.
54. Takens, F. 1981. Detecting strange attractors in turbulence, in Lecture Notes in Mathematics, 898: Dynamical Systems and Turbulence, D. A. Rand and L.-S. Young, eds. Springer-verlag, 366-381.
55. Temam, R. 1995. Navier-Stokes Equations and Nonlinear Functional Analysis, 2nd ed., CBMS-NSF regional conference series in applied mathematics, 66. SIAM, Philadelphia. 141 pp.
56. Whitney, H. 1936. Differentiable manifolds. Ann. Math., 37, 645-680.