Special Issue: International Sessions of Japan Earth and Planetary Science Joint Meeting 2005
- Article
- Open access
- Published:
Low-frequency variability of a two-layer ocean forced by periodic winds
Earth, Planets and Space volume 58, pages 1203–1212 (2006)
Abstract
To seek the variability of the oceanic subtropical gyre on interannual and longer time scales we have conducted numerical experiments with a two-layer quasigeostrophic model in a square basin bounded by no-slip walls. We find that when the amplitude of annually periodic wind forcing is increased, the time series of the total energy exhibit a transition to chaos in such a manner that the response frequency constitutes a quasi-devil’s staircase against the forcing amplitude; in particular, the n-cycles appear in descending order of n. The low-frequency modes may thus be produced by seasonal winds. Since, however, the power of the subharmonics is much weaker than that with the forcing frequency, their energy would be concealed by noise in the presence of stochastic wind forcing. The present result is in contrast with the case of the time-independent forcing in which we observe the intrinsic frequencies probably associated with the wave propagation, frequency locking and a cascade of period-doubling bifurcations.
References
Anderson, D. L. T. and P. D. Killworth, Non-linear propagation of long Rossby waves, Deep-Sea Res., 26, 1033–1050, 1979.
Auad, G., Interdecadal dynamics of the North Pacific Ocean, J. Phys. Oceanogr., 33, 2483–2503, 2003.
Berloff, P. S. and S. Meacham, The dynamics of an equivalent-barotropic model of the wind-driven circulation, J. Mar. Res., 55, 407–451, 1997.
Berloff, P. S. and S. Meacham, The dynamics of a simple baroclinic model of the wind-driven circulation, J. Phys. Oceanogr., 28, 361–388, 1998.
Berloff, P. S. and J. C. McWilliams, Large-scale, low-frequency variability in wind-driven ocean gyres, J. Phys. Oceanogr., 29, 1925–1949, 1999.
Cessi, P. and S. Louazel, Decadal oceanic response to stochastic wind forcing, J. Phys. Oceanogr., 31, 3020–3029, 2001.
Chang, K.-I., M. Ghil, K. Ide, and C.-C. A. Lai, Transition to aperiodic variability in a wind-driven double-gyre circulation model, J. Phys. Oceanogr., 31, 1260–1286, 2001.
Crutchfield, J., J. D. Farmer, N. Packard, and R. Shaw, Chaos, Sci. Amer., 255, 46–57, 1986.
Deser, C., Evidence for a wind-driven intensification of the Kuroshio Current Extension from the 1970s to the 1980s, J. Clim., 12, 1697–1706, 1999.
Devaney, R. L., An Introduction to Chaotic Dynamical Systems 2nd ed., 336 pp., Addison-Wesley, Redwood City, CA, 1989.
Dewar, W. K., Arrested fronts, J. Mar. Res., 49, 21–55, 1991.
Dijkstra, H. A., Nonlinear Physical Oceanography, 456 pp., Kluwer, Dordrecht, 2000.
Dijkstra, H. A. and C. A. Katsman, Temporal variability of the wind-driven quasi-geostrophic double gyre ocean circulation: Basic bifurcation diagrams, Geophys. Astrophys. Fluid Dyn., 85, 195–232, 1997.
Dijkstra, H. A. and W. Weijer, Stability of the global ocean circulation: Basic bifurcation diagrams, J. Phys. Oceanogr., 35, 933–948, 2005.
Flierl, G. R., Simple applications of McWilliams “A note on a consistent quasi-geostrophic model in a multiply connected domain,” Dyn. Atmos. Oceans, 1, 443–453, 1977.
Frankignoul, C., P. Müller, and E. Zorita, A simple model of the decadal response of the ocean to stochastic wind forcing, J. Phys. Oceanogr., 27, 1533–1546, 1997.
Gent, P. R. and J. C. McWilliams, Isopycnal mixing in ocean circulation models, J. Phys. Oceanogr., 20, 150–155, 1990.
Ghil, M., Y. Feliks, and L. U. Sushama, Barotropic and baroclinic aspects of the wind-driven ocean circulation, Physica D, 167, 1–35, 2002.
Grassberger, P., Do climatic attractor exist?, Nature, 323, 609–612, 1986.
Hasselmann, K., Stochastic climate models. I. Theory, Tellus, 28, 473–485, 1976.
Haltiner, G. J. and R. T. Williams, Numerical Prediction and Dynamic Meteorology 2nd ed., 477 pp., John Wiley & Sons, New York, 1980.
Hendershott, M. C., Single layer models of the general circulation, in General Circulation of the Ocean, edited by D. I. Abarbanel and W. R. Young, 291 pp., Springer-Verlag, New York, 1987.
Holland, W. R., The role of mesoscale eddies in the general circulation of the ocean—numerical experiments using a wind-driven quasigeostrophic model, J. Phys. Oceanogr., 8, 363–392, 1978.
Holland, W. R. and L. B. Lin, On the generation of mesoscale eddies and their contribution to the oceanic general circulation. I. A preliminary numerical experiment, J. Phys. Oceanogr., 5, 642–657, 1975.
Holland, W. R., D. E. Harrison, and A. J. Semtner, Jr., Eddy-resolving numerical models of large-scale ocean circulation, in Eddies in Marine Science, edited by A. R. Robinson, 609 pp., Springer-Verlag, New York, 1983.
Jiang, S., F.-F. Jin, and M. Ghil, Multiple equilibria, periodic, and aperiodic solutions in a wind-driven, double gyre, shallow-water model, J. Phys. Oceanogr., 25, 764–786, 1995.
Kamenkovich, V. M., V. A. Sheremet, A. R. Pastushkov, and S. O. Belotserkovsky, Analysis of the barotropic model of the subtropical gyre in the ocean for finite Reynolds numbers. Part I, J. Mar. Res., 53, 959–994, 1995.
LaCasce, J. H., Baroclinic Rossby waves in a square basin, J. Phys. Oceaongr., 30, 3161–3178, 2000.
Lorenz, E. N., Available potential energy and the maintenance of the general circulation, Tellus, 7, 157–167, 1955.
Luyten, J. R., J. Pedlosky, and H. Stommel, The ventilated thermocline, J. Phys. Oceanogr., 13, 292–309, 1983.
McCalpin, J. D. and D. B. Haidvogel, Phenomenology of the lowfrequency variability in a reduced-gravity, quasigeostrophic double-gyre model, J. Phys. Oceanogr., 26, 739–752, 1996.
McWilliams, J. C., A note on a consistent quasigeostrophic model in a multiply connected domain, Dyn. Atmos. Oceans, 1, 427–441, 1977.
Meacham, S. P., Low-frequency variability in the wind-driven circulation, J. Phys. Oceanogr., 30, 269–293, 2000.
Meacham, S. P. and P. S. Berloff, Barotropic, wind-driven circulation in a small basin, J. Mar. Res., 55, 523–563, 1997.
Miller, A. J., D. R. Cayan, T. P. Barnett, N. E. Graham, and J. M. Oberhuber, Interdecadal variability of the Pacific Ocean: model response to observed heat flux and wind stress anomalies, Clim. Dyn., 9, 287–302, 1994.
Nauw, J. J. and H. A. Dijkstra, The origin of low-frequency variability of double-gyre wind-driven flows, J. Mar. Res., 59, 567–597, 2001.
Orlanski, I., The influence of bottom topography on the stability of jets in a baroclinic fluid. J. Atmos. Sci., 26, 1216–1232, 1969.
Pedlosky, J., Geophysical Fluid Dynamics 2nd ed., 710 pp., Springer-Verlag, New York, 1987.
Pedlosky, J., The dynamics of the oceanic subtropical gyres, Science, 248, 316–322, 1990.
Pierce, D. W., T. P. Barnett, N. Schneider, R. Saravanan, D. Dommenget, and M. Latif, The role of ocean dynamics in producing decadal climate variability in the North Pacific, Clim. Dyn., 18, 51–70, 2001.
Primeau, F., Multiple equilibria and low-frequency variability of the wind-driven ocean circulation, J. Phys. Oceanogr., 32, 2236–2256, 2002.
Procaccia, I., Complex or just complicated?, Nature, 333, 498–499, 1988.
Qiu, B., Kuroshio Extension variability and forcing of the Pacific decadal oscillations: Responses and potential feedback, J. Phys. Oceanogr., 33, 2465–2482, 2003.
Qiu, B. and T. M. Joyce, Interannual variability in the mid- and low-latitude western North Pacific, J. Phys. Oceanogr., 22, 1062–1079, 1992.
Rhines, P. B. and W. R. Young, A theory of the wind-driven circulation I. Mid-ocean gyres, J. Mar. Res., 40 (Suppl.), 559–596, 1982.
Sakamoto, T., On discontinuities in the Sverdrup interior, J. Phys. Oceanogr., 29, 2457–2461, 1999.
Sakamoto, T., Determination of wind-driven ocean circulation inside closed characteristics, Geophys. Astrophys. Fluid Dyn., 94, 151–176, 2001.
Sakamoto, T., Western boundary current separation caused by a deep countercurrent, Geophys. Astrophys. Fluid Dyn., 96, 179–199, 2002.
Sakamoto, T., A route to Eulerian chaos in a two-layer wind-driven ocean, Fluid Dyn. Res., 34, 117–134, 2004.
Schneider, N., A. J. Miller, and D. W. Pierce, Anatomy of North Pacific decadal variability, J. Clim., 15, 586–605, 2002.
Simonnet, E. and H. A. Dijkstra, Spontaneous generation of low-frequency modes of variability in the wind-driven ocean circulation, J. Phys. Oceanogr., 32, 1747–1762, 2002.
Sura, P., F. Lunkeit, and K. Fraedrich, Decadal variability in a simplified wind-driven ocean model, J. Phys. Oceanogr., 30, 1917–1930, 2000.
Thompson, L. and C. A. Ladd, The response of the North Pacific Ocean to decadal variability in atmospheric forcing: Wind versus buoyancy forcing, J. Phys. Oceanogr., 34, 1373–1386, 2004.
Trenberth, K. E. and J. W. Hurrell, Decadal atmosphere-ocean variations in the Pacific, Clim. Dyn., 9, 303–319, 1994.
van der Vaart, P. C. F., H. M. Schuttelaars, D. Calvete, and H. A. Dijkstra, Instability of time-dependent wind-driven ocean gyres, Phys. Fluids, 14, 3601–3615, 2002.
Willmott, A. J., A note on the steepening of long Rossby waves, Deep-Sea Res., 32, 613–617, 1985.
Young, W. R., Baroclinic theories of the wind driven circulation, in General Circulation of the Ocean, edited by D. I. Abarbanel and W. R. Young, 291 pp., Springer-Verlag, New York, 1987.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Sakamoto, T. Low-frequency variability of a two-layer ocean forced by periodic winds. Earth Planet Sp 58, 1203–1212 (2006). https://doi.org/10.1186/BF03352011
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1186/BF03352011