Skip to main content
SpringerLink
Log in
Book cover

General Circulation of the Ocean pp 202–267Cite as

Single Layer Models of the General Circulation

  • Chapter

Part of the book series: Topics in Atmospheric and Oceanic Sciences ((TATM))

Abstract

Henry Stommel’s 1948 paper “The westward intensification of wind-driven ocean currents” began a new era in the study of ocean circulation because it suggested that the latitudinal variation of the Coriolis parameter so strongly constrained ocean flows that a great deal could be learned about them by isolating horizontal processes in a single layer model of the circulation and thus having to solve only two dimensional rather than three dimensional flow problems. The formal problem posed in this paper and its successors was solution, with appropriate boundary conditions at the coasts, of some truncation of the midlatitude barotropic vorticity equation

$$(\mathop \partial \nolimits_t - \psi _y \partial _x + \psi _x \partial _y )\left( {\nabla ^2 \psi + f} \right) = {{\left( {\mathop \tau \nolimits_x^y - \mathop \tau \nolimits_y^x } \right)} \over {\mathop \rho \nolimits_o \mathop D\nolimits_o }} - r\mathop \nabla \nolimits^2 \psi + \mathop A\nolimits_H \mathop \nabla \nolimits^4 \psi .$$
(1.1.1)

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, D. L. T. and A. E. Gill, 1975. Spin-up of a stratified ocean, with application to upwelling. Deep-Sea Res., 22, 583–596.

    Google Scholar 

  • Blandford, R. R., 1971. Boundary conditions in homogeneous ocean models. Deep-Sea Res., 18, 739–751.

    Google Scholar 

  • Bryan, K., 1963. A numerical investigation of a nonlinear model of a wind-driven ocean. J. Atmos. Sci., 20, 594–606.

    Article  Google Scholar 

  • Cane, M. A. and E. S. Sarachik, 1976. Forced baroclinic ocean motions. I. The linear equatorial unbounded case. J. Mar. Res., 34, 4, 629–665.

    Google Scholar 

  • Charney, J. G., 1955. The Gulf Stream as an inertial boundary layer. Proc. Nat. Acad. Sci. USA, 41, 10, 731–740.

    Article  Google Scholar 

  • Csanady, G. T., 1978. The arrested topographic wave. J. Phys. Oceanogr., 8, 47–62.

    Article  Google Scholar 

  • Fofonoff, N. P., 1954. Steady flow in a frictionless homogeneous ocean. J. Mar. Res., 13, 254–262.

    Google Scholar 

  • Fofonoff, N. P., 1962. Dynamics of ocean currents. Pp. 3–30. In: The Sea, 1: Physical Oceanography, M.N. Hill (ed.), Interscience, New York.

    Google Scholar 

  • Goldsbrough, G. R., 1933. Ocean currents produced by evaporation and precipitation. Proc. Roy. Soc. Lond. A, 141, 512–517.

    Article  Google Scholar 

  • Holland, W. R., 1967. On the wind-driven circulation in an ocean with bottom topography. Tellus, 19, 582–600.

    Article  Google Scholar 

  • Holland, W. R., 1973. Baroclinic and topographic influences on the transport in western boundary currents. Geophys. Fluid Dyn., 4, 187–210.

    Article  Google Scholar 

  • Holland, W. R. and A. D. Hirschman, 1972. A numerical calculation of the circulation in the North Atlantic Ocean. J. Phys. Oceanogr., 2, 4, 336–354.

    Article  Google Scholar 

  • Hough, S. S., 1898. On the application of harmonic analysis to the dynamical theory of the tides - Part II. On the general integration of Laplace’s dynamical equations. Phil. Trans. Roy. Soc. Lond. A, 191, 139–185.

    Article  Google Scholar 

  • Il’in, A. M. and V. M. Kamenkovich, 1964. The structure of the boundary layer in the two-dimensional theory of ocean currents, (in Russian) Okeanologiya, 4, 5, 756–769.

    Google Scholar 

  • Israeli, M., 1972. On trapped modes of rotating fluids in spherical shells. Studies in Appl. Mech., 51, 219–237.

    Google Scholar 

  • Kuo, H. -H. and G. Veronis, 1970. Distribution of tracers in the deep oceans of the world. Deep-Sea Res., 17, 29–46.

    Google Scholar 

  • Leetma, A., P. Niiler and H. Stommel, 1977. Does the Sverdrup Relation account for the Mid-Atlantic circulation? J. Mar. Res., 35, 1, 1–9.

    Google Scholar 

  • Lighthill, M. J., 1969. Dynamic response of the Indian Ocean to onset of the southwest monsoon. Phil. Trans. Roy. Soc. Lond. A, 265, 45–92.

    Article  Google Scholar 

  • Longuet-Higgins, M. S., 1964. Planetary waves on a rotating sphere. Proc. Roy. Soc. Lond. A, 279, 446–473.

    Article  Google Scholar 

  • Luyten, J. R., J. Pedlosky and H. Stommel, 1983. The ventilated thermo- cline. Phys. Oceanogr., 13, 292–309.

    Article  Google Scholar 

  • McCreary, J. P., 1976. Eastern tropical ocean response to changing wind systems: with application to El Nino. J. Phys. Oceanogr., 6, 5, 632–645.

    Article  Google Scholar 

  • McCreary, J. P., 1981. A linear stratified ocean model of the equatorial undercurrent. Phil. Trans. Roy. Soc. Lond. A, 298, 603–605.

    Article  Google Scholar 

  • Miles, J. W., 1974. On Laplace’s tidal equations. J. Fluid Mech., 66, 241–260.

    Article  Google Scholar 

  • Moore, D. W., 1963. Rossby waves in ocean circulation. Deep-Sea Res., 10, 735–747.

    Google Scholar 

  • Munk, W. H., 1950. On the wind-driven ocean circulation. J. Meteor., 7, 79–93.

    Article  Google Scholar 

  • Munk, W. H., G. W. Groves and G. F. Carrier, 1950. Note on the dynamics of the Gulf Stream. J. Mar. Res., 9, 218–238.

    Google Scholar 

  • Niiler, P. P., 1966. On the theory of wind-driven ocean circulation. Deep- Sea Res., 13, 597–606.

    Google Scholar 

  • Parsons, A. T., 1969. A two-layer model of Gulf Stream separation. J. Fluid Mech., 39, 511–528.

    Article  Google Scholar 

  • Pedlosky, J., 1965. A note on the western intensification of oceanic circulation. J. Mar. Res., 23, 207–209.

    Google Scholar 

  • Pedlosky, J., 1979. Geophysical Fluid Dynamics. Springer-Verlag, New York. 624 pp.

    Google Scholar 

  • Philander, S. G. H. and R. C. Pacanowski, 1980. The generation of equatorial currents. J. Geophys. Res., 85, C2, 1123–1136.

    Article  Google Scholar 

  • Phillips, N., 1966. The equations of motion for a shallow rotating atmosphere and the “traditional approximation.” J. Atmos. Sci., 23, 626–628.

    Article  Google Scholar 

  • Rhines, P. and W. R. Young, 1982. A theory of wind-driven circulation, I. Mid-ocean gyres. J. Mar. Res., 40, 559–596.

    Google Scholar 

  • Robinson, A. R., 1963. Wind-Driven Ocean Circulation. Blaisdell Publishing Company, New York, Toronto and London.

    Google Scholar 

  • Schmitz, W. J. and W. R. Holland, 1982. A preliminary comparison of selected numerical eddy-resolving general circulation experiments with observations. J. Mar. Res., 40, 1, 75–117.

    Google Scholar 

  • Stommel, H., 1948. The westward intensification of wind-driven ocean currents. Trans. Am. Geophys. Union, 29, 2, 202–206.

    Google Scholar 

  • Stommel, H., 1957a. A survey of ocean current theory. Deep-Sea Res., 4, 149–184.

    Article  Google Scholar 

  • Stommel, H., 1957b. The abyssal circulation of the ocean. Nature, 180, 733–734.

    Article  Google Scholar 

  • Stommel, H., 1965. The Gulf Stream: A Physical and Dynamical Description. Second Edition. University of California Press, Berkeley. 248 pp.

    Google Scholar 

  • Stommel, H. and A. B. Arons, 1960. On the abyssal circulation of the world ocean - I. Stationary planetary flow patterns on a sphere. Deep-Sea Res., 6, 140–154.

    Google Scholar 

  • Stommel, H., A. B. Arons and A. J. Faller, 1958. Some examples of stationary planetary flow patterns in bounded basins. Tellus, 10, 179–187.

    Article  Google Scholar 

  • Sverdrup, H., 1947. Wind-driven currents in a baroclinic ocean; with application to the equatorial currents of the eastern Pacific. Proc. Nat. Acad. Sci. USA, 33, 318–326.

    Article  Google Scholar 

  • Veronis, G., 1963. On inertially-controlled flow patterns in a β-plane ocean. Tellus, 15, 59–66.

    Article  Google Scholar 

  • Veronis, G., 1966a. Wind-driven ocean circulation - Part 1. Linear theory and perturbation analysis. Deep-Sea Res., 13, 17–29.

    Google Scholar 

  • Veronis, G., 1966b. Wind-driven ocean circulation - Part 2. Numerical solutions of the non-linear problem. Deep-Sea Res., 13, 30–55.

    Google Scholar 

  • Veronis, G., 1973. Large scale ocean circulation. Adv. Appl. Mech., 13, 1–92.

    Article  Google Scholar 

  • Veronis, G., 1981. Dynamics of large-scale ocean circulation. Pp. 140–183 (Chapter 5). In: Evolution of Physical Oceanography, B.A. Warren and C. Wunsch (eds.), The MIT Press, Cambridge and London.

    Google Scholar 

  • Welander, P., 1976. A zonally uniform regime in the ocean circulation. J. Phys. Oceanogr., 6, 121–124.

    Article  Google Scholar 

  • Worthington, L.V., 1976. On the North Atlantic circulation. The Johns Hopkins Hopkins Oceanographic Studies, 6. 110 pp.

    Google Scholar 

Download references

Authors
  1. M. C. Hendershott
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, 92093, USA

    Henry D. I. Abarbanel

  2. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    W. R. Young

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Hendershott, M.C. (1987). Single Layer Models of the General Circulation. In: Abarbanel, H.D.I., Young, W.R. (eds) General Circulation of the Ocean. Topics in Atmospheric and Oceanic Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4636-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4636-7_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9093-3

  • Online ISBN: 978-1-4612-4636-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation