Skip to main content

Boundary layers in large scale ocean circulation

  • 482 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 711)

Abstract

An asymptotic analysis is made of some boundary layer phenomena in the large scale ocean circulation. The equations of motion are formulated on the sphere and the nonlinear inertial terms are assumed to be negligible. After vertical integration this leads to a boundary value problem for the transport stream function which is of singular perturbation type.

Particular attention has been paid to the influence of the shape of the ocean boundaries on the characteristics of the flow. Use is made of the method of matched asymptotic expansions in constructing approximations of the solution of the problem. It turns out that the geometry of the eastern coast is felt throughout the ocean. When a part of the eastern coast coincides with a parallelcircle a free shear layer develops westward along that circle. Moreover this type of coastal shape gives rise to the formation of a narrow intense "eastern" boundary layer that leaves the coast and propagates westward. The intensity of this boundary layer depends on the given wind stress curl. The method of constructing approximations draws heavily on the diffusion like character of the boundary layer equations.

Keywords

  • Boundary Layer
  • Wind Stress
  • Eastern Coast
  • Free Shear Layer
  • Matched Asymptotic Expansion

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

  1. Andreyev, O.A. and B.A. Kagan, 1976: Parametrization of friction and calculation of the horizontal circulation in the world ocean. Izv., Atmospheric and Oceanic Physics, 12, 108–111.

    Google Scholar 

  2. Besjes, J.G., 1975: Singular perturbation problems for linear elliptic differential operators of arbitrary order. II. Degeneration to first order operators. J.Math.Anal.Appl., 49, 324–346.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Carrier, G.F. and A.R. Robinson, 1962: On the theory of the winddriven ocean circulation. J.Fluid Mech., 12, 49–80.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Eckhaus, W., 1972: Boundary layers in linear elliptic singular perturbation problems. SIAM Rev., 14, 225–270.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Eckhaus, W., to appear in 1979: Asymptotic analysis of singular perturbations. North-Holland, Amsterdam.

    MATH  Google Scholar 

  6. Evanson, A.J. and G. Veronis, 1975: Continuous representation of wind stress and wind stress curl over the world ocean. J.Mar.Res. 33, (supplement), 131.

    Google Scholar 

  7. Gill, A.E. and R.K. Smith, 1970: On similarity solutions of the differential equation ψzzzz + ψx = 0. Proc.Camb.Phil.Soc., 67, 163–171.

    CrossRef  MathSciNet  Google Scholar 

  8. Hellerman, S., 1967: An updated estimate of the wind stress on the world ocean. Mon.Weather Rev. 95, 607–626.

    CrossRef  Google Scholar 

  9. Kamenkovich, V.M., 1977: Fundamentals of ocean dynamics. Elsevier Oceanography Series, 16. Elsevier Scient. Publ.Comp. Amsterdam-Oxford-New York.

    CrossRef  Google Scholar 

  10. Krauss, W., 1973: Methods and results of theoretical oceanography I: Dynamics of the homogeneous and the quasihomogeneous ocean. Gebrüder Borntraeger, Berlin-Stuttgart.

    Google Scholar 

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

    CrossRef  Google Scholar 

  12. Munk, W.H. and G.F. Carrier, 1950: The wind-driven circulation in ocean basins of various shapes. Tellus, 2, 158–167.

    MathSciNet  Google Scholar 

  13. Pedlosky, J., 1969: Linear theory of the circulation of a stratified ocean. J. Fluid Mech., 35, 185–205.

    CrossRef  MATH  Google Scholar 

  14. Rattray, M., Jr. and P. Welander, 1975: A quasi-linear model of the combined wind-driven and thermohaline circulations in a rectangular β-plane ocean. J.Phys.Ocean., 5, 585–602.

    CrossRef  Google Scholar 

  15. Ruijter, W.P.M. de, 1978: Asymptotic Analysis of the Antarctic Circumpolar Current. Submitted for publication.

    Google Scholar 

  16. Ruijter, W.P.M. de, 1979: On the turning of the Agulhas Current and the associated transport of the Brasil Current. Submitted for publication.

    Google Scholar 

  17. Spillane, M. and P.P. Niiler, 1975: On the theory of the strong, midlatitude wind-driven ocean circulation, I. Geophys.Fluid Dyn., 7, 43–66.

    CrossRef  MATH  Google Scholar 

  18. Stommel, H., 1948: The westward intensification of wind-driven ocean currents. Trans.Amer.Geophys.Un., 29, 202–206.

    CrossRef  Google Scholar 

  19. Sverdrup, H.U., M.W. Johnson and R.H. Fleming, 1942: The Oceans. Prentice-Hall, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

de Ruijter, W. (1979). Boundary layers in large scale ocean circulation. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062950

Download citation

  • DOI: https://doi.org/10.1007/BFb0062950

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09245-2

  • Online ISBN: 978-3-540-35332-4

  • eBook Packages: Springer Book Archive