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A turbulent equatorial jet

Published online by Cambridge University Press:  28 March 2006

Robert R. Long
Robert R. Long
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore
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Abstract

A recent study of a laminar jet in a rotating spherical shell of fluid is extended to the case of a turbulent planetary jet at the equator of a rotating, stratified atmosphere or ocean. General forms of the velocity, density and pressure functions of both the mean motion and the turbulence are derived by a dimensional analysis applied to the mean and perturbation equations. The horizontal and vertical dimensions are estimated, based on the three characteristic constants of the problem, which are the momentum transfer, the stability and a rotation parameter. The estimates are in good agreement with the dimensions of the Cromwell current, i.e. the equatorial undercurrent of the Pacific Ocean.

To the first order of approximation, the mean axial velocity in the theory is independent of distance along the jet axis. The mean horizontal transverse velocity component is much smaller and decreases upstream. The mean vertical velocity is extremely small, also decreasing upstream. The two horizontal velocity components of the turbulence are of the same order and, in the undercurrent, are about one-fourth the mean axial velocity. The vertical turbulent component is much smaller. Finally, it is shown that the eddy-viscosity concept is inappropriate for this problem because at least one of the eddy coefficients would have to be negative.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 3 , November 1961 , pp. 465 - 477
Copyright
© 1961 Cambridge University Press

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References

Berson, A. 1910 Bericht über die aerologische Expedition des Königl. Aeronautischen Observatorium nach Ostafrika im Jahre 1910. Ergebn. Arb. Preuz. Aeronaut. Obs. Lindenberg : Braunschweig.
Birkhoff, G. 1950 Hydrodynamics, Chapter IV. Princeton University Press.
Boussinesq, J. 1903 Théorie analytique de la chaleur, Vol. 2, p. 172. Gauthier-Villars.
Cowling, T. G. 1953 Solar electrodynamics. Article in The Sun (Ed. G. P. Kuiper). University of Chicago Press.
Cromwell, T., Montgomery, R. B. & Stroup, E. D. 1954 Equatorial undercurrent in Pacific Ocean revealed by new methods. Science, 119, 648.Google Scholar
Fofonoff, N. P. & Montgomery, R. B. 1955 The equatorial undercurrent in the light of the vorticity equation. Tellus, 4, 518.Google Scholar
Fultz, D., Long, R. R., Owens, G. V., Bohan, W., Kaylor, R. & Weil, J. 1959 Studies of thermal convection in a rotating cylinder with some implications for large-scale atmospheric motions. Meteor. Monograph, 4.Google Scholar
Hess, S. L. 1951 The atmospheres of the other planets. The Compendium of Meterology, p. 391.Google Scholar
Hidaka, K. & Nagata, Y. 1958 Dynamical computation of the equatorial current system of the Pacific, with special application to the equatorial undercurrent. Geophys. J. Roy. Astr. Soc. 1, 198.Google Scholar
Knauss, J. A. 1960 Measurements of the Cromwell Current. Deep Sea Res. 6, 265.Google Scholar
Knauss, J. A. & King, J. F. 1958 Observations of the Pacific equatorial undercurrent. Nature, 182, 601.Google Scholar
Lettau, H. 1956 Theoretical notes on the dynamics of the equatorial atmosphere. Beitr. Phys. Atm. 29, 107.Google Scholar
Long, R. R. 1960 A laminar planetary jet. J. Fluid Mech. 7, 632.Google Scholar
Newton, C. W. 1959 Synoptic comparison of Jet Stream and Gulf Stream systems. The Atmosphere and Sea in Motion, p. 288. New York: The Rockefeller Institute Press.
Stommel, H. 1960 The Gulf Stream, p. 202. University of California Press.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, p. 89. Cambridge University Press.
Veronis, G. 1960 An approximate analysis of the equatorial undercurrent. Deep Sea Res. 6, 318.Google Scholar
Wasiutyński, J. 1946 Hydrodynamics and structure of stars and planets. Astrophysica Norvegica, 4, 497.Google Scholar