Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T01:35:41.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-dimensional turbulence on the surface of a sphere

Published online by Cambridge University Press:  12 April 2006

Cha-Mei Tang  and
Steven A. Orszag
Cha-Mei Tang
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge Present address: Applied Physics Laboratory, The Johns Hopkins University, Laurel, Maryland.
Steven A. Orszag
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Large-scale atmospheric flow shares certain attributes with two-dimensional turbulence. In this paper, we study the effect of spherical geometry on two-dimensional turbulence.

Energy transfer is multi-component in spherical geometry in contrast to energy transfer among triads of wave vectors in Cartesian geometry. It follows that energy transfer is more local in spherical than in Cartesian geometry. Enstrophy transfer to higher wavenumbers in spherical geometry is less than enstrophy transfer to higher wavenumbers in Cartesian geometry. Since both energy and enstrophy are inviscid constants of motion, the back transfer of energy is also less in spherical than in Cartesian geometry. Therefore, with a finite viscosity, enstrophy decays more slowly in spherical geometry than in Cartesian geometry. Here these conjectures are tested numerically by spectral methods. The numerical results agree well with the conjectures.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 2 , 26 July 1978 , pp. 305 - 319
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baer, F. 1972 J. Atmos. Sci. 29, 649.
Batchelor, G. K. 1969 Phys. Fluids Suppl. 12, II 233.
Charney, J. G. 1971 J. Atmos. Sci. 28, 1087.
Fjørtoft, R. 1953 Tellus 5, 225.
Herring, J. R., Orszag, S. A., Kraichnan, R. H. & Fox, D. G. 1974 J. Fluid Mech. 66, 417.
Horn, L. H. & Bryson, R. A. 1963 J. Geophys. Res. 68, 1059.
Julian, P. R., Washington, W. M., Hembree, L. & Ridley, C. 1970 J. Atmos. Sci. 27, 376.
Kraichnan, R. H. 1967 Phys. Fluids 10, 1417.
Lee, T. D. 1951 J. Appl. Phys. 22, 524.
Leith, C. E. 1971 J. Atmos. Sci. 28, 145.
Lilly, D. K. 1971 J. Fluid Mech. 45, 395.
Onsager, L. 1949 Nuovo Cimento Suppl. 6, 279.
Orszag, S. A. 1974 Mon. Weather Rev. 102, 56.
Tang, C. M. 1978 Comparison of spectral methods for flows on spheres. In preparation.
Wiin-Nielsen, A. 1967 Tellus 19, 540.