Formation of zonal band structure in forced two-dimensional turbulence on a rotating sphere

Toru Nozawa, Shigeo Yoden

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79 Citations (Scopus)


A series of numerical experiments on the forced two-dimensional turbulence on a rotating sphere were done to investigate the formation processes of zonal band structures and their sensitivity to two experimental parameters of the rotation rate and the forcing wave number. A high-resolution barotropic full spherical model of T199 truncation is used with a homogeneous and isotropic formulation of the vorticity forcing function. Three different flow regimes are obtained and one of them is a new regime previously unknown. In the cases of no rotation, a very large flow pattern is obtained as a result of the upward energy cascade to the lowest wave number. The pattern irregularly fluctuates with time. A zonal band structure that consists of alternating easterly and westerly jets becomes dominant with an increase in the rotation rate. The alternating jets, which are robust and persistent, are already formed to be discernible in the very early stage of the time integration. The width of the jets decrease and the number of those increases as the rotation rate increases. The upward cascade of the disturbance energy ceases owing to the effect of rotation around a characteristic wave number nβ at which the "β term" is comparable to the nonlinear Jacobian term. Scale separation between the scale of cascade arrest and the forcing scale allows a systematic alignment of the vortices elongated by the shear in the zonal mean zonal flow, and such an alignment maintains the zonal band structure. When the forcing wave number is small and the rotation rate is large, the band structure is confined in high latitudes yielding a circumpolar vortex with a strong easterly jet, and a wavy structure dominates in middle and low latitudes. This is the new flow regime that is found in this study. Any systematic phase relation is not established in these latitudes because the phases are scrambled by the forcing due to the insufficient scale separation, therefore, the alternating zonal band structure does not emerge.

Original languageEnglish
Pages (from-to)2081-2093
Number of pages13
JournalPhysics of Fluids
Issue number7
Publication statusPublished - Jul 1997
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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