|4. Discussions and Conclusions|
Numerical experiments were carried out using a high-resolution spectral model on 2-dimensional decaying turbulence on a rotating sphere. We examined what pattern appears finally and identified the conditions that must be satisfied for each type of pattern to appear, varying in a stepwise manner the experimental parameters of central wavenumber, which defines the initial energy spectrum, and rotational angular velocity of the sphere. The following conclusions were reached.
- Formation of the easterly polar vortex
In cases of high rotational angular velocity, an easterly polar vortex appears regardless of how the initial values are given. One especially notable finding was that, in contrast to the results of Yoden and Yamada(1993), the final pattern did not differ significantly even when the calculations were started from conditions of turbulence dominated by the non-linear term, if the initial energy is given in sufficiently high wavenumber regions. Therefore, it may be concluded with certainty that the formation of the easterly polar vortex is a universal feature of 2-dimensional decaying turbulence on a rotating sphere having high rotational speed.
The cause of the easterly polar vortex is believed to lie in the process of mixing and uniformization of absolute vorticity by turbulent conditions in the polar region. However, there may also be a large contribution from the momentum transfer effect by Rossby wave propagation from mid-to-low latitude regions. Further analysis is required to determine which of the mechanisms is more dominant.
- The appearance of the band structure
For high rotational angular velocity of the sphere, band structures of easterlies and westerlies arranged parallel in the zonal direction were obtained. It was found that, for such band structures to appear, not only must the rotational angular velocity be high, but it is also necessary for the initial energy to be given on sufficiently smaller scales than the Rhines scale. It is believed that this condition arises because it is necessary for the initial energy to be provided on sufficiently small scales (smaller than the Rhines scale) at which the dynamics of the non-linear terms dominate in order to create the non-uniformity in zonal or meridional directions when energy accumulation in large scales occur by inverse cascading.
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