Planetary-scale zonally non-symmetric temperature disturbances(called as ``pancake structures′′) appear near the equatorialstratopause in winter hemisphere. The disturbances are usuallyinterpreted as inertial instability (Hitchman et al., 1987and Hayashi et al., 1998, Hayashi et al., 2002).However, so-called ``inertial instability′′ is a symmetricinstability in rotating system (Boyd and Christidis, 1982,Dunkerton, 1981,1983, and Stevens, 1983). It has not beendiscussed neatly whether non-symmetric pancake structurescorrespond to symmetric inertial instability. The purpose ofthis study is to examine the physical mechanism of unstablenon-symmetric modes and unstable symmetric modes in equatorialatmosphere.
The linearized non-dimensional primitive equations on theequatorial beta plane are solved for investigating the linearstability problem on latitudinal shear flows. Values of Lamb′sparameter, E, are from 0.0031622 to 31622777. The results showthat non-symmetric unstable modes appear for E > 0.1 and thatsymmetric unstable modes appear for E > 1.204. Symmetric modesare most unstable for E greater than 16, otherwisenon-symmetric modes are most unstable.
In order to consider the physical difference of calculatedunstable modes, dispersion relations of modes are examinedfrom the viewpoint of resonance between neutral waves, thatis, the discussion that instabilities are caused by theresonance between modes with positive pseudomomentum and modeswith negative pseudomomentum (Cairns, 1979; Iga, 1993,1999).For small values of E in which only non-symmetric modes areunstable, resonance between equatorial Kelvin-wave mode andcontinuous modes occurs. This result suggests thatnon-symmetric instabilities are caused by unstable equatorialKelvin waves, and is consistent with the discussions of Boydand Christidis (1982) and Natarov and Boyd (2001).Unfortunately, for larger values of E in which both ofsymmetric and non-symmetric unstable modes appear, it is difficultto identify modes which are resonant since their dispersioncurves are hidden by superimposed dispersion curves ofcontinuous modes. However, the changes of dispersion curvesof most unstable mode with changing the values of E can beobserved. This suggests that the combination of neutral modeswhich are resonant are different for different values of E.
The future problem is to identify neutral modes hidden bycontinuous modes and to give physical interpretation on thedifference between symmetric modes and non-symmetric modes. |
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