The word barotropic refers to cases where there are no temperature gradients on constant pressure surfaces (i.e., there is no differential heating) and thus the flow does not vary with height. This means that the basic zonal winds do not vary with height as can be understood from thermal wind equations. Under such conditions, instabilities arise mainly through excessive horizontal curvature of the basic flow profile (Andrews et al., 1987). For barotropic waves in a shallow-atmospheric flow, where the height of the lower boundary is fixed, it may be shown (Houghton, 1986) that the condition for instability is the Rayleigh-Kuo criterion, which states that barotropic waves confined within a certain latitude band are stable unless the quantity
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