changes sign somewhere within the latitude band, where the ^-parameter is the latitudinal gradient of planetary vorticity defined as df 2Q cos óg p = -f «-Z± (5.46)
and where R is the planetary radius at the latitude in question. The barotropic instability condition is equivalent to saying that the meridional gradient of potential vorticity must change sign somewhere in a domain. While this may appear similar to inertial instability, barotropic instability is fundamentally different, not least because the Richardson number for barotropic conditions is poorly defined since the vertical wind shear in Equation (5.40) is zero.
The word baroclinic refers to cases where temperature does vary on constant pressure surfaces and thus, from the thermal wind equation, zonal winds do vary with height. Hence, baroclinic instabilities depend, broadly speaking, on the vertical curvature of the flow. However, the flow under baroclinic conditions may also have large horizontal curvature, and thus under these conditions the relevant instability criterion is the Charney-Stern criterion, which states that a shallow-atmosphere baroclinic wave confined within a certain latitude band is stable if the gradient of the potential vorticity does not change sign (e.g., Dowling, 1995). Baroclinic instabilities give rise to the midlatitude storms seen in the Earth's atmosphere, but their importance in the Jovian atmospheres is unclear. Baroclinic instabilities are important for Ri > 0.84.
This is a possible mechanism that has been proposed to account for the banded structure of the giant planets. If, in a condensing region of the atmosphere, the condensate enhances the greenhouse effect, then the increased thermal blanketing heats the atmosphere further thus enhancing vertical convection via positive feedback. Latitudinal temperature differences would then drive strong zonal winds from the thermal wind equation.
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