Baroclinic Instability and Isentropic Slope

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  • 1 Department of Atmospheric Sciences, University of Arizona, Tucson, Arizona
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Abstract

The wavelength of maximum baroclinic instability (WMI), maximum growth rate (MGR), phase velocities, and other quantities, are computed for an atmosphere with an internal 100-mb layer having various shears and lapse rates and positioned at various levels in a baroclinically unstable troposphere. It is found that the WMI, MGR, and other properties are more closely related to slope of the isentropes, Sθ, in the layer than to Richardson number, Ri, or to shear and lapse rate individually. The results for the layer positioned in the lower, middle and upper troposphere are similar but show systematic variations. The largest WMIs (3000–6000 km) are found for intermediate isentropic slopes of the order of those observed. Much smaller WMIs are found for small and very large isentropic slopes. The MGRs are of the order of 1 d−1 for small and intermediate slopes, but much larger for large slopes (Sθ ≳6 × 10−3 or Ri ≲ 0.5). The results suggest temporal and upward increases of WMI as shear and static stability develop in association with growth of the baroclinic wave. They also suggest typical WMIs somewhat larger than the 3100 km for the standard atmosphere.

Abstract

The wavelength of maximum baroclinic instability (WMI), maximum growth rate (MGR), phase velocities, and other quantities, are computed for an atmosphere with an internal 100-mb layer having various shears and lapse rates and positioned at various levels in a baroclinically unstable troposphere. It is found that the WMI, MGR, and other properties are more closely related to slope of the isentropes, Sθ, in the layer than to Richardson number, Ri, or to shear and lapse rate individually. The results for the layer positioned in the lower, middle and upper troposphere are similar but show systematic variations. The largest WMIs (3000–6000 km) are found for intermediate isentropic slopes of the order of those observed. Much smaller WMIs are found for small and very large isentropic slopes. The MGRs are of the order of 1 d−1 for small and intermediate slopes, but much larger for large slopes (Sθ ≳6 × 10−3 or Ri ≲ 0.5). The results suggest temporal and upward increases of WMI as shear and static stability develop in association with growth of the baroclinic wave. They also suggest typical WMIs somewhat larger than the 3100 km for the standard atmosphere.

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