The potential temperature is the equivalent temperature of an air parcel if it is compressed or expanded adiabatically (along a dry adiabat) to a reference pressure p0, usually 1 bar, and may be shown to be equal to

where R is the universal molar gas constant; and Cp is the molar heat capacity at constant pressure. In an atmosphere where temperature T falls with height at the dry adiabatic lapse rate, the potential temperature is constant with height and thus S is zero. For an atmosphere that is diabatically heated by, say, direct absorption of sunlight through gas or aerosol absorption, the temperature falls less quickly with height and may, as in the stratospheres of the giant planets, actually rise. In such cases

Table 5.1. Instability criteria (from Stone, 1976).

Dynamical mode (source)

Criteria for instability


Characteristic horizontal scale

Characteristic timescale

Barotropic instability

d 2u df

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