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- (ag|S|)-1/2

a is the thermal expansion coefficient (= 1/T) and t is the radiative relaxation time (from Stone, 1976).

a is the thermal expansion coefficient (= 1/T) and t is the radiative relaxation time (from Stone, 1976).

S is positive, and the atmosphere is convectively stableā€”a parcel displaced vertically and adiabatically will be cooler, and so less buoyant than the surrounding air, and will thus sink back to its original level (in fact, it may oscillate about its original level as we shall see in Section 5.3.2). If S is negative, then the temperature falls with height more quickly than the lapse rate. Such a situation is unstable since a parcel displaced vertically and adiabatically will be warmer, and so more buoyant, than the surrounding air and will thus continue to rise. Whether the atmosphere actually turns over or not depends on the magnitude of the instability and the viscosity of the air (Chamberlain and Hunten, 1987). Clearly static instability dominates for Ri < 0.

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