Mean Velocity Profiles in the Nonadiabatic Surface Layer

3 Mean Velocity Profiles in the Nonadiabatic Surface Layer 

The basic logarithmic velocity profile (16.66) is applicable only to adiabatic conditions. However, the atmosphere is seldom adiabatic, and the velocity profiles for stable and unstable conditions deviate from this logarithmic law. For the more frequently encountered nonadiabatic atmosphere (also called stratified), the Monin-Obukhov similarity theory is usually employed (Monin and Obukhov 1954). 

Case 1. If m(0 0, then qz 0 and Rf 0. For this case, positive values of n tend to be associated with positive values of 0 and vice versa. This case corresponds to an unstable atmosphere (decreasing potential temperature with height). If an air parcel moves upward because of a positive fluctuation in its velocity u v it rises to a region of lower potential temperature. However, the air parcel temperature changes adiabatically during this small rapid fluctuation, and its potential temperature remains constant. As a result, the air parcel potential temperature will exceed the potential temperature of its surroundings and will cause a positive potential temperature fluctuation 0 in its new position. 

Case 2. If u zQ 0, then cj, 0 and Rf 0. In this case, positive values of n occur with negative values of 0, and the atmosphere (using the same arguments as above) is stable. 

Case 3. If n 0 = 0 then qz = 0 and Rf = 0. This case corresponds to an adiabatic (neutral) atmosphere. 

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