Wind Profiles in the Nonadiabatic Surface Layer

In stable and unstable conditions the velocity profiles of the atmospheric surface layer deviate from the logarithmic law (16.57). In this section we will outline briefly the forms of velocity profiles in these conditions. Since the stratified-boundary-layer conservation equations cannot be solved (because of the closure problem), we must resort to empirical profiles, based largely on dimensional analysis. 

Suppose we are interested in the height dependence of some mean property / (say, velocity) in the surface layer. In carrying out a dimensional analysis, six quantities must be considered (g/7J)), po, q/pcp), xy, f. From the jt theorem, we have six quantities 

US choose xsjL and/(.r3)//o as these two groups, where/o is a group with the dimensions of/, formulated from ( /To), p, m, and qjpcp). Thus 

These equations are generalizations of the logarithmic layer equations to the case of a thermally stratified layer. We remind the reader that the adiabatic temperature profile in a stagnant layer is the familiar 1 C/100 m decrease. However, in the presence of a mean wind in the x direction with a logarithmic profile, the neutral temperature profile is given by 

We have not taken the space to derive this result, although it is obtained in the same manner as the logarithmic velocity law. 

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