Effects of Temperature on the Surface Layer

In our study of atmospheric turbulence we have to this point neglected any effects of buoyancy. In the atmosphere, however, buoyancy plays an important role in maintaining (or suppressing) the energy of the turbulence. Consequently, we must examine the effect of temperature stratification on the nature of turbulence in the surface layer. 

This typical behavior serves to point out that the atmosphere is seldom adiabatic. Thus it becomes essential in predicting velocities in the surface layer to consider the effects of temperature on the type of turbulence to be expected. 

All that we essentially want to do is to examine the differential equations for the dynamics of the kinetic energy of turbulence and for the dynamics of temperature fluctuations. We will not attempt to derive or discuss in any detail these two equations, as our interest is only in the physical interpretation of the terms in the equations. For complete treatment of the dynamics of atmospheric turbulence we refer the reader to Monin and Yaglom(1971, 1975). 

Let us consider a shear flow that is steady and homogeneous in the x X2 plane with the only nonzero mean velocity m 1( 3). The kinetic energy of the turbulence is given by jUjU j = j(u u -I- M2 2 + 3 3)- A measure of the effect of the turbulence on temperature fluctuations is the mean-square fluctuation 9 The dynamic equations governing and 9 in this situation reduce to 

These are the basic equations used in the description of atmospheric turbulence. The key feature of interest in this discussion is the buoyant production of turbulent kinetic energy, that is, term (D. In order to have a means of assessing the importance of this term, let us consider the ratio of terms and (D, 

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