ENERGY EQUATIONS 
while the corresponding coefficients on the molecular 
scale are established physical properties, varying in a 
predictable manner when other properties vary. 
It is apparent, then, that the general energy equa- 
tions cannot be applied successfully to the real atmos- 
phere until more is known about the eddy terms. The 
problem of these terms can be formulated more effec- 
tively if their mutual relationship, as shown by general 
equations, is taken into consideration. For example, 
whether eddy flux of thermal energy, —puxc,7', or eddy 
flux of enthalpy, —pv,(c,7' ++ pa), should be called the 
eddy flux of heat does not appear to be an important 
question. The latter, however, combines the flux of a 
property recognized as energy with an eddy term rec- 
ognized as work, and there may be some point in main- 
taining the distinction between energy and work. 
Tt is well known from observations that changes of 
potential and thermal energies, and sometimes latent- 
heat energies, are ten to a hundred times greater than 
changes of kinetic energy in the atmosphere. This dif- 
ference in magnitudes evidently is caused by some 
property of the atmosphere, but the energy equations 
give no clue to the nature of the property. Neither do 
the equations give any clue as to which factors are 
most important in determining changes of kinetic en- 
ergy. The equations, being in differential form, repre- 
sent relationships between instantaneous rates, but they 
tell nothing about the relative magnitudes of the vari- 
ous rates of work, flux, and changes of energy. The 
solution to the problem hes in conditions that are not 
reflected in the equations; specifically, it lies in the 
initial and boundary conditions. 
For example, increasing kinetic energy of the mean 
motion in the air near the surface of the earth may 
lead, because of perturbations set up by the roughness 
of the surface, to an increasing value of the eddy trans- 
formation function EL. This effect, as can be seen from 
the energy equations, results in a more rapid trans- 
formation of the mean kinetic energy into eddy kinetic 
energy, so that the mean energy may approach a limit- 
ing value. But the imereasing eddy energy implies 
greater turbulent fluctuations, hence stronger gradients 
of the unaveraged motion, and hence an increasing 
value of the molecular transformation function /,. As 
this function increases, the eddy energy is more rapidly 
transformed into thermal energy. The net results are 
that the mean and eddy kinetic energies may approach 
limiting values where energy is supplied by some source 
to the mean motion and degraded finally to thermal 
energy. 
The energy equations, however, quite clearly do not 
491 
tell the whole story. Some additional guiding principles 
are required to permit a complete solution to problems 
of this kind. Classical thermodynamics has such guiding 
principles—for example, the second law. There should 
be more attempts to formulate the necessary principles 
in studies of atmospheric energy. 
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