APPLICATIONS OF ENERGY PRINCIPLES TO THE GENERAL CIRCULATION 
By VICTOR P. STARR 
Massachusetts Institute of Technology 
INTRODUCTION 
Theoretical hydrodynamics and thermodynamics 
furnish the basic equations of energy which in the end 
must describe the energy transformations which take 
place in the atmosphere. These equations in themselves 
are not capable of furnishing a sufficient rational ex- 
planation of the causes of atmospheric processes, but 
nevertheless provide a guide to systematic exploration 
for purposes of finding empirically important facts con- 
cerning the behavior of the atmosphere. Thus their 
utility is much enhanced if consideration is given to 
observational data. 
The most important problem which confronts us in 
such an effort is therefore not one of merely stating the 
several pertinent equations in a formally complete man- 
ner, but rather one of discussing atmospheric processes 
as given by observations in terms of these relationships. 
To this end the principles involved must be moulded 
and recast in such a form as to permit the desired appli- 
cations to be made. In this procedure the failure to give 
proper cognizance to the special circumstances charac- 
teristic of the atmospheric processes dealt with can 
only lead to endless complications and needless con- 
fusion. 
Much of what has been written concerning this sub- 
ject has been deficient in two respects. In the first place, 
investigators have been prone to lump together various 
diverse forms of energy, thereby losing the advantages 
to be gained from the fact that each form of energy is 
produced from and converted to other forms in its own 
characteristic fashion, permitting individual study. 
Likewise for each form there exist specific modes of 
transfer and redistribution. Unless these specific char- 
acteristics are subject to scrutmy in detail, only very 
broad generalizations can be reached. Even here, how- 
ever, the implications of the balance of total energy for 
the globe have not yet been studied in sufficient detail 
as will be discussed later. 
In the second place, the modes of energy transfer 
within the atmosphere are so effective that no feature 
such as a cyclone can be treated independently without 
due allowance for exchanges of energy between it and 
the remaining atmosphere. It is therefore inappropriate 
to treat such a feature as in any sense a closed system. 
Modern trends are beginning to give proper cognizance 
to this circumstance, although much of the too 
restricted poimt of view permeates meteorological 
thought. 
In the present discourse only certain phases of the 
subject are discussed by way of illustrating a general 
approach. Thus the discussion which follows treats 
only the global balance of kinetic energy as an example 
of the study of one individual form of energy. In the 
last section the total energy balance is re-examined. It 
is of course true, as has already been stated, that it is 
also possible to study the global balance of other in- 
dividual forms of energy such as geopotential and in- 
ternal heat energy. A beginning in this direction has 
been made by Van Mieghem [10]. 
GLOBAL BALANCE OF KINETIC ENERGY 
General Considerations. One of the basic problems 
in the science of meteorology relates to the manner i 
which thermal energy received by the atmosphere 
through short-wave solar radiation becomes in part 
transformed into kinetic energy of motion relative to 
the rotating earth. Plausible estimates show that the 
fraction of the total energy so transformed is very 
small, but must nevertheless be sufficient to account 
for all air motions, in the absence of any other signifi- 
cant energy sources. Since the kinetic energy of orga- 
nized motions is contimually degraded and ultimately 
dissipated by turbulence and viscosity, the process of 
kinetic energy production must be a contmuous one 
with, probably, certain fluctuations about a mean rate 
when the whole atmosphere is considered. The purpose 
of this discussion is to examine this production process 
from a hydrodynamical point of view. 
Changes in the kinetic energy of a particle or system 
of particles can result only from the action of mechani- 
cal forces, and hence the rate of kinetic-energy produc- 
tion can be discussed in terms of the jomt action of 
such forces and the kinematics of existing motions. In 
this light it is not essential to inquire how systems of 
such forces and such motions in the atmosphere are re- 
lated to the thermodynamical processes which are ulti- 
mately responsible for their existence. In order to dem- 
onstrate the particular point in question as simply as 
possible we shall first consider an example of fluid mo- 
tion under circumstances which are somewhat artificial, 
but which still have theoretical terest. In view of the 
fact that the kinetic energy of vertical motions in the 
atmosphere is very small compared with the kinetic 
energy of the large-scale horizontal motions we shall 
consider only the latter. 
The approach used is one suggested by the beautiful 
classic paper of Osborne Reynolds [6] entitled ‘On the 
Dynamical Theory of Incompressible Viscous Fluids 
and the Determination of the Criterion.” Since Reyn- 
olds was concerned only with the dissipation of kinetic 
energy, his treatment must be modified im order to 
envisage also the process which creates kinetic energy. 
For this reason his assumption of incompressibility will 
be abandoned. Also, our restriction to the study of the 
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