B • TURBULENT FLOW 



bibliography of literature references is however supplied. This omission 

 may be partially excused on the grounds that the reader may turn for 

 such material to Townsend's book [1] on this general subject. Statistical 

 theories of turbulence are likewise excluded, and justifiably so since they 

 are the subject of Sec. C. Another fruitful source of information is the 

 book by Batchelor [2]. 



B,2. Nature of Turbulent Flow. When entering into the subject of 

 turbulent flow it is essential to understand that the kind of flows with 

 which we shall be dealing belong to a particular class known as shear 

 flows. These comprise flow fields in which relative velocities have been 

 induced by shear stresses, and they are distinguished by having arisen in 

 this way rather than by the action of pressures. They are therefore ro- 

 tational flows as opposed to potential flows, and they are usually more 

 restricted since their extent is governed by the range of action of the 

 stresses. They may be bounded by solid walls or they may be free. Com- 

 mon examples are boundary layers, pipe and channel flows, jets, and 

 wakes. 



It is equally important that we know why we restrict ourselves to 

 shear flow. The reason is that only in such flows can turbulent motions 

 arise and sustain themselves. When turbulence is found in a stream that 

 has no measurable mean shear, the turbulent motions themselves repre- 

 sent the decaying remnant of shear flows that existed somewhere up- 

 stream. Such a condition is not uncommon where upstream objects have 

 created wakes. Grids or coarse screens placed across a stream are com- 

 monly used to create a homogeneous fleld of turbulence for experimental 

 study. We shall not be concerned with this case. 



Our main task will be to describe turbulent shear flows and to examine 

 their laws of behavior. For the most part we shall be concerned with mean 

 flows, but we shall have some opportunity as we go along to look into the 

 flow itself, to find out what it contains, and to see reasons for certain 

 behavior patterns. Some generalizations which apply to the mechanics of 

 turbulent flows as a class can be made, and these we now take up. The 

 more quantitative and precise aspects must be left to later articles on 

 specific subjects. Since there is much about turbulent flow that has not 

 been put on a firm theoretical basis, some amount of rationalization is 

 involved, and this necessarily reflects individual viewpoints. It is hoped 

 that the following discussion will stimulate thought and show that turbu- 

 lent flow is a phenomenon that should arouse our curiosity. 



We begin first with the somewhat controversial questions: What is 

 turbulent flow, and why does it exist? When tangential stresses are ap- 

 plied to a fluid having internal friction, shearing motions are set up in line 

 with the stresses and in conformity to the shape of the boundaries. Within 

 this flow field, various kinds of secondary motions become possible. Regu- 



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