Experimental and Mathematical Descriptions of Turbulent Flows

The ultimate descriptio we would like to have of turbulent flow would be an explicit expression for V, 1/, and Vy, and as functions of time and position. Then we could predict the average and the fluctuating velocities at any point and any time. Currently it seems impossible to make such a description the problem Is much too complex. The next best thing is a statistical description of the flow, i.e., what fraction of the time V, v, Vy, etc., have certain values. So far most of the experimental and theoretical work done on turbulence has been directed at these statistical properties of the,flow. Below we give a set of definitions which are widely used in the turbulence literature to describe such statistical properties of the flow and some experimental values of the quantities so defined. 

Turbulent intensity, or simply intensity, is a measure of how strong, violent, or intense the turbulence is. (In the older literature it is often called level of turbulence or degree of turbulence.) Turbulent intensity is defined by 

Here v ) is the root mean square (rms) of the x component of the fluctuating component of the velocity. The relative intensity is defined by  

Here V is the erage of the absolute magnitude of the vector velocity, equal 

As discussed in Sec. 16.2, the average value of is zero, because it is positive as often as it is negative. However, (vl), the rms value of v, is not zero, because squaring before averaging removes the minus signs. 

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