Correlations and Scales
Definition: Correlation Tensor (Two-Point)
Consider a turbulent flow field as shown in Figure 1. Here
and
are the components of the velocity vectors and
is the distance between the two points. The two-point correlation tensor is defined as
![](formulas_4_correlation/image014.gif)
In a homogenous turbulent flow, the correlations (and all the statistics) are
independent of the shift of space origin. That is,
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