correlation coefficient

See correlation.

1. A measure of the persistence of the eddy velocity as a function of time and space.
   Two types are distinguished: 1) In the Eulerian correlation coefficient, the time difference is zero,

   

   where u′ is the eddy velocity. For homogeneous and homologous turbulence, this correlation tensor depends only on the difference (y₂ - y₁); when the turbulence is isotropic, the tensor is spherically symmetric and . 2) In the Lagrangian correlation coefficient, time and space are varied together in such a way that the same fluid parcel is being followed:

   

   When the flow is one-dimensional and the mean velocity is much greater than the eddy velocity, then a fixed point experiences approximately the same sequence of fluctuations as a fluid parcel. The Lagrangian correlation coefficient can then be converted into the Eulerian by a proper scaling. These correlation coefficients have the same form and meaning when any other fluctuating quantity is used, for example, temperature or pressure.