Isotropic Turbulence Preserving Similarity

In Taylor's statistical theory of turbulence [1] the simplest type of turbulent motion that has been discussed somewhat adequately is isotropic, in which the average feature round about a point is central-symmetric and indistinguishable from that round any other, and the mean square of any velocity component is a function of the time only, so that u²_i(t), (i = 1, 2, 3) depends neither on I, nor on the position of the point.