Foundations of Turbulence

The mathematical formulation of the problem of homogeneous turbulence is this: Given an infinite body of uniform fluid in which motions conform to the equations and, and given that at some initial instant the velocity of the fluid is a random function of position described by certain probability laws which are independent of position, to determine the probability laws that describe the motion of the fluid at subsequent times.

G. K. Batchelor in the Theory of Homogeneous Turbulence