Analogy between predictions of Kolmogorov and Yaglom

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment δu 1 and the second-order moment of δu 1 is presented in a slightly more general form relating the mean value of the product δu 1 (δu i ) 2 , where (δu i ) 2 is the sum of the square of the three velocity increments, to the second-order moment of δu i . In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu 1 (δθ) 2 , where (δθ) 2 is the square of the temperature increment. Both equations reduce to a 'four-thirds' relation for inertial-range separations and differ only through the appearance of the molecular Prandtl number for very small separations.