Analogy between predictions of Kolmogorov and Yaglom

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment delta u(1) and the second-order moment of delta u(1) is presented in a slightly more general form relating the mean value of the product delta u(1)(delta u(i))(2), where (delta u(i))(2) is the sum of the square of the three velocity increments, to the second-order moment of delta u(i). In this form, the relation is similar to that derived by Yaglom for the mean value of the product delta u(1)(delta theta)(2), where (delta theta)(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. These results are confirmed by experiments in a turbulent wake, albeit at relatively small values of the turbulence Reynolds number.