Analogy between predictions of Kolmogorov and Yaglom

Abstract

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment δu1 and the second-order moment of δu1 is presented in a slightly more general form relating the mean value of the product δu1(δui)2, where (δui)2 is the sum of the square of the three velocity increments, to the secondorder moment of δui. In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu1(δuθ)2 where (δuθ)2 is the square of the temperature increment. Both equations reduce to a ‘four-thirds’ relation for inertialrange 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.