Abstract
Making use of a simple mathematical model concerning the form of motion associated with each turbulent component, the relation between the space-correlation function and the Eulerian time-correlation function is theoretically studied. While the former correlation R(r) is given by 1-R(r)_??_r2/3, the latter R(t) is given by 1-R(t)_??_tm and the value of m is a function of U/√u2, where U and √u2 are the velocity of the mean flow and the turbulent velocity, respectively. The values of m lie between 2/3 and 1. The minimum value m=2/3 occurs when U_??_√u2, and the maximum value m=1 when U_??_√u2 It is further stressed that the functional form of Lagrangian correlation is exactly the same as that of Eulerian correlation in the case of U_??_√u2, from the view point that the decay-and rebuilding-process of turbulence plays a predominant rôle in both the two correlations.
