Kolmogorov two-thirds law ($S_2(r)=\beta (ϵr{)}^{2/3}$)

The second-order longitudinal structure function has the displayed form in the idealized inertial range of Kolmogorov 1941 theory. It predicts that the typical longitudinal velocity increment grows as the cube root of separation. Unlike the Kolmogorov four-fifths law, its exponent and coefficient are not exact consequences of the Navier-Stokes equation.