That’s where the new experiments from Küchler and company come in. Nevertheless, experiments and numerical simulations of the Navier-Stokes equation have provided some support for power-law dependencies of moments of various orders. K. P. Iyer et al., "Oscillations modulating power law exponents in isotropic turbulence: Comparison of experiments with simulations," Phys. Kolmogorov derived an asymptotic solution for this quantity in the inertial range from a suitably averaged form of the Navier-Stokes equation, and it has the form of a power law. The one exception is Kolmogorov’s so-called 4/5 law for the third-order statistical moment of the velocity increment (the difference in the fluid velocity at two points separated by a distance r). According to the power-law prediction, in the inertial range this quantity is proportional to the separation distance r raised to the r-independent power