Time Dependence of Eulerian Velocity Correlation for the Duration of Richardson’s Law

Abstract

It is shown that the effective temporal damping factor of the spectrum of the Eulerian velocity correlation becomes the function of κ^2⁄3t (κ: wave number, t: time) for the duration of Richardson’s four-thirds law in the steady, incompressible, homogeneous and isotropic turbulent flow. In addition, it is shown that this effect is caused by the time dependence of the effective Eulerian characteristic time, and is not contrary to the general understanding that the temporal damping factor of the spectrum of the Eulerian velocity correlation is the function of v₀κt (v₀: magnitude of the typical flow velocity).