Staircase scaling of short-time energy transfer in turbulence

Abstract

It is illustrated that a sharply truncated initial kinetic energy spectrum evolves to a staircase-shaped spectrum at short times. This effect is directly associated with the triadic nature of the energy transfer. A rigorous analysis leads to predictions on the time-dependence of this effect, and these predictions are verified by both direct numerical simulations and eddy-damped quasi-normal Markovian closure integrations.