On the Decay of Isotropic Turbulence

Abstract

We investigate the decay of freely-evolving, isotropic turbulence whose spectrum takes the form E(k→0)∼Ik⁴, I being Loitsyansky's integral. We report numerical simulations in a periodic domain whose dimensions, l_box, are much larger than the integral scale of the turbulence, l. We find that, provided l_box≫l and Re≫1, the turbulence evolves to a state in which Loitsyansky's integral is approximately constant and Kolmogorov's decay law, u²∼t^−10/7, holds true. The approximate conservation of I in fully-developed turbulence implies that the long-range interactions between remote eddies, as measured by the triple correlations, are very weak.