We investigate the decay of freely evolving isotropic turbulence. There are two canonical cases: E(k \,→\, 0)\,~\, Lk² and E(k \,→\, 0)\,~\, Ik⁴, L and I being the Saffman and Loitsyansky integrals respectively. We focus on the second of these. Numerical simulations are performed in a periodic domain whose dimensions, lbox , are much larger than the integral scale of the turbulence, l . We find that, provided that lbox \,\, l and Re\,\, 1 , the turbulence evolves to a state in which I is approximately constant and Kolmogorov's classical 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. This finding seems to be at odds with the non-local nature of the Biot-Savart law.
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Ishida et al. (2006) studied this question.