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On the decay of isotropic turbulence. (English) Zbl 1100.76028
Summary: We investigate the decay of freely evolving isotropic turbulence. There are two canonical cases: $$E(k\to 0)\sim Lk^2$$ and $$E(k\to 0)\sim Ik^4$$, $$L$$ 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, $$l_{box}$$, are much larger than the integral scale of the turbulence, $$l$$. We find that, provided that $$l_{box}\gg l$$ and $$Re\gg 1$$, the turbulence evolves to a state in which $$I$$ is approximately constant and Kolmogorov’s classical decay law, $$u^2\sim t^{-10/7}$$, holds true. The approximate conservation of $$l$$ 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 nonlocal nature of Biot-Savart law.

##### MSC:
 76F05 Isotropic turbulence; homogeneous turbulence
##### Keywords:
Loitsyansky integral; Kolmogorov decay law
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