zbMATH — the first resource for mathematics

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.

76F05 Isotropic turbulence; homogeneous turbulence
Full Text: DOI