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Isotropy and the Kármán-Howarth-Kolmogorov relation in experimental and numerical turbulence.

The evolutions of isotropy and the Kármán-Howarth-Kolmogorov (KHK) relation are studied experimentally and numerically in the lifetime of turbulence, i.e., developing, fully developed, and decaying states. The isotropy relations and the KHK relation are well satisfied when the turbulence is fully developed, but they are broken when the turbulence is developing or decaying. The turbulence shows opposite anisotropy in the developing and the decaying states. In response to the isotropy change, the KHK relation shows a variation of energy budget at each scale, which is consistent with an energy transfer from large to small scales. We also find that Taylor's frozen-eddy hypothesis and periodic boundary conditions, respectively, lead to an inherent phenomenon at large scales.