Large-Scale Coherence and Law of Decay of Two-Dimensional Turbulence

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At the short times, the enstrophy Ω of a two-dimensional flow, generated by a random Gaussian initial condition decays as Ω(t)∝ t⁻γ with γ≈ 0.7. After that, the flow undergoes transition to a different state characterized by the magnitude of the decay exponent γ≈ 0.4 (Yakhot, Wanderer, Phys.Rev.Lett. 93, 154502 (2004)). It is shown that the very existence of this transition and various characteristics of evolving flow crucially depend upon phase correlation between the large-scale modes containing only a few percent of total enstrophy.