Large-scale clustering of light small particles in developed turbulence

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34　Turbulence is composed of the hierarchy of coherent vortices [e.g., Figs. 1(d)–1(f)]. Therefore, we can estimate the lifetime of each coherent vortex by identifying and tracking their axes [Figs. 1(g)–1(i)]. Then, Tlife is evaluated by their average.

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45　These particle diameters are determined by the conditions sp ≈ sg and sp ≈ T, respectively. However, we may use smaller particles if the visualized vortices have a long lifetime. This is because, according to (11), vortices with scale ℓ are visualized by the particles with a diameter D in the range √12βνΤ(ℓ)/Κ(ℓ)≲D≲ √12βνΤ(ℓ). Although the estimated D can be larger than η, (5), and therefore (11), may be valid for D < ℓ and τp ≈ T.