Fig. 5: Statistical properties of vortex clusters and collective motion of vortices.
From: Inverse centrifugal effect induced by collective motion of vortices in rotating thermal convection
a Size distribution of vortex clusters. Solid curves represent fits to the experimental data \(p(N)=A{N}^{-b}{e}^{-N/{N}_{{{{{{{{\rm{c}}}}}}}}}}\). Results for Ra = 3.0 × 107. Symbols are as in (b). Inset: the fitting parameters, i. e., the exponent b (circles) and cutoff size Nc (triangles) as functions of Ra/Rac. The prefactor A is determined by the normalization relation: ΣNp(N) = 1. b The rescaled data \(p(N){{N}_{{{{{{{{\rm{c}}}}}}}}}}^{1.5}/A\) shown in a log-log frame as a function of N/Nc. All data collapse onto a master curve shown by the solid curve. See Supplementary Fig. 10 for a power-function compensated plot of p(N). c, d Correlations of the vortex velocity fluctuation as a function of l/H (c), and as a function of l/L (d). Solid symbols: experimental data for Ra = 3.0 × 107, Ra/Rac = 1.97. Open symbols: DNS data for Ra = 2.0 × 107, Ra/Rac = 2.26. The solid curves represent stretched exponential functions, \(C(l)=(1+a){e}^{{(-{c}_{1}l)}^{{c}_{2}}}-a\), fitted to the data (described in Supplementary Note 9). The vertical dashed line in (d) indicates the correlation length lc ≈ 0.3L determined by the zero-crossing position of C(l/L).
