Horizontal motion and distribution of the columnar vortex structures in rotating Rayleigh-Benard convection.

We report measurements of the horizontal motion of columnar vortex structures in rotating Rayleigh-Benard convection in a range of Rayleigh number $1\ast {10}^{7}\le Ra\le 3.8\ast {10}^{10}$, Ekman number $3.4\ast {10}^{-7}\le Ek\thinspace $and Prandtl number \textit{Pr}$=$4.4. With the reduced Rayleigh number ${Ra}^{\ast }=Ra{Ek}^{4/3}<80$, thermal plumes are vertically straightened to form convective columnar vortices that are advected laterally in a random manner. In the dilute-vortex limit ${Ra}^{\ast }\approx $80, horizontal motion of the columnar vortices possesses the characters of Brownian motions, in terms of a mean-square displacement ${<\Delta r}^{2}\left( t \right)>=4Dt$ linearly dependent on time and a power-spectral density \textbf{\textit{E}}($\omega )$ that follows an $\omega^{-2}$ roll-off. In a dense-vortex regime${\thinspace Ra}^{\ast }<$ 30, we find $<{\Delta r}^{2}\left( t \right)>=4Dt^{\alpha }$. With decreasing \textit{Ek} the constant $ D$ decreases, but the exponent $\alpha $ increases and exceeds 1.0. The PDF of the displacement $P(\Delta r(t))$, however, remains Gaussian with a variance $\sigma^{2}\propto t^{\alpha }$ for various \textit{Ek}. Horizontal distribution of the columnar vortices is quantified by applying Voronoi analysis to the vortex-core position data. In the dense-vortex regime the PDF of the Voronoi areas shows larger (smaller) probability of having large (small) Voronoi areas than that of randomly distributed vortices, indicating vortex clustering effect and the formation of vortex-grid structures.