Dynamics of air bubbles in Rayleigh-Be ìnard Convection: pair dispersion and effect of initial separation

Laboratory experiments were performed to uncover the dynamics of bubbles in Rayleigh-Benard (RB) convection at Ra$=$1.1x10$^{\mathrm{10}}$, where streams of 1-mm bubbles were released at various locations from the bottom of the RB tank along the path of the roll structure. 3D particle tracking velocimetry was used to track simultaneously a relatively large number of bubbles, and to quantify the pair dispersion for various initial separations in the range of 25$\le \eta \le $225, where $\eta $ is the local Kolmogorov length scale. Numerical simulation was carried out to further study the role of the bubble's path instability. Results show that the pair dispersion underwent a transition phase similar to the ballistic-to-diffusive (t$^{\mathrm{2}}$-to-t$^{\mathrm{1}})$ regime in the vicinity of the cell center; however, it approached to a bulk behavior t$^{\mathrm{1.5}}$ in the diffusive regime as the distance away from the cell center increased. At small initial separation, the pair dispersion exhibited t$^{\mathrm{1}}$ in the diffusive regime, indicating that the convective turbulence reduced the amplitude of the bubble's path instability. At large initial separations, the pair dispersion exhibited t$^{\mathrm{2}}$, showing the effect of the roll structure.