Experimental investigation of pair dispersion with small initial separation in convective turbulent flows

TL;DR

This experimental study investigates pair dispersion in turbulent convection across various scales, confirming theoretical predictions like exponential growth and Batchelor's and Richardson's laws, and measuring relevant constants.

Contribution

First experimental verification of exponential pair separation growth in turbulent convection and precise measurement of Batchelor and Richardson constants.

Findings

Exponential growth of pair separation observed in dissipative scales.

Measured Batchelor constant approximately 0.23.

Measured Richardson constant approximately 0.10.

Abstract

We report an experimental investigation of pair dispersions in turbulent thermal convection with initial separation r0 ranging from sub-Kolmogorov scale to scales in the inertial range. In the dissipative range of scales we observed for the first time in experiment the exponential growth of the separation between a pair of particles predicted by Batchelor and obtained a Batchelor constant 0.23\pm0.07. For large r0, it is found that, for almost all time range, both the mean-square separation and distance neighbor function exhibit the forms predicted by Batchelor, whereas the two quantities agree with Richardson's predictions for small r0. Moreover, the measured value of the Richardson constant g = 0.10 \pm 0.07, which is smaller than those found in other turbulence systems. We also demonstrate the crossover of the mean-square separation from the exponential to the Batchelor regimes in both temporal and spatial scales.