The relative dispersion process in two-dimensional free convection turbulence is investigated by direct numerical simulation. In the inertial range, the growth of relative separation, $r$, is expected as $<r^2(t)>propto t^5$ according to the Bolgiano-Obukhov scaling. The result supporting the scaling is obtained with exit-time statistics. Detailed investigation of exit-time PDF shows that the PDF is divided into two regions, the Region-I and -II, reflecting two types of separating processes: persistent expansion and random transitions between expansion and compression of relative separation. This is consistent with the physical picture of the self-similar telegraph model. In addition, a method for estimating the parameters of the model are presented. Comparing two turbulence cases, two-dimensional free convection and inverse cascade turbulence, the relation between the drift term of the model and nature of coherent structures is discussed.
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