  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.
