  In order to explain the observed unusually large dipion transition rates of
$\Upsilon(10870)$, the scalar resonance contributions in the re-scattering
model to the dipion transitions of $\Upsilon(4S)$ and $\Upsilon(5S)$ are
studied. Since the imaginary part of the re-scattering amplitude is expected to
be dominant, the large ratios of the transition rates of $\Upsilon(10870)$,
which is identified with $\Upsilon(5S)$, to that of $\Upsilon(4S)$ can be
understood as mainly coming from the difference between the $p$-values in their
decays into open bottom channels, and the ratios are estimated numerically to
be about 200-600 with reasonable choices of parameters. The absolute and
relative rates of $\Upsilon(5S)\to\Upsilon(1S,2S,3S)\pi^+\pi^-$ and
$\Upsilon(5S)\to\Upsilon(1S)K^+K^-$ are roughly consistent with data. We
emphasize that the dipion transitions observed for some of the newly discovered
$Y$ states associated with charmonia may have similar features to the dipion
transitions of $\Upsilon(5S)$. Measurements on the dipion transitions of
$\Upsilon(6S)$ could provide further test for this mechanism.
