  We investigate the correlations between the scalar meson configurations and
Okuba-Zweig-Iizuka (OZI) rule violations in the hadronic decays of heavy
quarkonia, e.g. $J/\psi$ and $\Upsilon$, into isoscalar vector meson ($\phi$
and $\omega$) and scalar mesons ($f_0(1710)$, $f_0(1500)$, and $f_0(1370)$). It
shows that the dramatic change of the values of the branching ratio fraction of
$\phi f_0/\omega f_0$ from low (e.g. in $J/\psi$ decays) to high energies (e.g.
in $\Upsilon$ decays) will not only test the glueball-$Q\bar{Q}$ mixings, but
also provide important information about the mysterious OZI-rule violations
within the scalars.
