  The Sweet-Parker layer in a system that exceeds a critical value of the
Lundquist number ($S$) is unstable to the plasmoid instability. In this paper,
a numerical scaling study has been done with an island coalescing system driven
by a low level of random noise. In the early stage, a primary Sweet-Parker
layer forms between the two coalescing islands. The primary Sweet-Parker layer
breaks into multiple plasmoids and even thinner current sheets through multiple
levels of cascading if the Lundquist number is greater than a critical value
$S_{c}\simeq4\times10^{4}$. As a result of the plasmoid instability, the system
realizes a fast nonlinear reconnection rate that is nearly independent of $S$,
and is only weakly dependent on the level of noise. The number of plasmoids in
the linear regime is found to scales as $S^{3/8}$, as predicted by an earlier
asymptotic analysis (Loureiro \emph{et al.}, Phys. Plasmas \textbf{14}, 100703
(2007)). In the nonlinear regime, the number of plasmoids follows a steeper
scaling, and is proportional to $S$. The thickness and length of current sheets
are found to scale as $S^{-1}$, and the local current densities of current
sheets scale as $S^{-1}$. Heuristic arguments are given in support of theses
scaling relations.
