  We present a numerical study of vorticity production and transport in the
two-dimensional Rayleigh-B\'enard (RB) convection. Direct numerical simulations
are carried out in the Rayleigh number ($Ra$) range $10^{5}\le Ra \le 10^{6}$,
the Prandtl number ($Pr$) of 0.71, and the aspect ratio ($\Gamma$) of the
convection cell range $0.75\le \Gamma \le 6$. We found that the flow structure
and temperature distribution vary with $\Gamma$ greatly due to multiple
vortices interaction. Further investigation on the vorticity production and
transport reveals that, in the RB convection, in addition to the vorticity
production due to wall shear stress, buoyancy produces significant vorticity in
the bulk region. The produced vorticity is transported via advection and
diffusion. An interesting finding is that the main vortices and the corner
vortices can be visualized via the contour of buoyancy-produced vorticity.
Although a vigorous definition of the vortex is still lacking in the community,
our efficient vortex visualization approach in the RB convection may shed light
on further research toward vortex identification. We also found that the
spatial distribution of vorticity flux along the wall is positively correlated
with that of the Nusselt number ($Nu$), suggesting the amount of vorticity that
enters the flow is directly related to the amount of thermal energy that enters
the flow.
