  We introduce a continuous (downscaling) data assimilation algorithm for the
2D B\'enard convection problem using vorticity or local circulation
measurements only. In this algorithm, a nudging term is added to the vorticity
equation to constrain the model. Our numerical results indicate that the
approximate solution of the algorithm is converging to the unknown reference
solution (vorticity and temperature) corresponding to the measurements of the
2D B\'enard convection problem when only spatial coarse-grain measurements of
vorticity are assimilated. Moreover, this convergence is realized using data
which is much more coarse than the resolution needed to satisfy rigorous
analytical estimates.
