simulation at the head of the plume, with contours from the predicted distribution to highlight the expected distribution. The high density region at the head of the plume and the rarefied regions at the sides of match well between the predicted and simulated densities.

![This shows the average density (averaging in the x-direction). The density increase at the head of the plume can be clearly seen. The white contours show the predicted distribution. The dashed black line shows the position of the slit used in Figure \[denprofile\]. The background distribution has been removed.[]{data-label="avden"}](figure6.eps){height="8cm"}

Next we compare the velocity distribution at the plume head with the distribution predicted by Equations \[vr\] and \[vthe\]. Figure \[plumeheadvel\] shows the predicted distributions (solid line) and the simulated distributions (dashed line) for the vertical and horizontal velocity. The horizontal scale uses the same scale as that of Figure \[transform\], but centers the zero position at the plume head. The velocity distributions are in general good agreement. It should be noted that the velocities are multiplied by a factor of $\rho(x=0)/\rho_{av}$ to give the correct magnitude of the velocity (i.e. the maximum value of $W/Cs \sim 0.21$ ). Note the good agreement in the velocity field 