also remains finite at the center of the jet.

The $y$-component of the three-velocity normalized by $\sqrt{2/(9\rho'_0\kappa{z_0})} \sim \delta$ is illustrated in Figure \[fig:vyplotsgamjet\] for the same set of $\zeta$ used in Figure \[fig:fpplotsgamjet\]. For $\xi > 0$, each solution initially has a positive ${v_y}$, which shows that the jet material expands away from the axis. The $y$-component of the three-velocity then reaches a relative maximum, one which increases slightly for larger $\Gamma_j$, before approaching a negative, constant value. This behavior is then inverted for negative $\xi$. Because the transverse velocity approaches a negative constant for $\xi >0$ and a positive constant for $\xi < 0$, we see that the jet entrains material from the ambient medium.

![The function $f_{\xi}$, which is the normalized $z$-component of the four-velocity, for $\zeta = 10$ and $\mu = e'/\rho'_0 = 0.1$, 1, and 10, which correspond to the blue, solid curve, the purple, dot-dashed curve, and the red, dashed curve, respectively. Increasing the value of $\mu$, we see, has little effect on the solution, while decreasing $\mu$ drastically widens the boundary layer.[]{data-label="fig:fpplotsmujet"}](Figure7.eps){width="3.5in"}

![The normalized density of scatterers for the same values of $\mu$ chosen in Figure \[fig:fpplotsmujet\]. The mean value of the density 