= Solution
{c}
For the approximate <similarity profile>, $F'=A\operatorname{erf}(\xi/\sqrt2)$, and therefore
$$
\boxed{V=-\Delta U\sqrt{CS}\,[Be^{-\xi^2/2}+D],\qquad
V(\pm\infty)=-\Delta U\sqrt{CS}\,D.}
$$
For the prescribed undisturbed horizontal streams, a suitable choice is \b[$D=0$], which gives zero transverse <velocity> at both far-field limits. Then $V=-\Delta U\sqrt{CS}\,B e^{-\xi^2/2}$ inside the layer. The nonzero internal crossflow is consistent with the streamwise widening of the <velocity> transition.
Another possible convention is to make the line $y=0$ a <streamline>, imposing $V(0)=0$. This requires $D=-B$, equivalently $F(0)=0$, and gives $V(\pm\infty)=\Delta U\sqrt{CS}\,B$. It therefore requires a uniform outer crossflow relative to the coordinates used for the centred <error function> profile. A single constant cannot impose both zero far-field crossflow and $V(0)=0$ unless $\Delta U=0$. The physical lateral <boundary conditions>, or the chosen material centreline, determine which convention is appropriate. Since $B,D=O(r)$, these transverse <velocities> are of order $\Delta U^2/U_c$ for fixed $C,S$.
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