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The shock front moves outward, until the pressure of the stellar wind equals the post-shock pressure and the contact discontinuity adjusts to equalize the the post-shock pressure and the confining external pressure of the disk wind $P(z)$.   In our case we are dealing with an oblique shock (Figure~\ref{fig:sketch}). Equations~\ref{RH1} to \ref{eqn:RH3} stay valid if only the velocity component perpendicular to the shock front is taken as $v_0$.   Figure~\ref{fig:sketch} shows the geometry of the problem. We use a cylindrical coordinate system $(z, \omega, \theta)$  with an origin on the central star. We place the $z$-axis along the jet outflow direction and assume rotational symmetry around the jet axis. Thus, the flow can effectively be written in $(z,\omega)$. We use the symbol $r$ to denote the spherical radius, i.e.\ the distance of any point to the star at the origin of the coordinate system. We treat the disk wind as an outer boundary condition with a given pressure profile and concentrate on the description of the stellar wind. To simplify the equations we adopt Kompaneets' approximation \citep{1960SPhD....5...46K} which states that there is no axial pressure gradient so that the pressure profile of the disk wind, which is given as a boundary condition, wind  extends through all layers of the outflow: \begin{equation}  P(z,\theta, \omega) P(z, \omega, \theta)  = P(z)\,. \end{equation}  With this we can write:  \begin{equation}