Formation of internal shock waves in bent jets

We discuss the circumstances under which the bending of a jet can generate an internal shock wave. The analysis is carried out for relativistic and non-relativistic astrophysical jets. The calculations are done by the method of characteristics for the case of steady simple waves. This generalises the non-relativistic treatment first used by Icke (1991). We show that it is possible to obtain an upper limit to the bending angle of a jet in order not to create a shock wave at the end of the curvature. This limiting angle has a value of 75 degrees for non-relativistic jets with a polytropic index k = 4/3, 135 degrees for non-relativistic jets with k = 5/3) and 50 degrees for relativistic jets with k = 5/3. We also discuss under which circumstances jets will form internal shock waves for smaller deflection angles.