抄録
When a plane jet of gas issues steadily from a symmetrical nozzle as a parallel supersonic stream into an external medium at rest, its behaviour is governed by the exist velocity as well as by the ratio of exit pressure to pressure in the external medium. As will be seen from Prandtl’s photographs, when this pressure ratio is nearly equal to unity, the jet has a periodic character to the first approximation, and its structure can be accounted for by the use of the linear theory due originally to Prandtl. When the pressure ratio departs from unity, however, the quantitative behaviours, such as the wave-length of the jet, cannot be fully explained unless the nonlinear character of the fundamental equation is taken into account.
In the present paper, the fundamental equation for the stream function is considered in the hodograph plane, and the true adiabatic relation is replaced by an approximate adiabatic one so that simple exact solutions may be obtained. Thus, it is shown that, if the exit velocity is not so close to the sonic velocity and the external pressure is not so lower than that at the exit, the jet has, to the present approximation, still a completely periodic structure in the downstream as in the case of the linear theory. An expression is obtained for the wave-length of jet and it is found that the agreement between our theoretical result and Prandtl’s experiments is very satisfactory.
