On supersonic flow behind a curved shock
1. When a sharp-edged cylindrical body is immersed in a uniform supersonic stream, a curved shock is attached to the nose, provided the body is not too thick. A solution is presented which accounts to a first approximation for the entropy gradients and vorticity downstream of the shock. On the approximation of shock-expansion theory the flow downstream of the shock is a simple wave in which the entropy and a characteristic parameter (a, say) of homentropic theory have the values occurring just on the nose in the real flow. The prediction thus obtained for the pressure on the body was shown by Mahony [1, 2] to be remarkably accurate at all Mach numbers and for virtually all shock strengths insufficient to cause any regions of subsonic flow. Now, as long as viscosity is neglected, any streamline in the field represents a potential body contour and hence, the parameter a is approximately constant along streamlines, downstream of the shock. This has been noted also by Mahony [2] and conjectured for hypersonic flow by Stocker [3]. The solution on this approximation, which is given below, predicts the same pressure on the body as shock-expansion theory, but a flow with entropy gradients and vorticity; it is slightly less accurate, but also considerably simpler, than Mahony's solution, from whose numerical results [1, 2] the error can be estimated. 2. Assume the gas to be inviscid and perfect, so that the pressure p, density p, and specific entropy S are related by (dp/dS)„ = p/c, and (dp/dp)s = a2 = yp/p, where 7 = cj.c„ . Since the flow is homenergetic,