Compatibility requirements for propagating curved shocks of non-uniform strengths in uniform flow

The compatibility requirements for curved shocks of nonuniform strength in uniform flow are derived, for shocks propagating in an elastic fluid. Thermodynamic influences are taken into account, but the effects of viscosity and heat conduction due to temperature gradients are neglected. It is shown that the local and global equations of balance of linear momentum and energy yield expressions for the surface derivatives of the jump in specific volume and the speed of displacement. The former depends on the normal component of the flow field ahead of the shock, while the latter also depends on the surface components of the flow field and the geometry of the shock surface. Furthermore, these results permit the determination of the surface derivatives of all other parameters relevant to the problem.