Notes on the Unsteady Rectilinear Motion of a Perfect Gas. Part 4: Some Studies on Centered Rarefaction Waves

摘要

A class of solutions for the equations of the unsteady, rectilinear motion of a perfect gas is constructed. The velocity is prescribed to be of the form u = A (x/t) + C. The homentropic, centered simple waves of the classical theory are included together with the homogeneous solutions of the Lagrangian equations of motion. Several more general flows are also obtained, i.e., among others the so-called Von Mises solutions. The generalizations admitted eliminate a difficulty found in the homogeneous solutions of the Lagrangian equations of motion when two different homogeneous flows are matched along a common particle path (jumps appear in temperature, density and entropy). By matching a homogeneous flow with a generalized flow no discontinuities in the parameters appear. Several details of the special cases included in the family are discussed, and it is pointed out that the family of solutions constructed has already been treated as the decay of a plane shock wave.