Spherical steepened wave in interstellar van der Waals dusty gas clouds.

This article investigates the one-dimensional, spherically symmetric flow of self-gravitating interstellar van der Waals dusty gas clouds using Guderley's exact similarity solution. It derives a transport equation for the jump in the velocity gradient across a singular surface and analyzes how parameters such as the van der Waals excluded volume, mass fraction of solid particles, ratio of specific heats of dust particles to gas, and the density ratio of solid particles to gas affect the evolution of steepened waves. The study finds that for both expansion and compression waves within certain parameter ranges, the jump in the velocity gradient decreases and eventually vanishes over time, while approaching a critical value leads to unbounded growth after a finite critical time. Additionally, increases in the van der Waals excluded volume, dust mass fraction, and specific heat ratio tend to amplify the jump, whereas an increase in the density ratio of solid particles to gas has the opposite effect. These results contribute to understanding the propagation of second-order discontinuities relevant to astrophysical plasmas, dust-molecular clouds, and star formation processes.