2008/06/06 by Stefano Finazzi, Mario Vietri, M. Vietri
Engineering · Physics and Astronomy · #Classical mechanics #Cosmology and Gravitation Theories #Diffusion #Fluid Dynamics and Turbulent Flows #Hydrostatic equilibrium #Instability #Mechanics #Moving shock #Perturbation (astronomy) #Physics #Shock (circulatory) #Shock wave #Solar and Space Plasma Dynamics #Thermodynamics #Vortex #Vorticity #astro-ph #physics.flu-dyn
paper · pdf · doi:10.1086/590952
35 pages, 7 Postscript figures, uses aastex.cls, to be published in ApJ, accepted on 5 Jun 2008
arxiv created 2008/06/06 · openalex publication_date 2008/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We perform a linear stability analysis for corrugations of a Newtonian shock, with particle pressure included, for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the conventional pressure waves and entropy/vorticity disturbances, two new perturbation modes exist, dominated by the particles' pressure and damped by diffusion. We show that, due to particle diffusion into the upstream region, the fluid will be perturbed also upstream; we treat these perturbation in the short-wavelength (WKBJ) regime. We then show how to construct a corrugational mode for the shock itself, one, that is, where the shock executes free oscillations (possibly damped or growing) and sheds perturbations away from itself; this global mode requires the new modes. Then, using the perturbed Rankine-Hugoniot conditions, we show that this leads to the determination of the corrugational eigenfrequency. We solve numerically the equations for the eigenfrequency in the WKBJ regime for the models of Amato & Blasi, showing that they are stable. We then discuss the differences between our treatment and previous work.