Building a weak shockwave from linear modes

Abstract

In shockwave theory, the density, velocity and pressure jumps are derived from the conservation equations. Here, we address the physics of a weak shock the other way around. We first show that the density profile of a weak shockwave in a fluid can be expressed as a sum of linear acoustic modes. The shock so built propagates at the speed of sound and matter is exactly conserved at the front crossing. Yet, momentum and energy are only conserved up to order 0 in powers of the shock amplitude. The density, velocity and pressure jumps are similar to those of a fluid shock, and an equivalent Mach number can be defined. A similar process is possible in magnetohydrodynamic. Yet, such a decomposition is found impossible for collisionless shocks due to the dispersive nature of ion acoustic waves. Weakly nonlinear corrections to their frequency do not solve the problem. Weak collisionless shocks could be inherently nonlinear, non-amenable to any linear superposition. Or they could be nonexistent, as hinted by recent works.

arXiv comment8 pages, 2 figures, to appear in Journal of Plasma Physics

References in corpus (5)

• Electron Preacceleration in Weak Quasi-perpendicular Shocks in High-beta Intracluster Medium
• Proton Acceleration in Weak Quasi-parallel Intracluster Shocks: Injection and Early Acceleration
• Electron Heating in Low Mach Number Perpendicular shocks. II. Dependence on the Pre-Shock Conditions
• Corrugation of relativistic magnetized shock waves
• Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas