Building a weak shockwave from linear modes

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of plasma physics 2022-02, Vol.88 (1), Article 905880108
Main Authors: Bret, Antoine, Narayan, Ramesh
Format: Article
Language:English
Subjects:
Conservation equations
Density
Energy
Energy conservation
Ion acoustic waves
Mach number
Magnetohydrodynamics
Plasma physics
Pressure jump
Shock waves
Velocity
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 magnetohydrodynamics. 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 non-existent, as hinted by recent works.
ISSN:0022-3778
1469-7807
DOI:10.1017/S0022377821001252