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Building a weak shockwave from linear modes

Published online by Cambridge University Press:  24 January 2022

Antoine Bret Open the ORCID record for Antoine Bret [Opens in a new window]  and
Ramesh Narayan Open the ORCID record for Ramesh Narayan [Opens in a new window]
Antoine Bret
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real, Spain
Ramesh Narayan*
Affiliation:
Harvard-Smithsonian Center for Astrophysics, Harvard University, 60 Garden St., Cambridge, MA 02138, USA
*
†Email address for correspondence: antoineclaude.bret@uclm.es
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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 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.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 1 , February 2022 , 905880108
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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