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Decay of plane shock waves in equilibrium flows

Published online by Cambridge University Press:  21 July 2025

Donner T. Schoeffler Open the ORCID record for Donner T. Schoeffler [Opens in a new window]  and
Joseph E. Shepherd
Donner T. Schoeffler*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
Joseph E. Shepherd
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
Corresponding author: Donner T. Schoeffler, dschoeff@caltech.edu
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Abstract

A new model is presented for the decay of plane shock waves in equilibrium flows with an arbitrary equation of state. A fundamental challenge for the accurate prediction of shock propagation using analytical modelling is to account for the coupling between a shock’s motion and the post-shock flow. Our model accomplishes this by neglecting only higher-order perturbations to the second velocity gradient, $u_{xx}$, in the incident simple wave. The second velocity gradient is generally small and exactly zero for centred expansion waves in a perfect gas, so neglecting its effect on the shock motion provides an accurate closure criterion for a shock-change equation. This second-order shock-change equation is derived for a general equation of state. The model is tested by comparison with numerical simulations for three problems: decay by centred waves in a perfect gas, decay by centred waves in equilibrium air and decay by the simple wave generated from the constant deceleration of piston in a perfect gas. The model is shown to be exceptionally accurate for a wide range of conditions, including small $\gamma$ and large shock Mach numbers. For a Mach 15 shock in equilibrium air, model errors are less than 2 % in the first 60 % of the shock’s decay. The analytical results possess a simple formulation but are applicable to fluids with a general equation of state, enabling new insight into this fundamental problem in shock wave physics.

JFM classification

Compressible Flows: Shock waves Compressible Flows: Gas dynamics

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JFM Papers
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Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A41
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© The Author(s), 2025. Published by Cambridge University Press

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