Entropy in selfsimilar shock profiles
In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that is smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.
 Authors:

^{[1]}
;
^{[1]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 U.S. Naval Research Lab., Stennis Space Center, MS (United States)
 Publication Date:
 Report Number(s):
 LAUR1526684
Journal ID: ISSN 00207462
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 International Journal of NonLinear Mechanics
 Additional Journal Information:
 Journal Volume: 95; Journal ID: ISSN 00207462
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; shock waves; entropy; Clausius Duhem
 OSTI Identifier:
 1372792
Margolin, Len G., Reisner, Jon Michael, and Jordan, Pedro M.. Entropy in selfsimilar shock profiles. United States: N. p.,
Web. doi:10.1016/j.ijnonlinmec.2017.07.003.
Margolin, Len G., Reisner, Jon Michael, & Jordan, Pedro M.. Entropy in selfsimilar shock profiles. United States. doi:10.1016/j.ijnonlinmec.2017.07.003.
Margolin, Len G., Reisner, Jon Michael, and Jordan, Pedro M.. 2017.
"Entropy in selfsimilar shock profiles". United States.
doi:10.1016/j.ijnonlinmec.2017.07.003. https://www.osti.gov/servlets/purl/1372792.
@article{osti_1372792,
title = {Entropy in selfsimilar shock profiles},
author = {Margolin, Len G. and Reisner, Jon Michael and Jordan, Pedro M.},
abstractNote = {In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that is smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.},
doi = {10.1016/j.ijnonlinmec.2017.07.003},
journal = {International Journal of NonLinear Mechanics},
number = ,
volume = 95,
place = {United States},
year = {2017},
month = {7}
}