Propagation of acceleration waves is impossible in classical viscous fluids. One could suppose that the same could occur in case of viscous fluids with structure. Speaking of adiabatic or isothermal cases I have found that propagation of acceleration waves is actually possible in a subclass of such continua. Only longitudinal waves carrying discontinuities in the first derivatives of the velocity are possible but not waves carrying discontinuities in the first derivatives of the angular velocity.
@article{RLINA_1979_8_67_3-4_252_0,
author = {Antonio Claudio Grioli},
title = {Sulla propagazione di onde di accelerazione in un fluido micropolare viscoso},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {66},
year = {1979},
pages = {252-258},
zbl = {0467.76010},
language = {it},
url = {http://dml.mathdoc.fr/item/RLINA_1979_8_67_3-4_252_0}
}
Grioli, Antonio Claudio. Sulla propagazione di onde di accelerazione in un fluido micropolare viscoso. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 66 (1979) pp. 252-258. http://gdmltest.u-ga.fr/item/RLINA_1979_8_67_3-4_252_0/
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