Sommario
Si studia la struttura delle onde d'urto piane in una classe di teorie dei fluidi dissipativi che risolvono le note difficoltà delle equazioni di Navier-Stokes-Fourier per le onde sonore di alta frequenza e per le onde d'accelerazione.
Si dimostra che una soluzione unica, continua e stabile esiste solo per numeri di Mach sufficientemente piccoli.
Summary
The structure of plane steady shock waves is investigated for a class of theories of heat-conducting and viscid fluids which avoid the well-known difficulties of the Navier-Stokes-Fourier equations for high-frequency sound waves and acceleration waves.
It is demonstrated that a unique continuous and stable shock structure exists only for sufficiently low Mach numbers.
This is a preview of subscription content, log in via an institution to check access.
References
Serrin P.,Mathematical Principles of Classical Fluid Mechanics, Handbuch der Physik VIII/1, Springer-Verlag, N.Y., 1959.
Truesdell C. A.,Termodinamica razionale, Accademia Nazionale dei Lincei, Roma, 1976.
Carrassi M. andMorro A., Il Nuovo Cimento,9B, 321, 1972.
Cattaneo C., Atti Sem. Mat. Fis. Modena,3, 3, 1948.
Müller I., Zeitschrift für physik,198, 329, 1967.
Dixon G.,Special Relativity, the foundation of macroscopic physics, Cambridge, 1978.
Bampi F. andMorro A.,Nonstationary thermodynamics and wave propagation in heat conductive viscous fluids, University of Genova, preprint 1980.
Jou D., Casas-Vazques J. andLebon G., J. Non-Equilibr. Thermodyn.,4, 349 (1979).
Müller I.,Zur Ausbreitungsgeschwindigkeit von Störungen in Kontinuierlichen Medien, Doctor Thesis, Darmstadt, 1966.
Kranyš, Il Nuovo Cimento,8B, 417 (1972).
Israel W., Ann. Phys.,100, 310 (1976).
Israel W. andStewart J. M., Proc. R. Soc. London,A 365, 43 (1979).
Bampi F. andMorro A., J. Math. Phys.,21, 1201 (1980).
Grad H., Comm. Pure and Appl. Math., vol. V, 257 (1952).
Stewart J. M., Proc. R. Soc. Lond.A 357, 59 (1977).
Bampi F. andMorro A., Wave Motion,2, 153 (1980).
Gilbarg D. andPaolucci D., J. Rat. Mech. An.,2, 617 (1953).
Jeffrey A. andKakutani T., SIAM Review,14, 582 (1972).
Germain P., Rev. Mod. Phys.,32, 951 (1960).
Germain P.,Shock waves, Jump Relations, and Structure, Advances in Appl. Mech.,
Lefschetz S.,Differential Equations: Geometric Theory, 2nd edition, New York.
Linzer M. andHornig D. F., Phys. Fluids,6, 166 (1963).
Author information
Authors and Affiliations
Additional information
Research supported by C.N.R., G.N.F.M.
Rights and permissions
About this article
Cite this article
Anile, A.M., Majorana, A. Shock structure for heat conducting and viscid fluids. Meccanica 16, 149–156 (1981). https://doi.org/10.1007/BF02128443
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02128443