Summary
This note investigates the oblique interaction between plane waves and shocks in materials described by a system of conservation equations. The interaction turns out to be accounted for by a relation allowing the explicit determination of the amplitudes of the emergent modes together with the acceleration and the angular velocity of the shock.
Zusammenfassung
Die schräge Wechselwirkung zwischen ebenen Stoß- und beschleunigungswelen in Kontinua wird untersucht, die durch ein System von Erhaltungsgleichungen beschrieben werden. Es wird gezeigt, daß die Wechselwirkung eine Bedingung erfüllt, aus der man die Amplitude der erzeugten Wellen, die Beschleunigung und die Winkelgeschwindigkeit der Stoßwelle gewinnt.
Similar content being viewed by others
References
D'iakov, S. P.: The interaction of shock waves with small perturbations. Sov. Phys. JETP6, 729–747 (1958).
Erpenbeck, J. J.: Stability of step shocks. Phys. Fluids5, 1181–1187 (1962).
Gardner, C. S.: Comment on “Stability of step shocks”. Phys. Fluids6, 1366–1367 (1963).
McKenzie, J. F., Westphal, K. O.: Interaction of linear waves with oblique shock waves. Phys. Fluids11, 2350–2362 (1968).
Fowles, G. R.: Conditional stability of shock waves — a criterion for detonation. Phys. Fluids19, 227–238 (1976).
Landau, L., Lifchitz, E.: Mécanique des fluides. Moscow: Mir 1971.
Brun, L.: Ondes de choc finies dans les solides elastiques, in: Mechanical waves in solids (Mandel, J., Brun, L., eds.). (CISM, Vol. 222.) Wien-New York: Springer 1975.
Morro, A.: Interaction of shock waves with acoustic waves. Atti Accad. Naz. Lincei.64, 177–185 (1978).
Morro, A.: Interaction of acoustic waves with shock waves in elastic solids. Z. Angew. Math. Phys.29, 822–827 (1978).
Morro, A.: Interaction of waves with shocks in magnetofluiddynamics. Acta Mech.35, 197–213 (1980).
Chen, P. J.: Growth and decay of waves in solids, in: Mechanics of solids III (Truesdell, C., ed.). Berlin-Heidelberg-New York: Springer 1973.
Boillat, G.: La Propagation des Ondes. Paris: Gauthier-Villars 1965.
Jeffrey, A., Taniuti, T.: Nonlinear wave propagation. New York: Academic Press 1964.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Morro, A. Oblique interaction of waves with shocks. Acta Mechanica 38, 241–248 (1981). https://doi.org/10.1007/BF01176467
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01176467