8^e Symposium International sur l'acoustique non linéaire / 8^th International Symposium on non linear acoustics

J. Phys. Colloques 40 (1979) C8-48-C8-52
DOI: 10.1051/jphyscol:1979810

REPRESENTATIONS LAGRANGIENNE ET EULERIENNE DE L'ACOUSTIQUE NON LINÉAIRE

B. POIREE

CETHEDEC, 26, boulevard Victor 75996 PARIS ARMEES

Résumé
A partir des équations de la mécanique des fluides écrites en variables de Lagrange (resp. en variables d'Euler), nous obtenons par petites perturbations, les équations du second ordre vérifiées par le champ acoustique lagrangien (resp. eulérien) dans le cas suivant : fluide parfait, initialement au repos, illimité, à caractéristiques C^∞, en présence d'une force extérieure. Après avoir relié champ acoustique lagrangien et champ acoustique eulérien, nous montrons l'équivalence entre les deux représentations en dehors des sources acoustiques.

Abstract
From the equations of fluid mechanics written in Lagrange variables (resp. Euler variables) we get by small perturbations the second order equations for the lagrangian (resp. eulerian) acoustic field in the following case : perfect fluid, initially at rest, unlimited, endowed with C^∞ characteristics, in the presence of an external force. We establish the correspondence between the lagrangian and eulerian acoustic fields and we deduce the equivalence between the two representations outside the acoustic sources.

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