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On the small-amplitude waves in an inhomogeneous moving medium. (English. Russian original) Zbl 0929.76012
Phys.-Dokl. 41, No. 11, 521-524 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 322-325 (1996).
Summary: Along with a conventional Eulerian representation of equations of hydrodynamics, the Lagrangian or combined Eulerian-Lagrangian description is often used in studies of waves in flows. In this paper, a special version of the Eulerian-Lagrangian representation is suggested; this results in a considerable simplification of the boundary conditions and especially of the equations that define both the acoustic and the acoustic-gravity internal and surface waves of small amplitude against the background of the three-dimensionally nonuniform flow. A specific choice of dependent variables for the description of the wave field was presented as a result of an analysis of the acoustic quantities that are invariant with respect to the interchange of the detector and the source of sound under the condition of the simultaneous and global reversal of the direction for the velocity vector of the flow unperturbed by the wave. A crucial feature of the proposed approach is the concept of the oscillatory displacement of the fluid particles, which is introduced below.

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q35 PDEs in connection with fluid mechanics