Acoustic wave propagation in viscothermal fluids, an electromagnetic analogy
Résumé
Acoustic wave propagation in viscothermal fluids, an electromagnetic analogy, Chapter, (68 pages), in a book, Fundamentals of acoustic waves propagation in periodic structures, metamaterials and porous media, to appear in editions Springer, 2020. Abstract: First, we recall the Navier-Stokes-Fourier model linearized equations, which govern the propagation of small amplitude, long wavelength waves in viscothermal uids; we specify how these equations are derived from several thermodynamic simplifications, and examine some of their solutions. Then, we analyze the general pattern of macroscopic nonlocal equations of propagation of small amplitude electromagnetic waves in effective homogeneous media, taking into account both the temporal and spatial dispersion. We argue that we lack a whole thermodynamics to fully precise all intervening quantities; proceeding by analogy, we then suggest that for the general acoustics of a homogeneous fluid, an analogous general pattern of nonlocal equations of propagation would arise, if we had sufficient thermodynamics. These ideas are finally implemented to obtain, within the available Navier-Stokes-Fourier's model, a nonlocal description of compressional waves.