NONLINEAR WAVE DYNAMICS OF LIQUID-SATURATED POROUS MEDIA

The propagation of plane longitudinal waves in a liquid-saturated porous media with cavities is considered in a linear elastic approximation. We show that, as distinct from the classical porous medium (Biot's medium) where two longitudinal nondispersive waves (a fast wave and a slow wave) can propagate, in a cavity-porous medium three dispersive longitudinal waves propagate, one of which is solely induced by available cavities in the material. The study of wave behavior is carried out by obtaining and analyzing the dispersion equation, a phase velocity and a group velocity. The frequency spectrum density is considered, which enables us to determine the degree of dispersion. At specific values of the system parameters with some regions of strong and weak dispersion, regions of normal and anomalous dispersion are identified. The propagation of nonlinear periodic (cnoidal) plane longitudinal waves and solitons in the liquid-saturated porous medium with cavities is studied on the assumption that the wave energy dissipation in the medium may be neglected. The effect of the nonlinear periodic wave velocity on the wave amplitude and wavenumber is shown. The influence of the system parameters-in particular, the size of spherical cavities on the main parameters (the amplitude and width) of localized waves-is identified. The obtained results are compared to classic soliton behavior.