ИСТИНА

Porous media are known to exhibit a considerably stronger elastic nonlinearity as compared with homogeneous fluid or solid media. This property stimulated a growing interest in studying nonlinear dynamics of poroelastic media. In the literature theoretical investigations of nonlinear acoustic wave interactions, in particular second harmonic generation in the one-dimensional case, were presented. In the case of nonlinear interaction of waves propagating in one direction in the absence of sound velocity dispersion the formation of a shock wave can start if the dissipation is not too high, and a particular three wave interaction could be hidden. In the present work generation of an acoustic wave by two other waves propagating at an angle to each other in a sandy sediment is studied. In order the energy and momentum conservation laws are satisfied such process is possible in the frequency range where there is a significant amount of velocity dispersion. To derive the equation for the slowly varying amplitude of the generated wave we started from the continuity equations for the densities and momenta of the liquid and solid phases of a sediment, obtained by Bykov and Nikolaevskii [Sov. Phys. Acoust. {\bf 36}, 342, 1990], which are equivalent essentially to the equations developed by Biot, but presented in a different form with a more explicit physical meaning. The possibility of an experimental observation of the generation of a sound wave by two pump waves is numerically estimated, which showed that the generated wave amplitude can reach a measurable value at a distance realistic for an acoustic-wave experiment in a sediment.