Аннотация: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.