  We introduce the eikonal approximation to study the effect of the large-scale
motion of cosmic fluids on their small-scale evolution. This approach consists
in collecting the impact of the long-wavelength displacement field into a
single or finite number of random variables, whose statistical properties can
be computed from the initial conditions. For a single dark matter fluid, we
show that we can recover the nonlinear propagators of renormalized perturbation
theory. These are obtained with no need to assume that the displacement field
follows the linear theory. Then we extend the eikonal approximation to many
fluids. In particular, we study the case of two non-relativistic components and
we derive their resummed propagators in the presence of isodensity modes.
Unlike the adiabatic case, where only the phase of small-scale modes is
affected by the large-scale advection field, the isodensity modes change also
the amplitude on small scales. We explicitly solve the case of cold dark
matter-baryon mixing and find that the isodensity modes induce only very small
corrections to the resummed propagators.
