We study the dynamics of passively advected Lagrangian tracers undergo
ing small vertical oscillations around an horizontal reference density
surface, in an Eulerian velocity field depending only on the horizont
al coordinates. The motion of the advected particles may be chaotic ev
en though the fluid (or, equivalently, the non-oscillating) particles
undergo regular motion and follow the streamlines of the Eulerian flow
. Slowly oscillating particles undergo large-time dispersion, a behavi
or which cannot be observed in the motion of non-oscillating particles
in the same fluid flow. The system studied here may be considered as
an idealized representation of the dynamics of free subsurface buoys o
r free balloons in the atmosphere; the results of this study indicate
that a proper evaluation of the parameters of the Lagrangian tracers s
hould be pursued in order to verify the motion of the Lagrangian trace
rs properly represents the behavior of true fluid particles.