  The effect of rarefaction acceleration on the propagation dynamics and
structure of relativistically hot jets is studied through relativistic
hydrodynamic simulations. We emphasize the nonlinear interaction of rarefaction
waves excited at the interface between a cylindrical jet and the surrounding
medium. From simplified one-dimensional models with radial jet structure, we
find that a decrease in the relativistic pressure due to the interacting
rarefaction waves in the central zone of the jet transiently yields a more
powerful boost of the bulk jet than that expected from single rarefaction
acceleration. This leads to a cyclic in-situ energy conversion between thermal
and bulk kinetic energies which induces radial oscillating motion of the jet.
The oscillation timescale is characterized by the initial pressure ratio of the
jet to the ambient medium, and follows a simple scaling relation $\tau_{\rm
oscillation} \propto (P_{\rm jet,0}/P_{\rm amb,0})^{1/2}$. It is confirmed from
extended two-dimensional simulations that this radial oscillating motion in the
one-dimensional system manifests as modulation of the structure of the jet in a
more realistic situation where a relativistically hot jet propagates through an
ambient medium. It is found that when the ambient medium has a power law
pressure distribution, the size of the reconfinement region along the
propagation direction of the jet in the modulation structure $\lambda$ evolves
according to a self-similar relation $\lambda \propto t^{\alpha/2}$ where
$\alpha$ is the power-law index of the pressure distribution.
