  We have studied three-dimensional hydrodynamic interactions of relativistic
extragalactic jets with two-phase ambient media. These jets propagate through a
denser homogeneous gas and then impact clouds with densities 100 to 1000 times
higher than the initial beam density. The deflection angle of the jet is
influenced more by the density contrast of the cloud than by the beam Mach
number of the jet. A relativistic jet with low relativistic beam Mach number
can eventually be slightly bent after it crosses the dense cloud; however, we
have not seen permanently bent structures in the interaction of a high
relativistic beam Mach number jet with a cloud. The relativistic jet impacts on
dense clouds do not necessarily destroy the clouds completely, and much of the
cloud body can survive as a coherent blob. This enhancement of cloud durability
is partly due to the geometric influence of the off-axis collisions we consider
and also arises from the lower rate of cloud fragmentation through the
Kelvin-Helmholtz instability for relativistic jets. To compare our simulations
with observed extragalactic radio jets, we have computed the approximate
surface distributions of synchrotron emission at different viewing angles.
These surface intensity maps show relativistic jets interacting with clouds can
produce synchrotron emission knots similar to structures observed in many
VLBI-scale radio sources. We find that the synchrotron emission increases
steeply at the moment of impact and the emission peaks right before the jet
passes through the cloud.
