  Active galactic nuclei (AGN) show a range of morphologies and dynamical
properties, which are determined not only by parameters intrinsic to the
central engine but also their interaction with the surrounding environment. We
investigate the connection of kiloparsec scale AGN jet properties to their
intrinsic parameters and surroundings. This is done using a suite of 40
relativistic hydrodynamic simulations spanning a wide range of engine
luminosities and opening angles. We explore AGN jet propagation with different
ambient density profiles, including $r^{-2}$ (self-similar solution) and
$r^{-1}$, which is more relevant for AGN host environments. The Fanaroff-Riley
(FR) morphological dichotomy arises naturally in our models. Jets with low
energy density compared to the ambient medium produce a center-brightened
emissivity distribution, while emissivity from relatively higher energy density
jets is dominated by a terminal bright spot. We observe recollimation shocks in
our simulations that can generate bright spots along the spine of the jet,
providing a possible explanation for "knots" observed in AGN jets. We
additionally find a scaling relation between the number of knots and the
jet-head-to-surroundings energy density ratio. This scaling relation is
generally consistent with the observations of the jets in M87 and Cygnus A. Our
model also correctly predicts M87 as FR I and Cygnus A as FR II. Our model can
be used to relate jet dynamical parameters such as jet head velocity, jet
opening angle, and external pressure to jet power and ambient density
estimates.
