  We have carried out relativistic three-dimensional simulations of high-power
radio sources propagating into asymmetric cluster environments. We offset the
environment by 0 or 1 core radii (equal to 144 kpc), and incline the jets by 0,
15, or 45{\deg} away from the environment centre. The different environment
encountered by each radio lobe provides a unique opportunity to study the
effect of environment on otherwise identical jets. We find that the jets become
unstable towards the end of the simulations, even with a Lorentz factor of 5;
they nevertheless develop typical FR II radio morphology. The jets propagating
into denser environments have consistently shorter lobe lengths and brighter
hotspots, while the axial ratio of the two lobes is similar. We reproduce the
recently reported observational anti-correlation between lobe length asymmetry
and environment asymmetry, corroborating the notion that observed large-scale
radio lobe asymmetry can be driven by differences in the underlying
environment.
