Three-dimensional numerical simulations of light supersonic hydrodynamic jets have been performed to quantify the crucial roles of the interstellar medium (ISM) and intracluster medium (ICM) in deÐning the gross morphologies of powerful radio galaxies. Such a jet emerges through a power-law atmosphere (ISM) of its host galaxy and then crosses into a hotter, but less dense, ICM. Our eight mediumresolution simulations are followed to lengths of 45 initial jet radii. Simulations with di †erent jet velocities, jet densities, extensions of the ISM (along the jetÏs axis), and inclination angles of the ISM/ICM interface are compared.The shear layer between the jet and the shock-processed gas is a †ected by nonlinear hydrodynamical instabilities. Complex patterns of asymmetric vortex rings and superposed streamwise vortex tubes arise in the cocoon, while internal shocks form in the jet. The lowÈMach number jets have higher growth rates of instabilities, in comparison with higher Mach number jets, and the Mach disks or "" working surfaces ÏÏ at the heads of the jets break down. The growth of Rayleigh-Taylor instabilities along the contact discontinuity between the shocked ambient plasma and the shocked jetÏs plasma appears to trigger the entrainment of heavier external gas into the jet. Greater tilts of the interface induce more wiggling and ribboning of the jets, but none of these simulations evinces substantial jet bending.