Simulations of slab jets propagating in constant atmospheres have been performed for a range of jet velocities and Mach numbers. A magnetic field is introduced in the form of closed field loops, and a local emissivity is computed in a cross section through the infinite slab which serves to trace jet and lobe morphology. The use of slab geometry allows study of asymmetric jet and lobe morphologies. Axisymmetry is broken by perturbing the jet at the inlet with a periodic sinusoidal oscillation in time of the jet's velocity. Sinusoidal oscillation is analogous to helical oscillation of a cylindrical jet. The observed morphology goes through three phases of evolution. At early times, the jet maintains approximate axisymmetry within a backflowing cocoon. At later times, when the jet has penetrated farther into the external medium, the symmetry is broken by sideways oscillation and the leading edge of the jet moves about within a growing lobe. The oscillation is the result of nonlinear resonant amplification of the initial perturbation by the Kelvin-Helmholtz instability. Ultimately the jet flaps chaotically within the growing lobe, and the flapping is driven by turbulent vorticies in the lobe. These simulations are suggestive of the physical processes which may contribute to asymmetric morphologies in radio galaxies. In particular, we confirm the basic picture of Scheuer's "dentist drill" model, and we have found that fluid motions in the lobe govern the location of the tip of the drill bit. We find that morphology is time-dependent on relatively short time scales. We also find a significant difference in morphology between transonic and supersonic jets, which is suggestive of the difference in morphology between FR I and FR II type radio sources.