We present models of astrophysical jets ejected from sources with a time-dependent ejection direction. The perturbations in the ejection direction are amplified as a result of a 'garden-hose' effect, resulting in a 'twisted filament' morphology for the jet. Because of this, at large distances from the source the motion of the material is mostly perpendicular to the direction of the jet filament, leading to a 'sideways interaction' between the jet and the surrounding environment. We derive simple models for the kinematics of the jet and for the jet-environment interaction. From these models, we compute emission-line intensity maps that can be directly compared with observations of stellar jets.