An idealized model of a vortex interacting with an initially straight frontal zone is developed. The nondivergent vortex flow is a smoothly varying analog to a Rankine Combined Vortex. Local advection and frontogenesis are calculated analytically at the initial time and used to approximate the temporal evolution of the system, during its early phases. Intuition suggests that the maximum deformation of the frontal zone should occur near the radius of maximum winds. Results confirm our intuition, but also provide insight into how frontogenesis proceeds in a real vortex. The calculations yield patterns surprisingly similar to observations of vortex interactions with zones of high gradient on several scales, and seem to explain the compelling similarities between observed vortex phenomena on widely different scales.