Translating vortex pairs with prescribed profiles

Abstract

We generate translating vortex pairs with smooth or more arbitrary profiles that reflect modern vortex pairs being generated using prescribed domains of vorticity. Instead of prescribing the domain, we fix the area of the vorticity and iteratively generate the vortex by prescribing the profile function defining the vorticity, which as a side effect produces a domain of vorticity dependent on the profile function and area. A large class of previously developed and new translating vortex pairs is developed for almost arbitrary vortex profiles using this methodology. This is further enhanced to produce solutions for flows on a rotating sphere.