Dynamics of corotating vortex filaments part 1: Analytical model

The interactions between two corotating vortex filaments of equal strength are investigated analytically. The Biot-Savart law is used to develop the equations of motion of the filaments, consistent with Crow's formulation. Consistent with previous work, two modes of motion are defined and analyzed for stability. It is demonstrated that the mutual induction between the vortices leads to unstable motion of the filaments in the antisymmetric mode over a significant range of frequencies. Furthermore, the oscillatory motion of the filaments is proven to have a preferred direction.