A moment model with variable length scale for the motion of a vortex pair in two-dimensional incompressible flows

A simple model for the motion of a vortex pair in two-dimensional inviscid flows is presented. In this model the motion of the vortex pair is expressed by a set of ordinary differential equations for the dipole moment, the length scale, and the centroid position. The length scale is the distance between the positive vortex and the negative vortex in the pair. A self-propelling velocity of the model vortex pair is introduced in response to a wide range of the length scale. If a background flow is a linear function of the position, the dipole moment and the length scale of the model are exact. This model works well for a separated vortex pair, although it is not applicable to an asymmetrically deformed vortex pair.