Numerical description of the motion of a point vortex pair on ovaloids

This paper presents a numerical study on the dynamics of point vortex pairs moving on convex closed surfaces (ovaloids) approximated by triangular icosahedral meshes. Firstly, both a discretized conformal mapping between the ovaloid and the unit sphere S2 and a least-squares fitting for this approximated conformal map in terms of a spherical harmonic expansion are obtained. Then, an approximation of the conformal spherical metric of the ovaloid is derived by obtaining a spherical harmonic expansion of the corresponding conformal factor and its gradient on S2. The equations of motion for a point vortex pair on S2 with this quasi-conformal metric are integrated by using the classical Gaussian collocation method for some particular models. (paper)