Merging of barotropic symmetric vortices. A case study for gulf stream rings

Abstract

We made numerical experiments to study the merging dynamics of axisymmetric barotropic ringlike vortices using a quasi-geostrophic model in a β-plane. We want to explore the initial conditions and the physical parameters that cause the merging or that affect the merging rates of ringlike structures. The initial vortices have a «realistic» shape,i.e., they are taken to simulate closely the horizontal structure of Gulf Stream rings. In the first set of experiments we change the initial conditions. The results agree with the classical solution that there is a critical initial separation distanced between the two vortices: for bigger merging distances the process cannot occur. The initial distance affects the merging rates and it determines the development of the lateral arms and the behaviour of the «near-field» vortices. The latter form near the elongated arms of the merging vortices; sometimes the arms of the merged vortex become unstable and get detached from the central merged vorticity region to form dipolar structures with «near-field» vortices. A second set of numerical simulations is done by changing the numerical model parameters. The results show that the merging is a nonlinear process very sensitive to the value of the nonlinear parameter, α, and that the β-effect does not alter appreciably the speed of merging but it affects the development of the arms.